Diabetes has become a major concern nowadays and its complications are affecting various organs of a diabetic patient. Therefore, a multi-dimensional technique including all parameters is required to detect the cause,...Diabetes has become a major concern nowadays and its complications are affecting various organs of a diabetic patient. Therefore, a multi-dimensional technique including all parameters is required to detect the cause, its proper diagnostic procedure and its prevention. In this present work, a technique has been introduced that seeks to build an implementation for the intelligence system based on neural networks. Moreover, it has been described that how the proposed technique can be used to determine the membership together with the non-membership functions in the intuitionistic environment. The dataset has been obtained from Pima Indians Diabetes Database (PIDD). In this work, a complete diagnostic procedure of diabetes has been introduced with seven layered structural frameworks of an Intuitionistic Neuro Sugeno Fuzzy System (INSFS). The first layer is the input, in which six factors have been taken as an input variable. Subsequently, a neural network framework has been developed by constructing IFN for all the six input variables, and then this input has been fuzzified by using triangular intuitionistic fuzzy numbers. In this work, we have introduced a novel optimization technique for the parameters involved in the INSFS. Moreover, an inference system has also been framed for the neural network known as INFS. The results have also been given in the form of tables, which describe each concluding factor.展开更多
In this paper,we discuss the structure of intuitionistic fuzzy(IF)homomorphisms,exact sequences and some other concepts in category of IF modules.We study on IF exact sequences and IF Hom functors in IFR-Mod and obtai...In this paper,we discuss the structure of intuitionistic fuzzy(IF)homomorphisms,exact sequences and some other concepts in category of IF modules.We study on IF exact sequences and IF Hom functors in IFR-Mod and obtain some results about them.If R is a commutative ring and 0→A~f→B~g→C is an exact sequence in IFR-Mod,where f is IF split homomorphism,then we show that Hom_(IF-R)(D,-)preserves the sequence for every D∈IFR-Mod.Also IF projective modules will be introduced and investigated in this paper.Finally we define product and coproduct of IF modules and show that if M is an R-module,A=(μ_(A),ν_(A))≤_(IF)M and e_(i)∈E(R)for any i∈I,then Hom(Пi2I 0IF Rei;A)=Πi2I Hom(0IF Rei;A).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
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
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 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
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
Intuitionistic trapezoidal fuzzy numbers and their operational laws are defined. Based on these operational laws, some aggregation operators, including intuitionistic trapezoidal fuzzy weighted arithmetic averaging op...Intuitionistic trapezoidal fuzzy numbers and their operational laws are defined. Based on these operational laws, some aggregation operators, including intuitionistic trapezoidal fuzzy weighted arithmetic averaging operator and weighted geometric averaging operator are proposed. Expected values, score function, and accuracy function of intuitionitsic trapezoidal fuzzy numbers are defined. Based on these, a kind of intuitionistic trapezoidal fuzzy multi-criteria decision making method is proposed. By using these aggregation operators, criteria values are aggregated and integrated intuitionistic trapezoidal fuzzy numbers of alternatives are attained. By comparing score function and accuracy function values of integrated fuzzy numbers, a ranking of the whole alternative set can be attained. An example is given to show the feasibility and availability of the method.展开更多
Aiming at the problems of convergence-slow and convergence-free of Discrete Particle Swarm Optimization Algorithm(DPSO) in solving large scale or complicated discrete problem, this article proposes Intuitionistic Fuzz...Aiming at the problems of convergence-slow and convergence-free of Discrete Particle Swarm Optimization Algorithm(DPSO) in solving large scale or complicated discrete problem, this article proposes Intuitionistic Fuzzy Entropy of Discrete Particle Swarm Optimization(IFDPSO) and makes it applied to Dynamic Weapon Target Assignment(WTA). First, the strategy of choosing intuitionistic fuzzy parameters of particle swarm is defined, making intuitionistic fuzzy entropy as a basic parameter for measure and velocity mutation. Second, through analyzing the defects of DPSO, an adjusting parameter for balancing two cognition, velocity mutation mechanism and position mutation strategy are designed, and then two sets of improved and derivative algorithms for IFDPSO are put forward, which ensures the IFDPSO possibly search as much as possible sub-optimal positions and its neighborhood and the algorithm ability of searching global optimal value in solving large scale 0-1 knapsack problem is intensified. Third, focusing on the problem of WTA, some parameters including dynamic parameter for shifting firepower and constraints are designed to solve the problems of weapon target assignment. In addition, WTA Optimization Model with time and resource constraints is finally set up, which also intensifies the algorithm ability of searching global and local best value in the solution of WTA problem. Finally, the superiority of IFDPSO is proved by several simulation experiments. Particularly, IFDPSO, IFDPSO1~IFDPSO3 are respectively effective in solving large scale, medium scale or strict constraint problems such as 0-1 knapsack problem and WTA problem.展开更多
In view of the fact that traditional air target threat assessment methods are difficult to reflect the combat characteristics of uncertain, dynamic and hybrid formation, an algorithm is proposed to solve the multi-tar...In view of the fact that traditional air target threat assessment methods are difficult to reflect the combat characteristics of uncertain, dynamic and hybrid formation, an algorithm is proposed to solve the multi-target threat assessment problems. The target attribute weight is calculated by the intuitionistic fuzzy entropy(IFE) algorithm and the time series weight is gained by the Poisson distribution method based on multi-times data. Finally,assessment and sequencing of the air multi-target threat model based on IFE and dynamic Vlse Kriterijumska Optimizacija I Kompromisno Resenje(VIKOR) is established with an example which indicates that the method is reasonable and effective.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
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
The aim of this paper is to propose a threat assessment method based on intuitionistic fuzzy measurement reasoning with orientaion to deal with the shortcomings of the method proposed in [Ying-Jie Lei et al., Journal ...The aim of this paper is to propose a threat assessment method based on intuitionistic fuzzy measurement reasoning with orientaion to deal with the shortcomings of the method proposed in [Ying-Jie Lei et al., Journal of Electronics and Information Technology 29(9)(2007)2077-2081] and [Dong-Feng Chen et al., Procedia Engineering 29(5)(2012)3302-3306] the ignorance of the influence of the intuitionistic index's orientation on the membership functions in the reasoning, which caused partial information loss in reasoning process. Therefore, we present a 3D expression of intuitionistic fuzzy similarity measurement, make an analysis of the constraints for intuitionistic fuzzy similarity measurement, and redefine the intuitionistic fuzzy similarity measurement. Moreover, in view of the threat assessment problem, we give the system variables of attribute function and assessment index, set up the reasoning system based on intuitionistic fuzzy similarity measurement with orientation, and design the reasoning rules, reasoning algorithms and fuzzy-resolving algorithms. Finally, through the threat assessment, some typical examples are cited to verify the validity and superiority of the method.展开更多
We study a multi-criteria fuzzy decision-making method based on weighted triangular intuitionistic fuzzy number correlation coefficients. Under the scenario that criteria weights for alternatives are completely unknow...We study a multi-criteria fuzzy decision-making method based on weighted triangular intuitionistic fuzzy number correlation coefficients. Under the scenario that criteria weights for alternatives are completely unknown, triangular intuitionistic fuzzy method can not only supplement the insufficiency of the method based on the distance but also endow more information to the estimation and reduce the loss of evaluation information.Among the triangular numbers, two boundary numbers are the maximum and minimum values of the interval respectively, and the medium number is the most possible value under subjective estimation. Using this method,we propose a new way to obtain the criteria weights with more information quantity. By ranking the relative closeness of the weighted correlation coefficients between each alternative, and the critical and ideal alternatives,we show the method to figure out the most suitable alternative based on the expected criteria. An illustrative example is also taken into account to prove the effectiveness of the model.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
Multiattribute decision making（MADM） problems, in which the weights and ratings of alternatives are expressed with intuitionistic fuzzy（IF） sets, are investigated.Firstly, the relative degrees of membership and th...Multiattribute decision making（MADM） problems, in which the weights and ratings of alternatives are expressed with intuitionistic fuzzy（IF） sets, are investigated.Firstly, the relative degrees of membership and the relative degrees of non-membership are formulated as IF sets, the weights and values of alternatives on both qualitative and quantitative attributes may be expressed as IF sets in a unified way.Then a MADM method based on generalized ordered weighted averaging operators is proposed.The proposed method is illustrated with a numerical example.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
Intuitionistic Fuzzy Set (IFS) can be used as a general tool for modeling problems of decision making under uncertainty where, the degree of rejection is defined simultaneously with the degree of acceptance of a piece...Intuitionistic Fuzzy Set (IFS) can be used as a general tool for modeling problems of decision making under uncertainty where, the degree of rejection is defined simultaneously with the degree of acceptance of a piece of information in such a way that these degrees are not complement to each other. Accordingly, an attempt is made to solve intuitionistic fuzzy linear programming problems using a technique based on an earlier technique proposed by Zimmermann to solve fuzzy linear programming problem. Our proposed technique does not require the existing ranking of intuitionistic fuzzy numbers. This method is also different from the existing weight assignment method or the Angelov’s method. A comparative study is undertaken and interesting results have been presented.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(IVIFS...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
文摘Diabetes has become a major concern nowadays and its complications are affecting various organs of a diabetic patient. Therefore, a multi-dimensional technique including all parameters is required to detect the cause, its proper diagnostic procedure and its prevention. In this present work, a technique has been introduced that seeks to build an implementation for the intelligence system based on neural networks. Moreover, it has been described that how the proposed technique can be used to determine the membership together with the non-membership functions in the intuitionistic environment. The dataset has been obtained from Pima Indians Diabetes Database (PIDD). In this work, a complete diagnostic procedure of diabetes has been introduced with seven layered structural frameworks of an Intuitionistic Neuro Sugeno Fuzzy System (INSFS). The first layer is the input, in which six factors have been taken as an input variable. Subsequently, a neural network framework has been developed by constructing IFN for all the six input variables, and then this input has been fuzzified by using triangular intuitionistic fuzzy numbers. In this work, we have introduced a novel optimization technique for the parameters involved in the INSFS. Moreover, an inference system has also been framed for the neural network known as INFS. The results have also been given in the form of tables, which describe each concluding factor.
文摘In this paper,we discuss the structure of intuitionistic fuzzy(IF)homomorphisms,exact sequences and some other concepts in category of IF modules.We study on IF exact sequences and IF Hom functors in IFR-Mod and obtain some results about them.If R is a commutative ring and 0→A~f→B~g→C is an exact sequence in IFR-Mod,where f is IF split homomorphism,then we show that Hom_(IF-R)(D,-)preserves the sequence for every D∈IFR-Mod.Also IF projective modules will be introduced and investigated in this paper.Finally we define product and coproduct of IF modules and show that if M is an R-module,A=(μ_(A),ν_(A))≤_(IF)M and e_(i)∈E(R)for any i∈I,then Hom(Пi2I 0IF Rei;A)=Πi2I Hom(0IF Rei;A).
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.
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“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.
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.
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.
基金supported by the National Natural Science Foundation of China (70771115).
文摘Intuitionistic trapezoidal fuzzy numbers and their operational laws are defined. Based on these operational laws, some aggregation operators, including intuitionistic trapezoidal fuzzy weighted arithmetic averaging operator and weighted geometric averaging operator are proposed. Expected values, score function, and accuracy function of intuitionitsic trapezoidal fuzzy numbers are defined. Based on these, a kind of intuitionistic trapezoidal fuzzy multi-criteria decision making method is proposed. By using these aggregation operators, criteria values are aggregated and integrated intuitionistic trapezoidal fuzzy numbers of alternatives are attained. By comparing score function and accuracy function values of integrated fuzzy numbers, a ranking of the whole alternative set can be attained. An example is given to show the feasibility and availability of the method.
基金supported by The National Natural Science Foundation of China under Grant Nos.61402517, 61573375The Foundation of State Key Laboratory of Astronautic Dynamics of China under Grant No. 2016ADL-DW0302+2 种基金The Postdoctoral Science Foundation of China under Grant Nos. 2013M542331, 2015M572778The Natural Science Foundation of Shaanxi Province of China under Grant No. 2013JQ8035The Aviation Science Foundation of China under Grant No. 20151996015
文摘Aiming at the problems of convergence-slow and convergence-free of Discrete Particle Swarm Optimization Algorithm(DPSO) in solving large scale or complicated discrete problem, this article proposes Intuitionistic Fuzzy Entropy of Discrete Particle Swarm Optimization(IFDPSO) and makes it applied to Dynamic Weapon Target Assignment(WTA). First, the strategy of choosing intuitionistic fuzzy parameters of particle swarm is defined, making intuitionistic fuzzy entropy as a basic parameter for measure and velocity mutation. Second, through analyzing the defects of DPSO, an adjusting parameter for balancing two cognition, velocity mutation mechanism and position mutation strategy are designed, and then two sets of improved and derivative algorithms for IFDPSO are put forward, which ensures the IFDPSO possibly search as much as possible sub-optimal positions and its neighborhood and the algorithm ability of searching global optimal value in solving large scale 0-1 knapsack problem is intensified. Third, focusing on the problem of WTA, some parameters including dynamic parameter for shifting firepower and constraints are designed to solve the problems of weapon target assignment. In addition, WTA Optimization Model with time and resource constraints is finally set up, which also intensifies the algorithm ability of searching global and local best value in the solution of WTA problem. Finally, the superiority of IFDPSO is proved by several simulation experiments. Particularly, IFDPSO, IFDPSO1~IFDPSO3 are respectively effective in solving large scale, medium scale or strict constraint problems such as 0-1 knapsack problem and WTA problem.
基金supported by the National Natural Science Foundation of China(61401363)the Science and Technology on Avionics Integration Laboratory and Aeronautical Science Foundation(20155153034)+1 种基金the Innovative Talents Promotion Plan in Shaanxi Province(2017KJXX-15)the Fundamental Research Funds for the Central Universities(3102016AXXX005)
文摘In view of the fact that traditional air target threat assessment methods are difficult to reflect the combat characteristics of uncertain, dynamic and hybrid formation, an algorithm is proposed to solve the multi-target threat assessment problems. The target attribute weight is calculated by the intuitionistic fuzzy entropy(IFE) algorithm and the time series weight is gained by the Poisson distribution method based on multi-times data. Finally,assessment and sequencing of the air multi-target threat model based on IFE and dynamic Vlse Kriterijumska Optimizacija I Kompromisno Resenje(VIKOR) is established with an example which indicates that the method is reasonable and effective.
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.
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 Foundation of State Key Laboratory of Astronautic Dynamics of China under Grant No.2012ADL-DW0301The National Natural Science Foundation of China under Grant Nos.61272011,61179010 and 60773209+1 种基金The Natural Science Foundation of Shaanxi Province of China under Grant Nos.2013JQ8035 and 2006F18The Postdoctoral Science Foundation of China under Grant No.2013M542331
文摘The aim of this paper is to propose a threat assessment method based on intuitionistic fuzzy measurement reasoning with orientaion to deal with the shortcomings of the method proposed in [Ying-Jie Lei et al., Journal of Electronics and Information Technology 29(9)(2007)2077-2081] and [Dong-Feng Chen et al., Procedia Engineering 29(5)(2012)3302-3306] the ignorance of the influence of the intuitionistic index's orientation on the membership functions in the reasoning, which caused partial information loss in reasoning process. Therefore, we present a 3D expression of intuitionistic fuzzy similarity measurement, make an analysis of the constraints for intuitionistic fuzzy similarity measurement, and redefine the intuitionistic fuzzy similarity measurement. Moreover, in view of the threat assessment problem, we give the system variables of attribute function and assessment index, set up the reasoning system based on intuitionistic fuzzy similarity measurement with orientation, and design the reasoning rules, reasoning algorithms and fuzzy-resolving algorithms. Finally, through the threat assessment, some typical examples are cited to verify the validity and superiority of the method.
基金the National Natural Science Foundation of China(Nos.71671016,71231001 and 71832001)the Fundamental Research Funds for the Central Universities of China(No.FRF-BR-15-001B)
文摘We study a multi-criteria fuzzy decision-making method based on weighted triangular intuitionistic fuzzy number correlation coefficients. Under the scenario that criteria weights for alternatives are completely unknown, triangular intuitionistic fuzzy method can not only supplement the insufficiency of the method based on the distance but also endow more information to the estimation and reduce the loss of evaluation information.Among the triangular numbers, two boundary numbers are the maximum and minimum values of the interval respectively, and the medium number is the most possible value under subjective estimation. Using this method,we propose a new way to obtain the criteria weights with more information quantity. By ranking the relative closeness of the weighted correlation coefficients between each alternative, and the critical and ideal alternatives,we show the method to figure out the most suitable alternative based on the expected criteria. An illustrative example is also taken into account to prove the effectiveness of the model.
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.
基金supported by the National Natural Science Foundation of China (70871117 70571086)
文摘Multiattribute decision making（MADM） problems, in which the weights and ratings of alternatives are expressed with intuitionistic fuzzy（IF） sets, are investigated.Firstly, the relative degrees of membership and the relative degrees of non-membership are formulated as IF sets, the weights and values of alternatives on both qualitative and quantitative attributes may be expressed as IF sets in a unified way.Then a MADM method based on generalized ordered weighted averaging operators is proposed.The proposed method is illustrated with a numerical example.
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.
文摘Intuitionistic Fuzzy Set (IFS) can be used as a general tool for modeling problems of decision making under uncertainty where, the degree of rejection is defined simultaneously with the degree of acceptance of a piece of information in such a way that these degrees are not complement to each other. Accordingly, an attempt is made to solve intuitionistic fuzzy linear programming problems using a technique based on an earlier technique proposed by Zimmermann to solve fuzzy linear programming problem. Our proposed technique does not require the existing ranking of intuitionistic fuzzy numbers. This method is also different from the existing weight assignment method or the Angelov’s method. A comparative study is undertaken and interesting results have been presented.
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.
