Due to the numerous variables to take into account as well as the inherent ambiguity and uncertainty,evaluating educational institutions can be difficult.The concept of a possibility Pythagorean fuzzy hypersoft set(pP...Due to the numerous variables to take into account as well as the inherent ambiguity and uncertainty,evaluating educational institutions can be difficult.The concept of a possibility Pythagorean fuzzy hypersoft set(pPyFHSS)is more flexible in this regard than other theoretical fuzzy set-like models,even though some attempts have been made in the literature to address such uncertainties.This study investigates the elementary notions of pPyFHSS including its set-theoretic operations union,intersection,complement,OR-and AND-operations.Some results related to these operations are also modified for pPyFHSS.Additionally,the similarity measures between pPyFHSSs are formulated with the assistance of numerical examples and results.Lastly,an intelligent decision-assisted mechanism is developed with the proposal of a robust algorithm based on similarity measures for solving multi-attribute decision-making(MADM)problems.A case study that helps the decision-makers assess the best educational institution is discussed to validate the suggested system.The algorithmic results are compared with the most pertinent model to evaluate the adaptability of pPyFHSS,as it generalizes the classical possibility fuzzy set-like theoretical models.Similarly,while considering significant evaluating factors,the flexibility of pPyFHSS is observed through structural comparison.展开更多
Ensuring a sustainable and eco-friendly environment is essential for promoting a healthy and balanced social life.However,decision-making in such contexts often involves handling vague,imprecise,and uncertain informat...Ensuring a sustainable and eco-friendly environment is essential for promoting a healthy and balanced social life.However,decision-making in such contexts often involves handling vague,imprecise,and uncertain information.To address this challenge,this study presents a novel multi-criteria decision-making(MCDM)approach based on picture fuzzy hypersoft sets(PFHSS),integrating the flexibility of Schweizer-Sklar triangular norm-based aggregation operators.The proposed aggregation mechanisms—weighted average and weighted geometric operators—are formulated using newly defined operational laws under the PFHSS framework and are proven to satisfy essential mathematical properties,such as idempotency,monotonicity,and boundedness.The decision-making model system-atically incorporates both benefit and cost-type criteria,enabling more nuanced evaluations in complex social or environmental decision problems.To enhance interpretability and practical relevance,the study conducts a sensitivity analysis on the Schweizer-Sklar parameter(Δ).The results show that varyingΔaffects the strictness of aggregation,thereby influencing the ranking stability of alternatives.A comparative analysis with existing fuzzy and hypersoft-based MCDM methods confirms the robustness,expressiveness,and adaptability of the proposed approach.Notably,the use of picture fuzzy sets allows for the inclusion of positive,neutral,and negative memberships,offering a richer representation of expert opinions compared to traditional models.A case study focused on green technology adoption for environmental sustainability illustrates the real-world applicability of the proposed method.The analysis confirms that the approach yields consistent and interpretable results,even under varying degrees of decision uncertainty.Overall,this work contributes an efficient and flexible MCDM tool that can support decision-makers in formulating policies aligned with sustainable and socially responsible outcomes.展开更多
Urban transportation planning involves evaluating multiple conflicting criteria such as accessibility,cost-effectiveness,and environmental impact,often under uncertainty and incomplete information.These complex decisi...Urban transportation planning involves evaluating multiple conflicting criteria such as accessibility,cost-effectiveness,and environmental impact,often under uncertainty and incomplete information.These complex decisions require input from various stakeholders,including planners,policymakers,engineers,and community representatives,whose opinions may differ or contradict.Traditional decision-making approaches struggle to effectively handle such bipolar and multivalued expert evaluations.To address these challenges,we propose a novel decisionmaking framework based on Pythagorean fuzzy N-bipolar soft expert sets.This model allows experts to express both positive and negative opinions on a multinary scale,capturing nuanced judgments with higher accuracy.It introduces algebraic operations and a structured aggregation algorithm to systematically integrate and resolve conflicting expert inputs.Applied to a real-world case study,the framework evaluated five urban transport strategies based on key criteria,producing final scores as follows:improving public transit(−0.70),optimizing traffic signal timing(1.86),enhancing pedestrian infrastructure(3.10),expanding bike lanes(0.59),and implementing congestion pricing(0.77).The results clearly identify enhancing pedestrian infrastructure as the most suitable option,having obtained the highest final score of 3.10.Comparative analysis demonstrates the framework’s superior capability in modeling expert consensus,managing uncertainty,and supporting transparent multi-criteria group decision-making.展开更多
This study introduces a novel distance measure(DM)for(p,q,r)-spherical fuzzy sets((p,q,to improve decision-making in complex and uncertain environments.Many existing distance measures eitherr)-SFSs)fail to satisfy ess...This study introduces a novel distance measure(DM)for(p,q,r)-spherical fuzzy sets((p,q,to improve decision-making in complex and uncertain environments.Many existing distance measures eitherr)-SFSs)fail to satisfy essential axiomatic properties or produce unintuitive outcomes.To address these limitations,we propose a new three-dimensional divergence-based DM that ensures mathematical consistency,enhances the discrimination of information,and adheres to the axiomatic framework of distance theory.Building on this foundation,we construct a multi-criteria decision-making(MCDM)model that utilizes the proposed DM to evaluate and rank alternatives effectively.The applicability and robustness of the model are validated through a practical case study,demonstrating that it leads to more rational,consistent,and reliable decision outcomes compared to existing approaches.展开更多
This paper introduces fuzzy N-bipolar soft(FN-BS)sets,a novel mathematical framework designed to enhance multi-criteria decision-making(MCDM)processes under uncertainty.The study addresses a significant limitation in ...This paper introduces fuzzy N-bipolar soft(FN-BS)sets,a novel mathematical framework designed to enhance multi-criteria decision-making(MCDM)processes under uncertainty.The study addresses a significant limitation in existing models by unifying fuzzy logic,the consideration of bipolarity,and the ability to evaluate attributes on a multinary scale.The specific contributions of the FN-BS framework include:(1)a formal definition and settheoretic foundation,(2)the development of two innovative algorithms for solving decision-making(DM)problems,and(3)a comparative analysis demonstrating its superiority over established models.The proposed framework is applied to a real-world case study on selecting vaccination programs across multiple countries,showcasing consistent DM outcomes and exceptional adaptability to complex and uncertain scenarios.These results position FN-BS sets as a versatile and powerful tool for addressing dynamic DM challenges.展开更多
Industrial Internet of Things(IIoT)service providers have become increasingly important in the manufacturing industry due to their ability to gather and process vast amounts of data from connected devices,enabling man...Industrial Internet of Things(IIoT)service providers have become increasingly important in the manufacturing industry due to their ability to gather and process vast amounts of data from connected devices,enabling manufacturers to improve operational efficiency,reduce costs,and enhance product quality.These platforms provide manufacturers with real-time visibility into their production processes and supply chains,allowing them to optimize operations and make informed decisions.In addition,IIoT service providers can help manufacturers create new revenue streams through the development of innovative products and services and enable them to leverage the benefits of emerging technologies such as Artificial Intelligence(AI)and machine learning.Overall,the implementation of IIoT platforms in the manufacturing industry is crucial for companies seeking to remain competitive and meet the ever-increasing demands of customers in the digital age.In this study,the evaluation criteria to be considered in the selection of IIoT service provider in small andmedium-sized(SME)manufacturing enterprises will be determined and IIoT service providers alternatives will be evaluated using the technique for order preference by similarity to an ideal solution(TOPSIS)method based on circular intuitionistic fuzzy sets.Based on the assessments conducted in accordance with the literature review and expert consultations,a set of 8 selection criteria has been established.These criteria encompass industry expertise,customer support,flexibility and scalability,security,cost-effectiveness,reliability,data analytics,as well as compatibility and usability.Upon evaluating these criteria,it was observed that the security criterion holds the highest significance,succeeded by cost-effectiveness,data analytics,flexibility and scalability,reliability,and customer support criteria,in descending order of importance.Following the evaluation of seven distinct alternatives against these criteria,it was deduced that the A6 alternative,a German service provider,emerged as the most favorable option.The identical issue was addressed utilizing sensitivity analysis alongside various multi-criteria decision-making(MCDM)methods,and after comprehensive evaluation,the outcomes were assessed.Spearman’s correlation coefficient was computed to ascertain the association between the rankings derived from solving the problem using diverse MCDM methods.展开更多
This socialized environment among educated and developed people causes themto focusmore on their appearance and health,which turns them towards medical-related treatments,leading us to discuss anti-aging treatment met...This socialized environment among educated and developed people causes themto focusmore on their appearance and health,which turns them towards medical-related treatments,leading us to discuss anti-aging treatment methods for each age group,particularly for urban people who are interested in this.Some anti-aging therapies are used to address the alterations brought on by aging in human life without the need for surgery or negative effects.Five anti-aging therapies such as microdermabrasion or dermabrasion,laser resurfacing anti-aging skin treatments,chemical peels,dermal fillers for aged skin,and botox injections are considered in this study.Based on the criteria of safety risk,investment cost,customer happiness,and side effects,the optimal alternative is picked.As a result,a NormalWiggly Hesitant Pythagorean Fuzzy Set(NWHPFS)is constructed and used in Multi-Criteria Decision-Making(MCDM)using traditional wavy mathematical approaches.The entropy approach is utilized to determine weight values,and the Normal Wiggly Hesitant Pythagorean-VlseKriterijumska Optimizacija I Kompromisno Resenje(NWHPF-VIKOR)method is utilized to rank alternatives using MCDM methodologies.Sensitivity analysis and comparative analysis were performed to ensure the robustness and reliability of the proposed method.The smart final choice will undoubtedly assist Decision Makers(DM)in making the right judgments,and the MCDM approach will undoubtedly assist individuals in understanding the medicine.展开更多
Green supplier selection is an important debate in green supply chain management(GSCM),attracting global attention from scholars,especially companies and policymakers.Companies frequently search for new ideas and stra...Green supplier selection is an important debate in green supply chain management(GSCM),attracting global attention from scholars,especially companies and policymakers.Companies frequently search for new ideas and strategies to assist them in realizing sustainable development.Because of the speculative character of human opinions,supplier selection frequently includes unreliable data,and the interval-valued Pythagorean fuzzy soft set(IVPFSS)provides an exceptional capacity to cope with excessive fuzziness,inconsistency,and inexactness through the decision-making procedure.The main goal of this study is to come up with new operational laws for interval-valued Pythagorean fuzzy soft numbers(IVPFSNs)and create two interaction operators-the intervalvalued Pythagorean fuzzy soft interaction weighted average(IVPFSIWA)and the interval-valued Pythagorean fuzzy soft interaction weighted geometric(IVPFSIWG)operators,and analyze their properties.These operators are highly advantageous in addressing uncertain problems by considering membership and non-membership values within intervals,providing a superior solution to other methods.Moreover,specialist judgments were calculated by the MCGDM technique,supporting the use of interaction AOs to regulate the interdependence and fundamental partiality of green supplier assessment aspects.Lastly,a statistical clarification of the planned method for green supplier selection is presented.展开更多
As an extension of overlap functions, pseudo-semi-overlap functions are a crucial class of aggregation functions. Therefore, (I, PSO)-fuzzy rough sets are introduced, utilizing pseudo-semi-overlap functions, and furth...As an extension of overlap functions, pseudo-semi-overlap functions are a crucial class of aggregation functions. Therefore, (I, PSO)-fuzzy rough sets are introduced, utilizing pseudo-semi-overlap functions, and further extended for applications in image edge extraction. Firstly, a new clustering function, the pseudo-semi-overlap function, is introduced by eliminating the symmetry and right continuity present in the overlap function. The relaxed nature of this function enhances its applicability in image edge extraction. Secondly, the definitions of (I, PSO)-fuzzy rough sets are provided, using (I, PSO)-fuzzy rough sets, a pair of new fuzzy mathematical morphological operators (IPSOFMM operators) is proposed. Finally, by combining the fuzzy C-means algorithm and IPSOFMM operators, a novel image edge extraction algorithm (FCM-IPSO algorithm) is proposed and implemented. Compared to existing algorithms, the FCM-IPSO algorithm exhibits more image edges and a 73.81% decrease in the noise introduction rate. The outstanding performance of (I, PSO)-fuzzy rough sets in image edge extraction demonstrates their practical application value.展开更多
Multi-criteria decision-making(MCDM)is essential for handling complex decision problems under uncertainty,especially in fields such as criminal justice,healthcare,and environmental management.Traditional fuzzy MCDM te...Multi-criteria decision-making(MCDM)is essential for handling complex decision problems under uncertainty,especially in fields such as criminal justice,healthcare,and environmental management.Traditional fuzzy MCDM techniques have failed to deal with problems where uncertainty or vagueness is involved.To address this issue,we propose a novel framework that integrates group and overlap functions with Aczel-Alsina(AA)operational laws in the intuitionistic fuzzy set(IFS)environment.Overlap functions capture the degree to which two inputs share common features and are used to find how closely two values or criteria match in uncertain environments,while the Group functions are used to combine different expert opinions into a single collective result.This study introduces four new aggregation operators:Group Overlap function-based intuitionistic fuzzy Aczel-Alsina(GOF-IFAA)Weighted Averaging(GOF-IFAAWA)operator,intuitionistic fuzzy Aczel-Alsina(GOF-IFAA)Weighted Geometric(GOF-IFAAWG),intuitionistic fuzzy Aczel-Alsina(GOF-IFAA)OrderedWeighted Averaging(GOF-IFAAOWA),and intuitionistic fuzzy Aczel-Alsina(GOF-IFAA)Ordered Weighted Geometric(GOF-IFAAOWG),which are rigorously defined and mathematically analyzed and offer improved flexibility in managing overlapping,uncertain,and hesitant information.The properties of these operators are discussed in detail.Further,the effectiveness,validity,activeness,and ability to capture the uncertain information,the developed operators are applied to the AI-based Criminal Justice Policy Selection problem.At last,the comparison analysis between prior and proposed studies has been displayed,and then followed by the conclusion of the result.展开更多
The implementation of Countermeasure Techniques(CTs)in the context of Network-On-Chip(NoC)based Multiprocessor System-On-Chip(MPSoC)routers against the Flooding Denial-of-Service Attack(F-DoSA)falls under Multi-Criter...The implementation of Countermeasure Techniques(CTs)in the context of Network-On-Chip(NoC)based Multiprocessor System-On-Chip(MPSoC)routers against the Flooding Denial-of-Service Attack(F-DoSA)falls under Multi-Criteria Decision-Making(MCDM)due to the three main concerns,called:traffic variations,multiple evaluation criteria-based traffic features,and prioritization NoC routers as an alternative.In this study,we propose a comprehensive evaluation of various NoC traffic features to identify the most efficient routers under the F-DoSA scenarios.Consequently,an MCDM approach is essential to address these emerging challenges.While the recent MCDM approach has some issues,such as uncertainty,this study utilizes Fuzzy-Weighted Zero-Inconsistency(FWZIC)to estimate the criteria weight values and Fuzzy Decision by Opinion Score Method(FDOSM)for ranking the routers with fuzzy Single-valued Neutrosophic under names(SvN-FWZIC and SvN-FDOSM)to overcome the ambiguity.The results obtained by using the SvN-FWZIC method indicate that the Max packet count has the highest importance among the evaluated criteria,with a weighted score of 0.1946.In contrast,the Hop count is identified as the least significant criterion,with a weighted score of 0.1090.The remaining criteria fall within a range of intermediate importance,with enqueue time scoring 0.1845,packet count decremented and traversal index scoring 0.1262,packet count incremented scoring 0.1124,and packet count index scoring 0.1472.In terms of ranking,SvN-FDOSM has two approaches:individual and group.Both the individual and group ranking processes show that(Router 4)is the most effective router,while(Router 3)is the lowest router under F-DoSA.The sensitivity analysis provides a high stability in ranking among all 10 scenarios.This approach offers essential feedback in making proper decisions in the design of countermeasure techniques in the domain of NoC-based MPSoC.展开更多
Cyber threat detection is a crucial aspect of contemporary cybersecurity due to the depth and complexity of cyberattacks.It is the identification of malicious activity,unauthorized access,and possible intrusions in ne...Cyber threat detection is a crucial aspect of contemporary cybersecurity due to the depth and complexity of cyberattacks.It is the identification of malicious activity,unauthorized access,and possible intrusions in networks and systems.Modern detection methods employ artificial intelligence and machine learning to study vast amounts of data,learn patterns,and anticipate potential threats.Real-time monitoring and anomaly detection improve the capacity to react to changing threats more rapidly.Cyber threat detection systems aim to reduce false positives and provide complete coverage against the broadest possible attacks.This research advocates for proactive measures and adaptive technologies in defending digital environments.Improvements in detection ability by organizations will assist in safeguarding assets and integrity in operations in this increasingly digital world.This paper draws on the categorization of cyber threat detection methods using hesitant bipolar fuzzy Frank operators.Categorization is a step that is necessary for systematic comparison and assessment of detection methods so that the most suitable method for particular cybersecurity requirements is chosen.Furthermore,this research manages uncertainty and vagueness that exists in decision-making by applying hesitant bipolar fuzzy logic.The importance of the work lies in how it fortifies cybersecurity architectures with a formal method of discovering optimal detection measures and improving responsiveness,resulting in holistic protection against dynamic threats.展开更多
While interval-valued picture fuzzy sets(IvPFSs)provide a powerful tool for modeling uncertainty and ambiguity in various fields,existing divergence measures for IvPFSs remain limited and often produce counterintuitiv...While interval-valued picture fuzzy sets(IvPFSs)provide a powerful tool for modeling uncertainty and ambiguity in various fields,existing divergence measures for IvPFSs remain limited and often produce counterintuitive results.To address these shortcomings,this paper introduces two novel divergencemeasures for IvPFSs,inspired by the Jensen-Shannon divergence.The fundamental properties of the proposed measures-non-degeneracy,symmetry,triangular inequality,and boundedness-are rigorously proven.Comparative analyses with existing measures are conducted through specific cases and numerical examples,clearly demonstrating the advantages of our approach.Furthermore,we apply the new divergence measures to develop an enhanced interval-valued picture fuzzy TOPSIS method for risk assessment in construction projects,showing the practical applicability and effectiveness of our contributions.展开更多
In this paper,a robust and consistent COVID-19 emergency decision-making approach is proposed based on q-rung linear diophantine fuzzy set(q-RLDFS),differential evolutionary(DE)optimization principles,and evidential r...In this paper,a robust and consistent COVID-19 emergency decision-making approach is proposed based on q-rung linear diophantine fuzzy set(q-RLDFS),differential evolutionary(DE)optimization principles,and evidential reasoning(ER)methodology.The proposed approach uses q-RLDFS in order to represent the evaluating values of the alternatives corresponding to the attributes.DE optimization is used to obtain the optimal weights of the attributes,and ER methodology is used to compute the aggregated q-rung linear diophantine fuzzy values(q-RLDFVs)of each alternative.Then the score values of alternatives are computed based on the aggregated q-RLDFVs.An alternative with the maximum score value is selected as a better one.The applicability of the proposed approach has been illustrated in COVID-19 emergency decision-making system and sustainable energy planning management.Moreover,we have validated the proposed approach with a numerical example.Finally,a comparative study is provided with the existing models,where the proposed approach is found to be robust to perform better and consistent in uncertain environments.展开更多
Multi-view clustering is a critical research area in computer science aimed at effectively extracting meaningful patterns from complex,high-dimensional data that single-view methods cannot capture.Traditional fuzzy cl...Multi-view clustering is a critical research area in computer science aimed at effectively extracting meaningful patterns from complex,high-dimensional data that single-view methods cannot capture.Traditional fuzzy clustering techniques,such as Fuzzy C-Means(FCM),face significant challenges in handling uncertainty and the dependencies between different views.To overcome these limitations,we introduce a new multi-view fuzzy clustering approach that integrates picture fuzzy sets with a dual-anchor graph method for multi-view data,aiming to enhance clustering accuracy and robustness,termed Multi-view Picture Fuzzy Clustering(MPFC).In particular,the picture fuzzy set theory extends the capability to represent uncertainty by modeling three membership levels:membership degrees,neutral degrees,and refusal degrees.This allows for a more flexible representation of uncertain and conflicting data than traditional fuzzy models.Meanwhile,dual-anchor graphs exploit the similarity relationships between data points and integrate information across views.This combination improves stability,scalability,and robustness when handling noisy and heterogeneous data.Experimental results on several benchmark datasets demonstrate significant improvements in clustering accuracy and efficiency,outperforming traditional methods.Specifically,the MPFC algorithm demonstrates outstanding clustering performance on a variety of datasets,attaining a Purity(PUR)score of 0.6440 and an Accuracy(ACC)score of 0.6213 for the 3 Sources dataset,underscoring its robustness and efficiency.The proposed approach significantly contributes to fields such as pattern recognition,multi-view relational data analysis,and large-scale clustering problems.Future work will focus on extending the method for semi-supervised multi-view clustering,aiming to enhance adaptability,scalability,and performance in real-world applications.展开更多
This study presents an innovative approach to calculating the failure probability of slopes by incorporating fuzzylimit-state functions,a method that significantly enhances the accuracy and efficiency of slope stabili...This study presents an innovative approach to calculating the failure probability of slopes by incorporating fuzzylimit-state functions,a method that significantly enhances the accuracy and efficiency of slope stability analysis.Unlike traditional probabilistic techniques,this approach utilizes a least squares support vector machine(LSSVM)optimized with a grey wolf optimizer(GWO)and K-fold cross-validation(CV)to approximate the limit-statefunction,thus reducing computational complexity.The novelty of this work lies in its application to one-dimensional(1D),two-dimensional(2D),and three-dimensional(3D)slope models,demonstrating its versatility andhigh precision.The proposed method consistently achieves error margins within 3%of Monte Carlo simulation(MCS)results,while substantially reducing computation time,particularly for 2D and 3D models.This makes theapproach highly practical for real-world engineering applications.Furthermore,by applying fuzzy mathematics tohandle uncertainties in geotechnical properties,the method offers a more realistic and comprehensive understandingof slope stability.As water is the main factor influencing the stability of slopes,this aspect is investigatedby calculating the phreatic line after the change in water level.Relevant examples are used to show that the failureprobability of a slope under water wading condition can increase by more than 20%(increase rates in 1D,2D and3D conditions being 25%,27%and 31%,respectively)compared with the natural condition.The influence ofdiverse fuzzy membership functions—linear,normal,and Cauchy—on failure probability is also considered.Thisresearch not only provides a strategy for better calculation of the slope failure probability but also pioneers theintegration of computational intelligence,fuzzy logic and fluid-dynamics in geotechnical engineering,presentingan innovative and efficient tool for slope stability analysis.展开更多
Feature selection methods rooted in rough sets confront two notable limitations:their high computa-tional complexity and sensitivity to noise,rendering them impractical for managing large-scale and noisy datasets.The ...Feature selection methods rooted in rough sets confront two notable limitations:their high computa-tional complexity and sensitivity to noise,rendering them impractical for managing large-scale and noisy datasets.The primary issue stems from these methods’undue reliance on all samples.To overcome these challenges,we introduce the concept of cross-similarity grounded in a robust fuzzy relation and design a rapid and robust feature selection algorithm.Firstly,we construct a robust fuzzy relation by introducing a truncation parameter.Then,based on this fuzzy relation,we propose the concept of cross-similarity,which emphasizes the sample-to-sample similarity relations that uniquely determine feature importance,rather than considering all such relations equally.After studying the manifestations and properties of cross-similarity across different fuzzy granularities,we propose a forward greedy feature selection algorithm that leverages cross-similarity as the foundation for information measurement.This algorithm significantly reduces the time complexity from O(m2n2)to O(mn2).Experimental findings reveal that the average runtime of five state-of-the-art comparison algorithms is roughly 3.7 times longer than our algorithm,while our algorithm achieves an average accuracy that surpasses those of the five comparison algorithms by approximately 3.52%.This underscores the effectiveness of our approach.This paper paves the way for applying feature selection algorithms grounded in fuzzy rough sets to large-scale gene datasets.展开更多
With the increasing complexity of hotel selection,traditional decision-making models often struggle to account for uncertainty and interrelated criteria.Multi-criteria decision-making(MCDM)techniques,particularly thos...With the increasing complexity of hotel selection,traditional decision-making models often struggle to account for uncertainty and interrelated criteria.Multi-criteria decision-making(MCDM)techniques,particularly those based on fuzzy logic,provide a robust framework for handling such challenges.This paper presents a novel approach to MCDM within the framework of Circular Intuitionistic Fuzzy Sets(C-IFS)by combining three distinct methodologies:Weighted Aggregated Sum Product Assessment(WASPAS),an Alternative Ranking Order Method Accounting for Two-Step Normalization(AROMAN),and the CRITIC method(Criteria Importance Through Inter-criteria Correlation).To address the dynamic nature of traveler preferences in hotel selection,the study employs a comprehensive set of criteria encompassing aspects such as location proximity,amenities,pricing,customer reviews,environmental impact,safety,booking flexibility,and cultural experiences.The CRITIC method is used to determine the importance of each criterion by assessing intercriteria correlations.AROMAN is employed for the systematic evaluation of alternatives,considering their additive relationships and providing a weighted assessment.WASPAS further analyzes the results obtained from AROMAN,incorporating both positive and negative aspects for a comprehensive evaluation.The integration of C-IFS enhances the model’s ability to manage uncertainty and imprecision in the decision-making process.Through a case study,we demonstrate the effectiveness of this integrated approach,offering decision-makers valuable insights for selecting the most suitable hotel option in alignment with the diverse preferences of contemporary travelers.This research contributes to the evolving field of decision science by showcasing the practical applicability of these methodologies within a C-IFS framework for complex decision scenarios.展开更多
In this manuscript,the notion of a hesitant fuzzy soft fixed point is introduced.Using this notion and the concept of Suzuki-type(μ,ν)-weak contraction for hesitant fuzzy soft set valued-mapping,some fixed point res...In this manuscript,the notion of a hesitant fuzzy soft fixed point is introduced.Using this notion and the concept of Suzuki-type(μ,ν)-weak contraction for hesitant fuzzy soft set valued-mapping,some fixed point results are established in the framework of metric spaces.Based on the presented work,some examples reflecting decision-making problems related to real life are also solved.The suggested method’s flexibility and efficacy compared to conventional techniques are demonstrated in decision-making situations involving uncertainty,such as choosing the best options in multi-criteria settings.We noted that the presented work combines and generalizes two major concepts,the idea of soft sets and hesitant fuzzy set-valued mapping from the existing literature.展开更多
Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable ...Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable as we point out in this paper. In the paper, we give a general definition of fuzzy cardinal numbers. Based on this definition, we not only obtain a large part of results with re spect to cardinal numbers, but also give a few of new properties of fuzzy cardinal numbers.展开更多
基金supported by the Deanship of Graduate Studies and Scientific Research at Qassim University(QU-APC-2024-9/1).
文摘Due to the numerous variables to take into account as well as the inherent ambiguity and uncertainty,evaluating educational institutions can be difficult.The concept of a possibility Pythagorean fuzzy hypersoft set(pPyFHSS)is more flexible in this regard than other theoretical fuzzy set-like models,even though some attempts have been made in the literature to address such uncertainties.This study investigates the elementary notions of pPyFHSS including its set-theoretic operations union,intersection,complement,OR-and AND-operations.Some results related to these operations are also modified for pPyFHSS.Additionally,the similarity measures between pPyFHSSs are formulated with the assistance of numerical examples and results.Lastly,an intelligent decision-assisted mechanism is developed with the proposal of a robust algorithm based on similarity measures for solving multi-attribute decision-making(MADM)problems.A case study that helps the decision-makers assess the best educational institution is discussed to validate the suggested system.The algorithmic results are compared with the most pertinent model to evaluate the adaptability of pPyFHSS,as it generalizes the classical possibility fuzzy set-like theoretical models.Similarly,while considering significant evaluating factors,the flexibility of pPyFHSS is observed through structural comparison.
基金supported by the National Natural Science Foundation of China(No.62172095).
文摘Ensuring a sustainable and eco-friendly environment is essential for promoting a healthy and balanced social life.However,decision-making in such contexts often involves handling vague,imprecise,and uncertain information.To address this challenge,this study presents a novel multi-criteria decision-making(MCDM)approach based on picture fuzzy hypersoft sets(PFHSS),integrating the flexibility of Schweizer-Sklar triangular norm-based aggregation operators.The proposed aggregation mechanisms—weighted average and weighted geometric operators—are formulated using newly defined operational laws under the PFHSS framework and are proven to satisfy essential mathematical properties,such as idempotency,monotonicity,and boundedness.The decision-making model system-atically incorporates both benefit and cost-type criteria,enabling more nuanced evaluations in complex social or environmental decision problems.To enhance interpretability and practical relevance,the study conducts a sensitivity analysis on the Schweizer-Sklar parameter(Δ).The results show that varyingΔaffects the strictness of aggregation,thereby influencing the ranking stability of alternatives.A comparative analysis with existing fuzzy and hypersoft-based MCDM methods confirms the robustness,expressiveness,and adaptability of the proposed approach.Notably,the use of picture fuzzy sets allows for the inclusion of positive,neutral,and negative memberships,offering a richer representation of expert opinions compared to traditional models.A case study focused on green technology adoption for environmental sustainability illustrates the real-world applicability of the proposed method.The analysis confirms that the approach yields consistent and interpretable results,even under varying degrees of decision uncertainty.Overall,this work contributes an efficient and flexible MCDM tool that can support decision-makers in formulating policies aligned with sustainable and socially responsible outcomes.
文摘Urban transportation planning involves evaluating multiple conflicting criteria such as accessibility,cost-effectiveness,and environmental impact,often under uncertainty and incomplete information.These complex decisions require input from various stakeholders,including planners,policymakers,engineers,and community representatives,whose opinions may differ or contradict.Traditional decision-making approaches struggle to effectively handle such bipolar and multivalued expert evaluations.To address these challenges,we propose a novel decisionmaking framework based on Pythagorean fuzzy N-bipolar soft expert sets.This model allows experts to express both positive and negative opinions on a multinary scale,capturing nuanced judgments with higher accuracy.It introduces algebraic operations and a structured aggregation algorithm to systematically integrate and resolve conflicting expert inputs.Applied to a real-world case study,the framework evaluated five urban transport strategies based on key criteria,producing final scores as follows:improving public transit(−0.70),optimizing traffic signal timing(1.86),enhancing pedestrian infrastructure(3.10),expanding bike lanes(0.59),and implementing congestion pricing(0.77).The results clearly identify enhancing pedestrian infrastructure as the most suitable option,having obtained the highest final score of 3.10.Comparative analysis demonstrates the framework’s superior capability in modeling expert consensus,managing uncertainty,and supporting transparent multi-criteria group decision-making.
文摘This study introduces a novel distance measure(DM)for(p,q,r)-spherical fuzzy sets((p,q,to improve decision-making in complex and uncertain environments.Many existing distance measures eitherr)-SFSs)fail to satisfy essential axiomatic properties or produce unintuitive outcomes.To address these limitations,we propose a new three-dimensional divergence-based DM that ensures mathematical consistency,enhances the discrimination of information,and adheres to the axiomatic framework of distance theory.Building on this foundation,we construct a multi-criteria decision-making(MCDM)model that utilizes the proposed DM to evaluate and rank alternatives effectively.The applicability and robustness of the model are validated through a practical case study,demonstrating that it leads to more rational,consistent,and reliable decision outcomes compared to existing approaches.
文摘This paper introduces fuzzy N-bipolar soft(FN-BS)sets,a novel mathematical framework designed to enhance multi-criteria decision-making(MCDM)processes under uncertainty.The study addresses a significant limitation in existing models by unifying fuzzy logic,the consideration of bipolarity,and the ability to evaluate attributes on a multinary scale.The specific contributions of the FN-BS framework include:(1)a formal definition and settheoretic foundation,(2)the development of two innovative algorithms for solving decision-making(DM)problems,and(3)a comparative analysis demonstrating its superiority over established models.The proposed framework is applied to a real-world case study on selecting vaccination programs across multiple countries,showcasing consistent DM outcomes and exceptional adaptability to complex and uncertain scenarios.These results position FN-BS sets as a versatile and powerful tool for addressing dynamic DM challenges.
文摘Industrial Internet of Things(IIoT)service providers have become increasingly important in the manufacturing industry due to their ability to gather and process vast amounts of data from connected devices,enabling manufacturers to improve operational efficiency,reduce costs,and enhance product quality.These platforms provide manufacturers with real-time visibility into their production processes and supply chains,allowing them to optimize operations and make informed decisions.In addition,IIoT service providers can help manufacturers create new revenue streams through the development of innovative products and services and enable them to leverage the benefits of emerging technologies such as Artificial Intelligence(AI)and machine learning.Overall,the implementation of IIoT platforms in the manufacturing industry is crucial for companies seeking to remain competitive and meet the ever-increasing demands of customers in the digital age.In this study,the evaluation criteria to be considered in the selection of IIoT service provider in small andmedium-sized(SME)manufacturing enterprises will be determined and IIoT service providers alternatives will be evaluated using the technique for order preference by similarity to an ideal solution(TOPSIS)method based on circular intuitionistic fuzzy sets.Based on the assessments conducted in accordance with the literature review and expert consultations,a set of 8 selection criteria has been established.These criteria encompass industry expertise,customer support,flexibility and scalability,security,cost-effectiveness,reliability,data analytics,as well as compatibility and usability.Upon evaluating these criteria,it was observed that the security criterion holds the highest significance,succeeded by cost-effectiveness,data analytics,flexibility and scalability,reliability,and customer support criteria,in descending order of importance.Following the evaluation of seven distinct alternatives against these criteria,it was deduced that the A6 alternative,a German service provider,emerged as the most favorable option.The identical issue was addressed utilizing sensitivity analysis alongside various multi-criteria decision-making(MCDM)methods,and after comprehensive evaluation,the outcomes were assessed.Spearman’s correlation coefficient was computed to ascertain the association between the rankings derived from solving the problem using diverse MCDM methods.
基金funded by the Korean Government(MSIT)Grant NRF-2022R1C1C1006671.
文摘This socialized environment among educated and developed people causes themto focusmore on their appearance and health,which turns them towards medical-related treatments,leading us to discuss anti-aging treatment methods for each age group,particularly for urban people who are interested in this.Some anti-aging therapies are used to address the alterations brought on by aging in human life without the need for surgery or negative effects.Five anti-aging therapies such as microdermabrasion or dermabrasion,laser resurfacing anti-aging skin treatments,chemical peels,dermal fillers for aged skin,and botox injections are considered in this study.Based on the criteria of safety risk,investment cost,customer happiness,and side effects,the optimal alternative is picked.As a result,a NormalWiggly Hesitant Pythagorean Fuzzy Set(NWHPFS)is constructed and used in Multi-Criteria Decision-Making(MCDM)using traditional wavy mathematical approaches.The entropy approach is utilized to determine weight values,and the Normal Wiggly Hesitant Pythagorean-VlseKriterijumska Optimizacija I Kompromisno Resenje(NWHPF-VIKOR)method is utilized to rank alternatives using MCDM methodologies.Sensitivity analysis and comparative analysis were performed to ensure the robustness and reliability of the proposed method.The smart final choice will undoubtedly assist Decision Makers(DM)in making the right judgments,and the MCDM approach will undoubtedly assist individuals in understanding the medicine.
基金funded by King Saud University,Riyadh,Saudi Arabia.
文摘Green supplier selection is an important debate in green supply chain management(GSCM),attracting global attention from scholars,especially companies and policymakers.Companies frequently search for new ideas and strategies to assist them in realizing sustainable development.Because of the speculative character of human opinions,supplier selection frequently includes unreliable data,and the interval-valued Pythagorean fuzzy soft set(IVPFSS)provides an exceptional capacity to cope with excessive fuzziness,inconsistency,and inexactness through the decision-making procedure.The main goal of this study is to come up with new operational laws for interval-valued Pythagorean fuzzy soft numbers(IVPFSNs)and create two interaction operators-the intervalvalued Pythagorean fuzzy soft interaction weighted average(IVPFSIWA)and the interval-valued Pythagorean fuzzy soft interaction weighted geometric(IVPFSIWG)operators,and analyze their properties.These operators are highly advantageous in addressing uncertain problems by considering membership and non-membership values within intervals,providing a superior solution to other methods.Moreover,specialist judgments were calculated by the MCGDM technique,supporting the use of interaction AOs to regulate the interdependence and fundamental partiality of green supplier assessment aspects.Lastly,a statistical clarification of the planned method for green supplier selection is presented.
文摘As an extension of overlap functions, pseudo-semi-overlap functions are a crucial class of aggregation functions. Therefore, (I, PSO)-fuzzy rough sets are introduced, utilizing pseudo-semi-overlap functions, and further extended for applications in image edge extraction. Firstly, a new clustering function, the pseudo-semi-overlap function, is introduced by eliminating the symmetry and right continuity present in the overlap function. The relaxed nature of this function enhances its applicability in image edge extraction. Secondly, the definitions of (I, PSO)-fuzzy rough sets are provided, using (I, PSO)-fuzzy rough sets, a pair of new fuzzy mathematical morphological operators (IPSOFMM operators) is proposed. Finally, by combining the fuzzy C-means algorithm and IPSOFMM operators, a novel image edge extraction algorithm (FCM-IPSO algorithm) is proposed and implemented. Compared to existing algorithms, the FCM-IPSO algorithm exhibits more image edges and a 73.81% decrease in the noise introduction rate. The outstanding performance of (I, PSO)-fuzzy rough sets in image edge extraction demonstrates their practical application value.
基金supported by“1 Decembrie 1918”University of Alba Iulia,510009 Alba Iuliasupported in part by the HEC-NRPU project,under the grant No.14566.
文摘Multi-criteria decision-making(MCDM)is essential for handling complex decision problems under uncertainty,especially in fields such as criminal justice,healthcare,and environmental management.Traditional fuzzy MCDM techniques have failed to deal with problems where uncertainty or vagueness is involved.To address this issue,we propose a novel framework that integrates group and overlap functions with Aczel-Alsina(AA)operational laws in the intuitionistic fuzzy set(IFS)environment.Overlap functions capture the degree to which two inputs share common features and are used to find how closely two values or criteria match in uncertain environments,while the Group functions are used to combine different expert opinions into a single collective result.This study introduces four new aggregation operators:Group Overlap function-based intuitionistic fuzzy Aczel-Alsina(GOF-IFAA)Weighted Averaging(GOF-IFAAWA)operator,intuitionistic fuzzy Aczel-Alsina(GOF-IFAA)Weighted Geometric(GOF-IFAAWG),intuitionistic fuzzy Aczel-Alsina(GOF-IFAA)OrderedWeighted Averaging(GOF-IFAAOWA),and intuitionistic fuzzy Aczel-Alsina(GOF-IFAA)Ordered Weighted Geometric(GOF-IFAAOWG),which are rigorously defined and mathematically analyzed and offer improved flexibility in managing overlapping,uncertain,and hesitant information.The properties of these operators are discussed in detail.Further,the effectiveness,validity,activeness,and ability to capture the uncertain information,the developed operators are applied to the AI-based Criminal Justice Policy Selection problem.At last,the comparison analysis between prior and proposed studies has been displayed,and then followed by the conclusion of the result.
文摘The implementation of Countermeasure Techniques(CTs)in the context of Network-On-Chip(NoC)based Multiprocessor System-On-Chip(MPSoC)routers against the Flooding Denial-of-Service Attack(F-DoSA)falls under Multi-Criteria Decision-Making(MCDM)due to the three main concerns,called:traffic variations,multiple evaluation criteria-based traffic features,and prioritization NoC routers as an alternative.In this study,we propose a comprehensive evaluation of various NoC traffic features to identify the most efficient routers under the F-DoSA scenarios.Consequently,an MCDM approach is essential to address these emerging challenges.While the recent MCDM approach has some issues,such as uncertainty,this study utilizes Fuzzy-Weighted Zero-Inconsistency(FWZIC)to estimate the criteria weight values and Fuzzy Decision by Opinion Score Method(FDOSM)for ranking the routers with fuzzy Single-valued Neutrosophic under names(SvN-FWZIC and SvN-FDOSM)to overcome the ambiguity.The results obtained by using the SvN-FWZIC method indicate that the Max packet count has the highest importance among the evaluated criteria,with a weighted score of 0.1946.In contrast,the Hop count is identified as the least significant criterion,with a weighted score of 0.1090.The remaining criteria fall within a range of intermediate importance,with enqueue time scoring 0.1845,packet count decremented and traversal index scoring 0.1262,packet count incremented scoring 0.1124,and packet count index scoring 0.1472.In terms of ranking,SvN-FDOSM has two approaches:individual and group.Both the individual and group ranking processes show that(Router 4)is the most effective router,while(Router 3)is the lowest router under F-DoSA.The sensitivity analysis provides a high stability in ranking among all 10 scenarios.This approach offers essential feedback in making proper decisions in the design of countermeasure techniques in the domain of NoC-based MPSoC.
基金funded by Ongoing Research Funding program(ORF-2025-749),King Saud University,Riyadh,Saudi Arabia.
文摘Cyber threat detection is a crucial aspect of contemporary cybersecurity due to the depth and complexity of cyberattacks.It is the identification of malicious activity,unauthorized access,and possible intrusions in networks and systems.Modern detection methods employ artificial intelligence and machine learning to study vast amounts of data,learn patterns,and anticipate potential threats.Real-time monitoring and anomaly detection improve the capacity to react to changing threats more rapidly.Cyber threat detection systems aim to reduce false positives and provide complete coverage against the broadest possible attacks.This research advocates for proactive measures and adaptive technologies in defending digital environments.Improvements in detection ability by organizations will assist in safeguarding assets and integrity in operations in this increasingly digital world.This paper draws on the categorization of cyber threat detection methods using hesitant bipolar fuzzy Frank operators.Categorization is a step that is necessary for systematic comparison and assessment of detection methods so that the most suitable method for particular cybersecurity requirements is chosen.Furthermore,this research manages uncertainty and vagueness that exists in decision-making by applying hesitant bipolar fuzzy logic.The importance of the work lies in how it fortifies cybersecurity architectures with a formal method of discovering optimal detection measures and improving responsiveness,resulting in holistic protection against dynamic threats.
基金the Deanship of Research and Graduate Studies at King Khalid University for funding this work through Small Research Project under grant number RGP1/141/46.
文摘While interval-valued picture fuzzy sets(IvPFSs)provide a powerful tool for modeling uncertainty and ambiguity in various fields,existing divergence measures for IvPFSs remain limited and often produce counterintuitive results.To address these shortcomings,this paper introduces two novel divergencemeasures for IvPFSs,inspired by the Jensen-Shannon divergence.The fundamental properties of the proposed measures-non-degeneracy,symmetry,triangular inequality,and boundedness-are rigorously proven.Comparative analyses with existing measures are conducted through specific cases and numerical examples,clearly demonstrating the advantages of our approach.Furthermore,we apply the new divergence measures to develop an enhanced interval-valued picture fuzzy TOPSIS method for risk assessment in construction projects,showing the practical applicability and effectiveness of our contributions.
文摘In this paper,a robust and consistent COVID-19 emergency decision-making approach is proposed based on q-rung linear diophantine fuzzy set(q-RLDFS),differential evolutionary(DE)optimization principles,and evidential reasoning(ER)methodology.The proposed approach uses q-RLDFS in order to represent the evaluating values of the alternatives corresponding to the attributes.DE optimization is used to obtain the optimal weights of the attributes,and ER methodology is used to compute the aggregated q-rung linear diophantine fuzzy values(q-RLDFVs)of each alternative.Then the score values of alternatives are computed based on the aggregated q-RLDFVs.An alternative with the maximum score value is selected as a better one.The applicability of the proposed approach has been illustrated in COVID-19 emergency decision-making system and sustainable energy planning management.Moreover,we have validated the proposed approach with a numerical example.Finally,a comparative study is provided with the existing models,where the proposed approach is found to be robust to perform better and consistent in uncertain environments.
基金funded by the Research Project:THTETN.05/24-25,VietnamAcademy of Science and Technology.
文摘Multi-view clustering is a critical research area in computer science aimed at effectively extracting meaningful patterns from complex,high-dimensional data that single-view methods cannot capture.Traditional fuzzy clustering techniques,such as Fuzzy C-Means(FCM),face significant challenges in handling uncertainty and the dependencies between different views.To overcome these limitations,we introduce a new multi-view fuzzy clustering approach that integrates picture fuzzy sets with a dual-anchor graph method for multi-view data,aiming to enhance clustering accuracy and robustness,termed Multi-view Picture Fuzzy Clustering(MPFC).In particular,the picture fuzzy set theory extends the capability to represent uncertainty by modeling three membership levels:membership degrees,neutral degrees,and refusal degrees.This allows for a more flexible representation of uncertain and conflicting data than traditional fuzzy models.Meanwhile,dual-anchor graphs exploit the similarity relationships between data points and integrate information across views.This combination improves stability,scalability,and robustness when handling noisy and heterogeneous data.Experimental results on several benchmark datasets demonstrate significant improvements in clustering accuracy and efficiency,outperforming traditional methods.Specifically,the MPFC algorithm demonstrates outstanding clustering performance on a variety of datasets,attaining a Purity(PUR)score of 0.6440 and an Accuracy(ACC)score of 0.6213 for the 3 Sources dataset,underscoring its robustness and efficiency.The proposed approach significantly contributes to fields such as pattern recognition,multi-view relational data analysis,and large-scale clustering problems.Future work will focus on extending the method for semi-supervised multi-view clustering,aiming to enhance adaptability,scalability,and performance in real-world applications.
基金Ministry of Education,Center for Scientific Research and Development of Higher Education Institutions“Innovative Application of Virtual Simulation Technology in Vocational Education Teaching”Special Project,Project No.ZJXF2022110.
文摘This study presents an innovative approach to calculating the failure probability of slopes by incorporating fuzzylimit-state functions,a method that significantly enhances the accuracy and efficiency of slope stability analysis.Unlike traditional probabilistic techniques,this approach utilizes a least squares support vector machine(LSSVM)optimized with a grey wolf optimizer(GWO)and K-fold cross-validation(CV)to approximate the limit-statefunction,thus reducing computational complexity.The novelty of this work lies in its application to one-dimensional(1D),two-dimensional(2D),and three-dimensional(3D)slope models,demonstrating its versatility andhigh precision.The proposed method consistently achieves error margins within 3%of Monte Carlo simulation(MCS)results,while substantially reducing computation time,particularly for 2D and 3D models.This makes theapproach highly practical for real-world engineering applications.Furthermore,by applying fuzzy mathematics tohandle uncertainties in geotechnical properties,the method offers a more realistic and comprehensive understandingof slope stability.As water is the main factor influencing the stability of slopes,this aspect is investigatedby calculating the phreatic line after the change in water level.Relevant examples are used to show that the failureprobability of a slope under water wading condition can increase by more than 20%(increase rates in 1D,2D and3D conditions being 25%,27%and 31%,respectively)compared with the natural condition.The influence ofdiverse fuzzy membership functions—linear,normal,and Cauchy—on failure probability is also considered.Thisresearch not only provides a strategy for better calculation of the slope failure probability but also pioneers theintegration of computational intelligence,fuzzy logic and fluid-dynamics in geotechnical engineering,presentingan innovative and efficient tool for slope stability analysis.
基金supported by the Anhui Provincial Department of Education University Research Project(2024AH051375)Research Project of Chizhou University(CZ2022ZRZ06)+1 种基金Anhui Province Natural Science Research Project of Colleges and Universities(2024AH051368)Excellent Scientific Research and Innovation Team of Anhui Colleges(2022AH010098).
文摘Feature selection methods rooted in rough sets confront two notable limitations:their high computa-tional complexity and sensitivity to noise,rendering them impractical for managing large-scale and noisy datasets.The primary issue stems from these methods’undue reliance on all samples.To overcome these challenges,we introduce the concept of cross-similarity grounded in a robust fuzzy relation and design a rapid and robust feature selection algorithm.Firstly,we construct a robust fuzzy relation by introducing a truncation parameter.Then,based on this fuzzy relation,we propose the concept of cross-similarity,which emphasizes the sample-to-sample similarity relations that uniquely determine feature importance,rather than considering all such relations equally.After studying the manifestations and properties of cross-similarity across different fuzzy granularities,we propose a forward greedy feature selection algorithm that leverages cross-similarity as the foundation for information measurement.This algorithm significantly reduces the time complexity from O(m2n2)to O(mn2).Experimental findings reveal that the average runtime of five state-of-the-art comparison algorithms is roughly 3.7 times longer than our algorithm,while our algorithm achieves an average accuracy that surpasses those of the five comparison algorithms by approximately 3.52%.This underscores the effectiveness of our approach.This paper paves the way for applying feature selection algorithms grounded in fuzzy rough sets to large-scale gene datasets.
基金supported by the Princess Nourah bint Abdulrahman University Researchers Supporting Project Number(PNURSP2025R259)Princess Nourah bint Abdulrahman University,Riyadh,Saudi Arabia+1 种基金supported by the Researchers Supporting Project Number(UM-DSR-IG-2023-07)Almaarefa University,Riyadh,Saudi Arabia.
文摘With the increasing complexity of hotel selection,traditional decision-making models often struggle to account for uncertainty and interrelated criteria.Multi-criteria decision-making(MCDM)techniques,particularly those based on fuzzy logic,provide a robust framework for handling such challenges.This paper presents a novel approach to MCDM within the framework of Circular Intuitionistic Fuzzy Sets(C-IFS)by combining three distinct methodologies:Weighted Aggregated Sum Product Assessment(WASPAS),an Alternative Ranking Order Method Accounting for Two-Step Normalization(AROMAN),and the CRITIC method(Criteria Importance Through Inter-criteria Correlation).To address the dynamic nature of traveler preferences in hotel selection,the study employs a comprehensive set of criteria encompassing aspects such as location proximity,amenities,pricing,customer reviews,environmental impact,safety,booking flexibility,and cultural experiences.The CRITIC method is used to determine the importance of each criterion by assessing intercriteria correlations.AROMAN is employed for the systematic evaluation of alternatives,considering their additive relationships and providing a weighted assessment.WASPAS further analyzes the results obtained from AROMAN,incorporating both positive and negative aspects for a comprehensive evaluation.The integration of C-IFS enhances the model’s ability to manage uncertainty and imprecision in the decision-making process.Through a case study,we demonstrate the effectiveness of this integrated approach,offering decision-makers valuable insights for selecting the most suitable hotel option in alignment with the diverse preferences of contemporary travelers.This research contributes to the evolving field of decision science by showcasing the practical applicability of these methodologies within a C-IFS framework for complex decision scenarios.
基金funded by National Science,Research and Innovation Fund(NSRF)King Mongkut's University of Technology North Bangkok with Contract No.KMUTNB-FF-68-B-46.
文摘In this manuscript,the notion of a hesitant fuzzy soft fixed point is introduced.Using this notion and the concept of Suzuki-type(μ,ν)-weak contraction for hesitant fuzzy soft set valued-mapping,some fixed point results are established in the framework of metric spaces.Based on the presented work,some examples reflecting decision-making problems related to real life are also solved.The suggested method’s flexibility and efficacy compared to conventional techniques are demonstrated in decision-making situations involving uncertainty,such as choosing the best options in multi-criteria settings.We noted that the presented work combines and generalizes two major concepts,the idea of soft sets and hesitant fuzzy set-valued mapping from the existing literature.
文摘Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable as we point out in this paper. In the paper, we give a general definition of fuzzy cardinal numbers. Based on this definition, we not only obtain a large part of results with re spect to cardinal numbers, but also give a few of new properties of fuzzy cardinal numbers.
