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
As a generalization of fuzzy set,hesitant probabilistic fuzzy set and pythagorean triangular fuzzy set have their own unique advantages in describing decision information.As modern socioeconomic decision-making proble...As a generalization of fuzzy set,hesitant probabilistic fuzzy set and pythagorean triangular fuzzy set have their own unique advantages in describing decision information.As modern socioeconomic decision-making problems are becoming more and more complex,it also becomes more and more difficult to appropriately depict decision makers’cognitive information in decision-making process.In order to describe the decision information more comprehensively,we define a pythagorean probabilistic hesitant triangular fuzzy set(PPHTFS)by combining the pythagorean triangular fuzzy set and the probabilistic hesitant fuzzy set.Firstly,the basic operation and scoring function of the pythagorean probabilistic hesitant triangular fuzzy element(PPHTFE)are proposed,and the comparison rule of two PPHTFEs is given.Then,some pythagorean probabilistic hesitant triangular fuzzy aggregation operators are developed,and their properties are also studied.Finally,a multi-attribute decision-making(MADM)model is constructed based on the proposed operators under the pythagorean probabilistic hesitant triangular fuzzy information,and an illustration example is given to demonstrate the practicability and validity of the proposed decision-making method.展开更多
This paper introduces a new aggregation model by using induced and heavy aggregation operators in distances measures such as the Hamming distance.It is called the induced heavy ordered weighted averaging（OWA） dista...This paper introduces a new aggregation model by using induced and heavy aggregation operators in distances measures such as the Hamming distance.It is called the induced heavy ordered weighted averaging（OWA） distance（IHOWAD） operator.This paper studies some of its main properties and a wide range of particular cases such as the induced heavy OWA（IHOWA） operator,the induced OWA distance（IOWAD） operator and the heavy OWA distance（HOWAD） operator.This approach is generalized by using generalized and quasi-arithmetic means obtaining the induced generalized IHOWAD（IGHOWAD） operator and the Quasi-IHOWAD operator.An application of the new approach in a decision making problem regarding the selection of strategies is developed.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
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 Key Research and Development Project of Hunan Province(2019SK2331)the Natural Science Foundation of Hunan Province(2019JJ40099,2019JJ40100,2020JJ4339)+2 种基金the Key Scientific Research Project of Hunan Education Department(18A317,19A202)the Scientific Research Fund of Hunan Provincial Education Department(20B272)the Innovation Foundation for Postgraduate of Hunan Institute of Science and Technology(YCX2020A34).
文摘As a generalization of fuzzy set,hesitant probabilistic fuzzy set and pythagorean triangular fuzzy set have their own unique advantages in describing decision information.As modern socioeconomic decision-making problems are becoming more and more complex,it also becomes more and more difficult to appropriately depict decision makers’cognitive information in decision-making process.In order to describe the decision information more comprehensively,we define a pythagorean probabilistic hesitant triangular fuzzy set(PPHTFS)by combining the pythagorean triangular fuzzy set and the probabilistic hesitant fuzzy set.Firstly,the basic operation and scoring function of the pythagorean probabilistic hesitant triangular fuzzy element(PPHTFE)are proposed,and the comparison rule of two PPHTFEs is given.Then,some pythagorean probabilistic hesitant triangular fuzzy aggregation operators are developed,and their properties are also studied.Finally,a multi-attribute decision-making(MADM)model is constructed based on the proposed operators under the pythagorean probabilistic hesitant triangular fuzzy information,and an illustration example is given to demonstrate the practicability and validity of the proposed decision-making method.
基金supported by the projects JC2009-00189 and A/023879/09 from the Spanish Ministry of Science and Innovation
文摘This paper introduces a new aggregation model by using induced and heavy aggregation operators in distances measures such as the Hamming distance.It is called the induced heavy ordered weighted averaging（OWA） distance（IHOWAD） operator.This paper studies some of its main properties and a wide range of particular cases such as the induced heavy OWA（IHOWA） operator,the induced OWA distance（IOWAD） operator and the heavy OWA distance（HOWAD） operator.This approach is generalized by using generalized and quasi-arithmetic means obtaining the induced generalized IHOWAD（IGHOWAD） operator and the Quasi-IHOWAD operator.An application of the new approach in a decision making problem regarding the selection of strategies is developed.
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.
