Under the context of China's green agricultural transformation,the risk assessment of agricultural supply chain financing must balance economic benefits and environmental sustainability.However,existing studies of...Under the context of China's green agricultural transformation,the risk assessment of agricultural supply chain financing must balance economic benefits and environmental sustainability.However,existing studies often overlook the evaluation of overall supply chain risks and the long-term needs of sustainable agricultural development.To address this gap,this paper constructs a financial risk assessment index system for green agricultural supply chains.Building upon the traditional TOPSIS method,we integrate intuitionistic fuzzy set theory,entropy weight method,and expert scoring to develop a risk assessment approach that combines fuzzy information with objective weighting.This method reduces uncertainties in the evaluation process and establishes a comprehensive framework.Empirical validation using real-world data from agricultural enterprises further confirms the feasibility and practicality of the model.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
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
Fuzzy homomorphism is an important research content of fuzzy group theory, different fuzzy mappings will produce different fuzzy homomorphisms. In this paper, the fuzzy homomorphism of groups is generalized. Firstly, ...Fuzzy homomorphism is an important research content of fuzzy group theory, different fuzzy mappings will produce different fuzzy homomorphisms. In this paper, the fuzzy homomorphism of groups is generalized. Firstly, the θ-intuitionistic fuzzy mapping is defined, and the θ-intuitionistic fuzzy homomorphism of groups is obtained. The properties of intuitionistic fuzzy subgroups and intuitionistic fuzzy normal subgroups are studied under the θ-intuitionistic fuzzy homomorphism of groups, and the fundamental theorem of θ-intuitionistic fuzzy homomorphism is proved.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
The main goal of informal computing is to overcome the limitations of hypersensitivity to defects and uncertainty while maintaining a balance between high accuracy,accessibility,and cost-effectiveness.This paper inves...The main goal of informal computing is to overcome the limitations of hypersensitivity to defects and uncertainty while maintaining a balance between high accuracy,accessibility,and cost-effectiveness.This paper investigates the potential applications of intuitionistic fuzzy sets(IFS)with rough sets in the context of sparse data.When it comes to capture uncertain information emanating fromboth upper and lower approximations,these intuitionistic fuzzy rough numbers(IFRNs)are superior to intuitionistic fuzzy sets and pythagorean fuzzy sets,respectively.We use rough sets in conjunction with IFSs to develop several fairly aggregation operators and analyze their underlying properties.We present numerous impartial laws that incorporate the idea of proportionate dispersion in order to ensure that the membership and non-membership activities of IFRNs are treated equally within these principles.These operations lead to the development of the intuitionistic fuzzy rough weighted fairly aggregation operator(IFRWFA)and intuitionistic fuzzy rough ordered weighted fairly aggregation operator(IFRFOWA).These operators successfully adjust to membership and non-membership categories with fairness and subtlety.We highlight the unique qualities of these suggested aggregation operators and investigate their use in the multiattribute decision-making field.We use the intuitionistic fuzzy rough environment’s architecture to create a novel strategy in situation involving several decision-makers and non-weighted data.Additionally,we developed a novel technique by combining the IFSs with quaternion numbers.We establish a unique connection between alternatives and qualities by using intuitionistic fuzzy quaternion numbers(IFQNs).With the help of this framework,we can simulate uncertainty in real-world situations and address a number of decision-making problems.Using the examples we have released,we offer a sophisticated and systematically constructed illustrative scenario that is intricately woven with the complexity ofmedical evaluation in order to thoroughly assess the relevance and efficacy of the suggested methodology.展开更多
To address the fuzziness and variability in determining customer demand importance,a dynamic analysis method based on intuitionistic fuzzy numbers is proposed.First,selected customers use intuitionistic fuzzy numbers ...To address the fuzziness and variability in determining customer demand importance,a dynamic analysis method based on intuitionistic fuzzy numbers is proposed.First,selected customers use intuitionistic fuzzy numbers to represent the importance of each demand.Then,the preference information is aggregated using customer weights and time period weights through the intuitionistic fuzzy ordered weighted average operator,yielding a dynamic vector of the subjective importance of the demand index.Finally,the feasibility of the proposed method is demonstrated through an application example of a vibrating sorting screen.展开更多
Intuitionistic fuzzy sets(IFSs) are useful means to describe and deal with vague and uncertain data.An intuitionistic fuzzy C-means algorithm to cluster IFSs is developed.In each stage of the intuitionistic fuzzy C-me...Intuitionistic fuzzy sets(IFSs) are useful means to describe and deal with vague and uncertain data.An intuitionistic fuzzy C-means algorithm to cluster IFSs is developed.In each stage of the intuitionistic fuzzy C-means method the seeds are modified,and for each IFS a membership degree to each of the clusters is estimated.In the end of the algorithm,all the given IFSs are clustered according to the estimated membership degrees.Furthermore,the algorithm is extended for clustering interval-valued intuitionistic fuzzy sets(IVIFSs).Finally,the developed algorithms are illustrated through conducting experiments on both the real-world and simulated data sets.展开更多
In this paper, we introduce the notion of intuitionistic fuzzy α-generalized closed sets in intuitionistic fuzzy minimal structure spaces and investigate some of their properties. Further, we introduce and study the ...In this paper, we introduce the notion of intuitionistic fuzzy α-generalized closed sets in intuitionistic fuzzy minimal structure spaces and investigate some of their properties. Further, we introduce and study the concept of intuitionistic fuzzy α-generalized minimal continuous functions.展开更多
Intuitionistic fuzzy set （IFS） is a set of 2-tuple arguments, each of which is characterized by a membership degree and a nonmembership degree. The generalized form of IFS is interval-valued intuitionistic fuzzy set...Intuitionistic fuzzy set （IFS） is a set of 2-tuple arguments, each of which is characterized by a membership degree and a nonmembership degree. The generalized form of IFS is interval-valued intuitionistic fuzzy set （IVIFS）, whose components are intervals rather than exact numbers. IFSs and IVIFSs have been found to be very useful to describe vagueness and uncertainty. However, it seems that little attention has been focused on the clustering analysis of IFSs and IVIFSs. An intuitionistic fuzzy hierarchical algorithm is introduced for clustering IFSs, which is based on the traditional hierarchical clustering procedure, the intuitionistic fuzzy aggregation operator, and the basic distance measures between IFSs： the Hamming distance, normalized Hamming, weighted Hamming, the Euclidean distance, the normalized Euclidean distance, and the weighted Euclidean distance. Subsequently, the algorithm is extended for clustering IVIFSs. Finally the algorithm and its extended form are applied to the classifications of building materials and enterprises respectively.展开更多
Using the idea of Atanassov, we define the notion of intuitionistic Menger spaces as a netural generalizations of Menger spaces due to Menger. We also obtain a new generalized contraction mapping and utilize this cont...Using the idea of Atanassov, we define the notion of intuitionistic Menger spaces as a netural generalizations of Menger spaces due to Menger. We also obtain a new generalized contraction mapping and utilize this contraction mapping to prove the existance theorems of solutions to differential equations in intuitionistic Menger spaces.展开更多
In order to measure the uncertain information of a type- 2 intuitionistic fuzzy set （T21FS）, an entropy measure of T21FS is presented by using the constructive principles. The proposed entropy measure is also proved...In order to measure the uncertain information of a type- 2 intuitionistic fuzzy set （T21FS）, an entropy measure of T21FS is presented by using the constructive principles. The proposed entropy measure is also proved to satisfy all of the constructive principles. Further, a novel concept of the type-2 triangular in- tuitionistic trapezoidal fuzzy set （T2TITrFS） is developed, and a geometric interpretation of the T2TITrFS is given to comprehend it completely or correctly in a more intuitive way. To deal with a more general uncertain complex system, the constructive principles of an entropy measure of T2TITrFS are therefore proposed on the basis of the axiomatic definition of the type-2 intuitionisic fuzzy entropy measure. This paper elicits a formula of type-2 triangular intuitionistic trapezoidal fuzzy entropy and verifies that it does sa- tisfy the constructive principles. Two examples are given to show the efficiency of the proposed entropy of T2TITrFS in describing the uncertainty of the type-2 intuitionistic fuzzy information and illustrate its application in type-2 triangular intuitionistic trapezodial fuzzy decision making problems.展开更多
This paper presents a general framework for the study of relation-based intuitionistic fuzzy rough sets determined by two intuitionistic fuzzy implicators.By employing two intuitionistic fuzzy implicators I and J,I -l...This paper presents a general framework for the study of relation-based intuitionistic fuzzy rough sets determined by two intuitionistic fuzzy implicators.By employing two intuitionistic fuzzy implicators I and J,I -lower and J-upper approximations of intuitionistic fuzzy sets with respect to an intuitionistic fuzzy approximation space are first defined.Properties of(I,J) -intuitionistic fuzzy rough approximation operators are then examined.The connections between special types of intuitionistic fuzzy relations and properties of (I,J)-intuitionistic fuzzy approximation operators are also established.展开更多
By using the unsymmetrical scale instead of the symmetrical scale,the multiplicative intuitionistic fuzzy sets(MIFSs) reflect our intuition more objectively.Each element in a MIFS is expressed by an ordered pair which...By using the unsymmetrical scale instead of the symmetrical scale,the multiplicative intuitionistic fuzzy sets(MIFSs) reflect our intuition more objectively.Each element in a MIFS is expressed by an ordered pair which is called a multiplicative intuitionistic fuzzy number(MIFN)and is based on the unbalanced scale(i.e.,Saaty’s 1-9 scale).In order to describe the derivatives and differentials for multiplicative intuitionistic fuzzy information more comprehensively,in this paper,we firstly propose two new basic operational laws for MIFNs,which are the subtraction law and the division law.Secondly,we describe the change values of MIFNs when considering them as variables,classify these change values based on the basic operational laws for MIFNs,and depict the convergences of sequences of MIFNs by the subtraction and division laws.Finally,we focus on the multiplicative intuitionistic fuzzy functions and derive some basic results related to their continuities,derivatives and differentials,and also give their application in selecting the configuration of a computer.展开更多
The multiple attribute group decision making problem in which the input arguments take the form of intuitionistic uncertain linguistic information is studied in the paper.Based on the operational principles of intuiti...The multiple attribute group decision making problem in which the input arguments take the form of intuitionistic uncertain linguistic information is studied in the paper.Based on the operational principles of intuitionistic uncertain linguistic variables and the concept of the expected value and accuracy function,some new dependent aggregation operators with intuitionistic uncertain linguistic information including the dependent intuitionistic uncertain linguistic ordered weighted average(DIULOWA)operator,the dependent intuitionistic uncertain linguistic ordered weighted geometric(DIULOWG)operator,the generalized dependent intuitionistic uncertain linguistic ordered weighted aggregation(GDIULOWA)operator and so on are developed,in which the associated weights only depend on the aggregated arguments.Also,we study some desirable properties of the aggregation operators.Moreover,the approach of multiple attribute group decision making with intuitionistic uncertain linguistic information based on the developed operators is proposed.Finally,an illustrative numerical example is given to show the practicality and effectiveness of the proposed approaches.展开更多
The concept of the degree of similarity between interval-valued intuitionistic fuzzy sets （IVIFSs） is introduced, and some distance measures between IVIFSs are defined based on the Hamming distance, the normalized H...The concept of the degree of similarity between interval-valued intuitionistic fuzzy sets （IVIFSs） is introduced, and some distance measures between IVIFSs are defined based on the Hamming distance, the normalized Hamming distance, the weighted Hamming distance, the Euclidean distance, the normalized Euclidean distance, and the weighted Euclidean distance, etc. Then, by combining the Hausdorff metric with the Hamming distance, the Euclidean distance and their weighted versions, two other similarity measures between IVIFSs, i. e., the weighted Hamming distance based on the Hausdorff metric and the weighted Euclidean distance based on the Hausdorff metric, are defined, and then some of their properties are studied. Finally, based on these distance measures, some similarity measures between IVIFSs are defined, and the similarity measures are applied to pattern recognitions with interval-valued intuitionistic fuzzy information.展开更多
Similarity measure is an essential tool to compare and determine the degree of similarity between intuitionistic fuzzy sets (IFSs). In this paper, a new similarity measure between intuitionistic fuzzy sets based on th...Similarity measure is an essential tool to compare and determine the degree of similarity between intuitionistic fuzzy sets (IFSs). In this paper, a new similarity measure between intuitionistic fuzzy sets based on the mid points of transformed triangular fuzzy numbers is proposed. The proposed similarity measure provides reasonable results not only for the sets available in the literature but also gives very reasonable results, especially for fuzzy sets as well as for most intuitionistic fuzzy sets. To provide supportive evidence, the proposed similarity measure is tested on certain sets available in literature and is also applied to pattern recognition and medical diagnosis problems. It is observed that the proposed similarity measure provides a very intuitive quantification.展开更多
The notion of the interval-valued intuitionistic fuzzy set （IVIFS） is a generalization of that of the Atanassov＇s intuitionistic fuzzy set. The fundamental characteristic of IVIFS is that the values of its membersh...The notion of the interval-valued intuitionistic fuzzy set （IVIFS） is a generalization of that of the Atanassov＇s intuitionistic fuzzy set. The fundamental characteristic of IVIFS is that the values of its membership function and non-membership function are intervals rather than exact numbers. There are various averaging operators defined for IVlFSs. These operators are not monotone with respect to the total order of IVIFS, which is undesirable. This paper shows how such averaging operators can be represented by using additive generators of the product triangular norm, which simplifies and extends the existing constructions. Moreover, two new aggregation operators based on the t.ukasiewicz triangular norm are proposed, which are monotone with respect to the total order of IVIFS. Finally, an application of the interval-valued intuitionistic fuzzy weighted averaging operator is given to multiple criteria decision making.展开更多
In the paper, in order to further study the properties of filters of BL-algebras, we propose the concepts of the （∈γ, ∈γ Vqδ）-intuitionistic fuzzy filters and （∈γ, ∈γ Vqδ）- intuitionistic fuzzy soft filt...In the paper, in order to further study the properties of filters of BL-algebras, we propose the concepts of the （∈γ, ∈γ Vqδ）-intuitionistic fuzzy filters and （∈γ, ∈γ Vqδ）- intuitionistic fuzzy soft filters of BL-algebras and derive some related results. Finally, we discuss the properties of images and inverse images of （∈γ, ∈γ Vqδ）-intuitionistic fuzzy soft filters of BL-algebras.展开更多
The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational law...The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational laws of intuitionistic fuzzy numbers are introduced, and the score function and accuracy function are presented to compare the intuitionistic fuzzy numbers. The intuitionistic fuzzy ordered weighted averaging （IFOWA） operator which is an extension of the well-known ordered weighted averaging （OWA） operator is investigated to aggregate the intuitionistic fuzzy information. In order to determine the weights of intuitionistic fuzzy ordered weighted averaging operator, a linear goal programming procedure is proposed for learning the weights from data. Finally, an example is illustrated to verify the effectiveness and practicability of the developed method.展开更多
文摘Under the context of China's green agricultural transformation,the risk assessment of agricultural supply chain financing must balance economic benefits and environmental sustainability.However,existing studies often overlook the evaluation of overall supply chain risks and the long-term needs of sustainable agricultural development.To address this gap,this paper constructs a financial risk assessment index system for green agricultural supply chains.Building upon the traditional TOPSIS method,we integrate intuitionistic fuzzy set theory,entropy weight method,and expert scoring to develop a risk assessment approach that combines fuzzy information with objective weighting.This method reduces uncertainties in the evaluation process and establishes a comprehensive framework.Empirical validation using real-world data from agricultural enterprises further confirms the feasibility and practicality of the model.
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Fuzzy homomorphism is an important research content of fuzzy group theory, different fuzzy mappings will produce different fuzzy homomorphisms. In this paper, the fuzzy homomorphism of groups is generalized. Firstly, the θ-intuitionistic fuzzy mapping is defined, and the θ-intuitionistic fuzzy homomorphism of groups is obtained. The properties of intuitionistic fuzzy subgroups and intuitionistic fuzzy normal subgroups are studied under the θ-intuitionistic fuzzy homomorphism of groups, and the fundamental theorem of θ-intuitionistic fuzzy homomorphism is proved.
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 King Khalid University through a large group research project under Grant Number R.G.P.2/449/44.
文摘The main goal of informal computing is to overcome the limitations of hypersensitivity to defects and uncertainty while maintaining a balance between high accuracy,accessibility,and cost-effectiveness.This paper investigates the potential applications of intuitionistic fuzzy sets(IFS)with rough sets in the context of sparse data.When it comes to capture uncertain information emanating fromboth upper and lower approximations,these intuitionistic fuzzy rough numbers(IFRNs)are superior to intuitionistic fuzzy sets and pythagorean fuzzy sets,respectively.We use rough sets in conjunction with IFSs to develop several fairly aggregation operators and analyze their underlying properties.We present numerous impartial laws that incorporate the idea of proportionate dispersion in order to ensure that the membership and non-membership activities of IFRNs are treated equally within these principles.These operations lead to the development of the intuitionistic fuzzy rough weighted fairly aggregation operator(IFRWFA)and intuitionistic fuzzy rough ordered weighted fairly aggregation operator(IFRFOWA).These operators successfully adjust to membership and non-membership categories with fairness and subtlety.We highlight the unique qualities of these suggested aggregation operators and investigate their use in the multiattribute decision-making field.We use the intuitionistic fuzzy rough environment’s architecture to create a novel strategy in situation involving several decision-makers and non-weighted data.Additionally,we developed a novel technique by combining the IFSs with quaternion numbers.We establish a unique connection between alternatives and qualities by using intuitionistic fuzzy quaternion numbers(IFQNs).With the help of this framework,we can simulate uncertainty in real-world situations and address a number of decision-making problems.Using the examples we have released,we offer a sophisticated and systematically constructed illustrative scenario that is intricately woven with the complexity ofmedical evaluation in order to thoroughly assess the relevance and efficacy of the suggested methodology.
文摘To address the fuzziness and variability in determining customer demand importance,a dynamic analysis method based on intuitionistic fuzzy numbers is proposed.First,selected customers use intuitionistic fuzzy numbers to represent the importance of each demand.Then,the preference information is aggregated using customer weights and time period weights through the intuitionistic fuzzy ordered weighted average operator,yielding a dynamic vector of the subjective importance of the demand index.Finally,the feasibility of the proposed method is demonstrated through an application example of a vibrating sorting screen.
基金supported by the National Natural Science Foundation of China for Distinguished Young Scholars(70625005)
文摘Intuitionistic fuzzy sets(IFSs) are useful means to describe and deal with vague and uncertain data.An intuitionistic fuzzy C-means algorithm to cluster IFSs is developed.In each stage of the intuitionistic fuzzy C-means method the seeds are modified,and for each IFS a membership degree to each of the clusters is estimated.In the end of the algorithm,all the given IFSs are clustered according to the estimated membership degrees.Furthermore,the algorithm is extended for clustering interval-valued intuitionistic fuzzy sets(IVIFSs).Finally,the developed algorithms are illustrated through conducting experiments on both the real-world and simulated data sets.
文摘In this paper, we introduce the notion of intuitionistic fuzzy α-generalized closed sets in intuitionistic fuzzy minimal structure spaces and investigate some of their properties. Further, we introduce and study the concept of intuitionistic fuzzy α-generalized minimal continuous functions.
基金supported by the National Natural Science Foundation of China (70571087)the National Science Fund for Distinguished Young Scholars of China (70625005)
文摘Intuitionistic fuzzy set （IFS） is a set of 2-tuple arguments, each of which is characterized by a membership degree and a nonmembership degree. The generalized form of IFS is interval-valued intuitionistic fuzzy set （IVIFS）, whose components are intervals rather than exact numbers. IFSs and IVIFSs have been found to be very useful to describe vagueness and uncertainty. However, it seems that little attention has been focused on the clustering analysis of IFSs and IVIFSs. An intuitionistic fuzzy hierarchical algorithm is introduced for clustering IFSs, which is based on the traditional hierarchical clustering procedure, the intuitionistic fuzzy aggregation operator, and the basic distance measures between IFSs： the Hamming distance, normalized Hamming, weighted Hamming, the Euclidean distance, the normalized Euclidean distance, and the weighted Euclidean distance. Subsequently, the algorithm is extended for clustering IVIFSs. Finally the algorithm and its extended form are applied to the classifications of building materials and enterprises respectively.
文摘Using the idea of Atanassov, we define the notion of intuitionistic Menger spaces as a netural generalizations of Menger spaces due to Menger. We also obtain a new generalized contraction mapping and utilize this contraction mapping to prove the existance theorems of solutions to differential equations in intuitionistic Menger spaces.
基金supported by the National Natural Science Foundation of China(7137115670971017)the Research Grants Council of the Hong Kong Special Administrative Region,China(City U112111)
文摘In order to measure the uncertain information of a type- 2 intuitionistic fuzzy set （T21FS）, an entropy measure of T21FS is presented by using the constructive principles. The proposed entropy measure is also proved to satisfy all of the constructive principles. Further, a novel concept of the type-2 triangular in- tuitionistic trapezoidal fuzzy set （T2TITrFS） is developed, and a geometric interpretation of the T2TITrFS is given to comprehend it completely or correctly in a more intuitive way. To deal with a more general uncertain complex system, the constructive principles of an entropy measure of T2TITrFS are therefore proposed on the basis of the axiomatic definition of the type-2 intuitionisic fuzzy entropy measure. This paper elicits a formula of type-2 triangular intuitionistic trapezoidal fuzzy entropy and verifies that it does sa- tisfy the constructive principles. Two examples are given to show the efficiency of the proposed entropy of T2TITrFS in describing the uncertainty of the type-2 intuitionistic fuzzy information and illustrate its application in type-2 triangular intuitionistic trapezodial fuzzy decision making problems.
基金supported by grants from the National Natural Science Foundation of China(Nos.61075120, 60673096 and 60773174)the Natural Science Foundation of Zhejiang Province in China(No.Y107262).
文摘This paper presents a general framework for the study of relation-based intuitionistic fuzzy rough sets determined by two intuitionistic fuzzy implicators.By employing two intuitionistic fuzzy implicators I and J,I -lower and J-upper approximations of intuitionistic fuzzy sets with respect to an intuitionistic fuzzy approximation space are first defined.Properties of(I,J) -intuitionistic fuzzy rough approximation operators are then examined.The connections between special types of intuitionistic fuzzy relations and properties of (I,J)-intuitionistic fuzzy approximation operators are also established.
基金supported in part by the National Natural Science Foundation of China(71571123,71771155)
文摘By using the unsymmetrical scale instead of the symmetrical scale,the multiplicative intuitionistic fuzzy sets(MIFSs) reflect our intuition more objectively.Each element in a MIFS is expressed by an ordered pair which is called a multiplicative intuitionistic fuzzy number(MIFN)and is based on the unbalanced scale(i.e.,Saaty’s 1-9 scale).In order to describe the derivatives and differentials for multiplicative intuitionistic fuzzy information more comprehensively,in this paper,we firstly propose two new basic operational laws for MIFNs,which are the subtraction law and the division law.Secondly,we describe the change values of MIFNs when considering them as variables,classify these change values based on the basic operational laws for MIFNs,and depict the convergences of sequences of MIFNs by the subtraction and division laws.Finally,we focus on the multiplicative intuitionistic fuzzy functions and derive some basic results related to their continuities,derivatives and differentials,and also give their application in selecting the configuration of a computer.
基金Supported by the National Natural Science Foundation of China(71761027)Ningbo Natural Science Foundation(2015A610161)。
文摘The multiple attribute group decision making problem in which the input arguments take the form of intuitionistic uncertain linguistic information is studied in the paper.Based on the operational principles of intuitionistic uncertain linguistic variables and the concept of the expected value and accuracy function,some new dependent aggregation operators with intuitionistic uncertain linguistic information including the dependent intuitionistic uncertain linguistic ordered weighted average(DIULOWA)operator,the dependent intuitionistic uncertain linguistic ordered weighted geometric(DIULOWG)operator,the generalized dependent intuitionistic uncertain linguistic ordered weighted aggregation(GDIULOWA)operator and so on are developed,in which the associated weights only depend on the aggregated arguments.Also,we study some desirable properties of the aggregation operators.Moreover,the approach of multiple attribute group decision making with intuitionistic uncertain linguistic information based on the developed operators is proposed.Finally,an illustrative numerical example is given to show the practicality and effectiveness of the proposed approaches.
基金The National Natural Science Foundation of China (No70571087)the National Science Fund for Distinguished Young Scholarsof China (No70625005)
文摘The concept of the degree of similarity between interval-valued intuitionistic fuzzy sets （IVIFSs） is introduced, and some distance measures between IVIFSs are defined based on the Hamming distance, the normalized Hamming distance, the weighted Hamming distance, the Euclidean distance, the normalized Euclidean distance, and the weighted Euclidean distance, etc. Then, by combining the Hausdorff metric with the Hamming distance, the Euclidean distance and their weighted versions, two other similarity measures between IVIFSs, i. e., the weighted Hamming distance based on the Hausdorff metric and the weighted Euclidean distance based on the Hausdorff metric, are defined, and then some of their properties are studied. Finally, based on these distance measures, some similarity measures between IVIFSs are defined, and the similarity measures are applied to pattern recognitions with interval-valued intuitionistic fuzzy information.
文摘Similarity measure is an essential tool to compare and determine the degree of similarity between intuitionistic fuzzy sets (IFSs). In this paper, a new similarity measure between intuitionistic fuzzy sets based on the mid points of transformed triangular fuzzy numbers is proposed. The proposed similarity measure provides reasonable results not only for the sets available in the literature but also gives very reasonable results, especially for fuzzy sets as well as for most intuitionistic fuzzy sets. To provide supportive evidence, the proposed similarity measure is tested on certain sets available in literature and is also applied to pattern recognition and medical diagnosis problems. It is observed that the proposed similarity measure provides a very intuitive quantification.
基金supported by the National Natural Science Foundation of China (71171048)the Scientific Research and Innovation Project for College Graduates of Jiangsu Province (CXZZ11 0185)+1 种基金the Scientific Research Foundation of Graduate School of Southeast University (YBJJ1135)the State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University (RCS2011K002)
文摘The notion of the interval-valued intuitionistic fuzzy set （IVIFS） is a generalization of that of the Atanassov＇s intuitionistic fuzzy set. The fundamental characteristic of IVIFS is that the values of its membership function and non-membership function are intervals rather than exact numbers. There are various averaging operators defined for IVlFSs. These operators are not monotone with respect to the total order of IVIFS, which is undesirable. This paper shows how such averaging operators can be represented by using additive generators of the product triangular norm, which simplifies and extends the existing constructions. Moreover, two new aggregation operators based on the t.ukasiewicz triangular norm are proposed, which are monotone with respect to the total order of IVIFS. Finally, an application of the interval-valued intuitionistic fuzzy weighted averaging operator is given to multiple criteria decision making.
基金Supported by the Graduate Independent Innovation Foundation of Northwest University(YZZ12061)
文摘In the paper, in order to further study the properties of filters of BL-algebras, we propose the concepts of the （∈γ, ∈γ Vqδ）-intuitionistic fuzzy filters and （∈γ, ∈γ Vqδ）- intuitionistic fuzzy soft filters of BL-algebras and derive some related results. Finally, we discuss the properties of images and inverse images of （∈γ, ∈γ Vqδ）-intuitionistic fuzzy soft filters of BL-algebras.
基金supported by the National Natural Science Foundation of China (70771025)the Fundamental Research Funds for the Central Universities of Hohai University (2009B04514)Humanities and Social Sciences Foundations of Ministry of Education of China(10YJA630067)
文摘The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational laws of intuitionistic fuzzy numbers are introduced, and the score function and accuracy function are presented to compare the intuitionistic fuzzy numbers. The intuitionistic fuzzy ordered weighted averaging （IFOWA） operator which is an extension of the well-known ordered weighted averaging （OWA） operator is investigated to aggregate the intuitionistic fuzzy information. In order to determine the weights of intuitionistic fuzzy ordered weighted averaging operator, a linear goal programming procedure is proposed for learning the weights from data. Finally, an example is illustrated to verify the effectiveness and practicability of the developed method.
