TODIM Method for Multiple Attribute Group Decision Making under 2-Tuple Linguistic Neutrosophic Environment

Wang, Jie; Wei, Guiwu; Lu, Mingyue

doi:10.3390/sym10100486

Cited by 102 publications

(56 citation statements)

References 59 publications

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“…Finally, an illustrative example is given to demonstrate the efficiency of the similarity measures for selecting the desirable ERP system. In the future, the application of the proposed Dice similarity measure of PFSs needs to be explored in decision making, [73][74][75][76][77][78][79][80][81][82][83][84] risk analysis 85,86 and many other fields under uncertain environment. [87][88][89][90][91][92][93][94]…”

Section: Discussionmentioning

confidence: 99%

The generalized Dice similarity measures for Pythagorean fuzzy multiple attribute group decision making

2019

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The Pythagorean fuzzy set (PFS) is characterized by two functions expressing the degree of membership and the degree of nonmembership, which square sum of them is equal or less than 1. It was proposed as a generalization of a fuzzy set to deal with indeterminate and inconsistent information. In this study, we shall present some novel Dice similarity measures of PFSs and the generalized Dice similarity measures of PFSs and indicates that the Dice similarity measures and asymmetric measures (projection measures) are the special cases of the generalized Dice similarity measures in some parameter values. Then, we propose the generalized Dice similarity measures‐based multiple attribute group decision‐making models with Pythagorean fuzzy information. Then, we apply the generalized Dice similarity measures between PFSs to multiple attribute group decision making. Finally, an illustrative example is given to demonstrate the efficiency of the similarity measures for selecting the desirable ERP system.

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Section: Discussionmentioning

confidence: 99%

The generalized Dice similarity measures for Pythagorean fuzzy multiple attribute group decision making

2019

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“…Thus, the intuitionistic fuzzy set (IFS) was constructed; in the IFS each intuitionistic fuzzy set is characterized by the functions of membership degree and non-membership degree between 0 and 1, and the sum of these are limited to 1. Subsequent to these studies, more and more scholars have studied the IFS in relation to many multiple attribute decision making (MADM) problems [3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Xu [17] has defined some intuitionistic fuzzy weighted average operators.…”

Section: Introductionmentioning

confidence: 99%

Dual Hesitant Pythagorean Fuzzy Heronian Mean Operators in Multiple Attribute Decision Making

Tang

Wang

et al. 2019

Mathematics

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On account of the indeterminacy and subjectivity of decision makers (DMs) in complexity decision-making environments, the evaluation information over alternatives presented by DMs is usually fuzzy and ambiguous. As the generalization of intuitionistic fuzzy sets (IFSs), the Pythagorean fuzzy set (PFS) is more useful in expressing fuzzy and ambiguous information. Meanwhile, in order to consider human hesitance, dual hesitant Pythagorean fuzzy sets (DHPFSs) are presented, which can be more valid for handling real multiple attribute decision-making (MADM) problems. To fuse the information in DHPFSs more effectively, in this article, some dual hesitant Pythagorean fuzzy Heronian mean operators, which can consider the relationships between arguments being fused, are defined and studied. Evidently, the new proposed operators can obtain more exact results than other existing methods. In addition, some important properties of these Heronian mean (HM) operators are discussed. Subsequently, the defined aggregation operators are used in MADM with dual hesitant Pythagorean fuzzy numbers (DHPFNs), and the MADM model is developed. In accordance with the defined operators and the built model, the dual hesitant Pythagorean fuzzy generalized weighted Heronian mean (DHPFGWHM) operator and dual hesitant Pythagorean fuzzy generalized geometric weighted Heronian mean (DHPFGGWHM) operator are applied to deal with the green supplier selection in supply chain management, and the availability and superiority of the proposed operators are analyzed by comparing them with some existing approaches. The method presented in this paper can effectively solve the MADM problems in which the decision-making information is expressed by DHPFNs and the attributes are interactive.

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“…Li et al gave some methods for multiple attribute group decision‐making based on intuitionistic fuzzy Dombi Hamy mean operators. The IFS and their extensions have received more and more attention since its appearance . A new extension of IFS, namely, the Pythagorean fuzzy set (PFS), has been developed.…”

Section: Introductionmentioning

confidence: 99%

Bidirectional project method for dual hesitant Pythagorean fuzzy multiple attribute decision‐making and their application to performance assessment of new rural construction

Tang

Wei

et al. 2019

Int J Intell Syst

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The dual hesitant Pythagorean fuzzy set (DHPFS) consists of two parts, that is, the membership hesitancy function and the nonmembership hesitancy function, supporting a more exemplary and flexible access to assign values for each element in the domain. It is very suitable to handle the situation that there are various possible values in membership and nonmembership degrees to depict the true circumstance. The bidirectional project method of DHPFS calculates method considered not only the bidirectional projection magnitudes and the distance but also includes angle between objects evaluated. Therefore, this paper proposes a bidirectional project method of DHPFS to handle the multiple attribute decision-making (MADM) problem under the dual hesitant Pythagorean fuzzy environment. Through the measure between each alternative decision matrix and the positive and negative ideal alternative matrix, the ranking order all alternatives can be used to select the best alternative. Furthermore, a model for MADM has been given. Finally, a numerical example for performance assessment of new rural construction has been given to demonstrate the application of bidirectional project method of DHPFS, and we used the dual hesitant Pythagorean weighted Bonferroni mean to compare its reasonable and effectiveness. K E Y W O R D Sbidirectional project method, dual hesitant Pythagorean fuzzy set, multiple attribute decision-making, new rural construction, performance assessment 1 | INTRODUCTION Atanassov 1,2 introduced the concept of intuitionistic fuzzy set (IFS) characterized by a membership function and a nonmembership function, which is a generalization of the concept of fuzzy set, 3 whose basic component is only a membership function. For the IFS, the sum of the membership and nonmembership degrees of each ordered pair is less than or equal to 1. Xu 4 developed the intuitionistic fuzzy weighted averaging (IFWA) operator, the intuitionistic fuzzy ordered weighted averaging (IFOWA) operator, and the intuitionistic fuzzy hybrid aggregation (IFHA) operator. Xu 5 developed some geometric aggregation operators, such as the intuitionistic fuzzy weighted geometric (IFWG) operator, the intuitionistic fuzzy ordered weighted geometric (IFOWG) operator, and the intuitionistic fuzzy hybrid geometric (IFHG) operator and gave an application of the IFHG operator to multiple attribute group decision-making with intuitionistic fuzzy information. Zhao and Wei 6 proposed some intuitionistic fuzzy Einstein hybrid aggregation operators for multiple attribute decision-making (MADM). Li et al 7 gave some methods for multiple attribute group decision-making based on intuitionistic fuzzy Dombi Hamy mean operators. The IFS and their extensions have received more and more attention since its appearance. A new extension of IFS, namely, the Pythagorean fuzzy set (PFS), 31,32 has been developed. The PFS is also characterized by the membership and nonmembership degrees. The difference between PFS and IFS is that the square sum of the membership and nonmembership de...

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TODIM Method for Multiple Attribute Group Decision Making under 2-Tuple Linguistic Neutrosophic Environment

Cited by 102 publications

References 59 publications

The generalized Dice similarity measures for Pythagorean fuzzy multiple attribute group decision making

The generalized Dice similarity measures for Pythagorean fuzzy multiple attribute group decision making

Dual Hesitant Pythagorean Fuzzy Heronian Mean Operators in Multiple Attribute Decision Making

Bidirectional project method for dual hesitant Pythagorean fuzzy multiple attribute decision‐making and their application to performance assessment of new rural construction

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