Power Average of Trapezoidal Intuitionistic Fuzzy Numbers Using Strict t-Norms and t-Conorms

Wan, Shouhong; Yi, Zhihong

doi:10.1109/tfuzz.2015.2501408

Cited by 52 publications

(31 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition, considering that MM operator has the superiority of compatibility, we can also study some new aggregation operators on the basis of Muirhead mean operator, for example, extend them to linguistic intuitionistic fuzzy sets (LIFSs), Pythagorean fuzzy sets (PFSs), generalized orthopair fuzzy sets [51] and trapezoidal intuitionistic fuzzy numbers [52] and so on.…”

Section: Discussionmentioning

confidence: 99%

Some Muirhead Mean Operators for Intuitionistic Fuzzy Numbers and Their Applications to Group Decision Making

Лю

2017

PLoS ONE

View full text Add to dashboard Cite

Muirhead mean (MM) is a well-known aggregation operator which can consider interrelationships among any number of arguments assigned by a variable vector. Besides, it is a universal operator since it can contain other general operators by assigning some special parameter values. However, the MM can only process the crisp numbers. Inspired by the MM’ advantages, the aim of this paper is to extend MM to process the intuitionistic fuzzy numbers (IFNs) and then to solve the multi-attribute group decision making (MAGDM) problems. Firstly, we develop some intuitionistic fuzzy Muirhead mean (IFMM) operators by extending MM to intuitionistic fuzzy information. Then, we prove some properties and discuss some special cases with respect to the parameter vector. Moreover, we present two new methods to deal with MAGDM problems with the intuitionistic fuzzy information based on the proposed MM operators. Finally, we verify the validity and reliability of our methods by using an application example, and analyze the advantages of our methods by comparing with other existing methods.

show abstract

Section: Discussionmentioning

confidence: 99%

Some Muirhead Mean Operators for Intuitionistic Fuzzy Numbers and Their Applications to Group Decision Making

Лю

2017

PLoS ONE

View full text Add to dashboard Cite

show abstract

“…The dual triple T S N ( , , ) is an utility tool to define the generalized operational laws for a variety of different fuzzy environments. [10][11][12][13][14][15] The concepts of t-norm and t-conorm are given as follows:…”

Section: T-norm and Its Dual T-conormmentioning

confidence: 99%

“…The main tool we used to reach this purpose is a triple T S N ( , , ), where T is a t-norm, S a t-conorm and N a fuzzy complement. In a triple T S N ( , , )，when T and S are dual with respect to N , 9 the triple is called dual triple which has been used by some researchers to define the generalized operational laws for a variety of different fuzzy environments, such as IFS, 10,11 trapezoidal IFS, 12 interval-valued hesitant fuzzy set, 13 dual hesitant fuzzy set 14 and interval type-2 hesitant fuzzy set. 15 In the multiattribute decision making (MADM) problems, the classic fuzzy set theory application field, information aggregation is an important and pervasive activity of the MADM process.…”

mentioning

confidence: 99%

Pythagorean fuzzy Bonferroni means based on T‐norm and its dual T‐conorm

et al. 2019

View full text Add to dashboard Cite

For multiple‐attribute decision making problems in Pythagorean fuzzy environment, few existing aggregation operators consider interrelationships among the attributes. To deal with this issue, this article extends the Bonferroni means to Pythagorean fuzzy sets (PFSs) to provide Pythagorean Fuzzy Bonferroni means. We first extend t‐norm and its dual t‐conorm to propose the generalized operational laws for PFSs, which can be considered as the extensions of the known ones. Based on these new laws, Pythagorean fuzzy weighted Bonferroni mean operator and Pythagorean fuzzy weighted geometric Bonferroni mean operator are developed, both of them can capture the correlations among Pythagorean fuzzy input arguments and their desired properties and special cases are also investigated in detail. At last, a novel approach is proposed based on the developed operators with its effectiveness being proved by an investment selection problem.

show abstract

“…Additionally, a normalized TIFN is also called a normal TIFN in the sequel. Definition Let

{\overset{a}{true}}_{i} = false(({\underset{̲}{a}}_{i}, a_{i}, {\bar{a}}_{i}), w_{{\overset{a}{true}}_{i}}, u_{{\overset{a}{true}}_{i}} false) false(i = 1, 2 false)

be two normalized TIFNs and

λ \geq 0

, then the operation laws are defined as follows: (1)

{\overset{a}{true}}_{1} ⨁ {\overset{a}{true}}_{2} = false(({\underset{̲}{a}}_{1} + {\underset{̲}{a}}_{2} - {\underset{̲}{a}}_{1} {\underset{̲}{a}}_{2}, a_{1} + a_{2} - a_{1} a_{2}, {\bar{a}}_{1} + {\bar{a}}_{2} - {\bar{a}}_{1} {\bar{a}}_{2}), w_{{\overset{a}{true}}_{1}} w_{{\overset{a}{true}}_{2}}, u_{{\overset{a}{true}}_{1}} + u_{{\overset{a}{true}}_{2}} - u_{{\overset{a}{true}}_{1}} u_{{\overset{a}{true}}_{2}} false)

; (2)

λ {\overset{a}{true}}_{1} = false((1 - {(1 - \underset{̲}{a})}^{λ}, 1 - {(1 - a)}^{λ}, 1 - {(1 - \bar{a})}^{λ}), w_{{\tilde{a}}_{1}}^{λ}, 1 - {false(1 - u_{{\overset{a}{true}}_{1}} false)}^{λ} false)

. …”

Section: Operation Laws and Weighted Average Operator For Tifnsmentioning

confidence: 99%

Triangular norm-based cuts and possibility characteristics of triangular intuitionistic fuzzy numbers for decision making

2018

Int. J. Intell. Syst.

Self Cite

View full text Add to dashboard Cite

Triangular intuitionistic fuzzy numbers (TIFNs) is one of the useful tools to manage the fuzziness and vagueness in expressing decision data and solving decision making problems. In this paper, triangular norm (t‐norm) based cuts of TIFNs are developed to synthesize the membership and nonmembership functions in describing the cut sets, then the possibility characteristics of TIFNs, i.e., the possibility mean, the possibility variance, and the possibility mean‐standard deviation ratio, are given. Thereby, on the ground of the possibility mean‐standard deviation ratio, a ranking method of TIFNs is introduced. With these elements, an approach to multiple attributes decision making (MADM) is proposed and illustrated by a numerical example. It is shown that the approach to MADM comprehensively considers both the membership and nonmembership functions and can lead to objective and reasonable results.

show abstract

Power Average of Trapezoidal Intuitionistic Fuzzy Numbers Using Strict t-Norms and t-Conorms

Cited by 52 publications

References 42 publications

Some Muirhead Mean Operators for Intuitionistic Fuzzy Numbers and Their Applications to Group Decision Making

Some Muirhead Mean Operators for Intuitionistic Fuzzy Numbers and Their Applications to Group Decision Making

Pythagorean fuzzy Bonferroni means based on T‐norm and its dual T‐conorm

Triangular norm-based cuts and possibility characteristics of triangular intuitionistic fuzzy numbers for decision making

Contact Info

Product

Resources

About