A New Method for Ranking Canonical Intuitionistic Fuzzy Numbers

Peng, Zuming; Chen, Qiang

doi:10.1007/978-1-4471-4856-2_73

Cited by 4 publications

(4 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Ranking of IFNs, is necessary in some practical application of IFNs, is discussed by many authors [13,15,17,18,22,26,27,29,36,46]. In the rest of this section, some of the existing ranking methods will be reviewed.…”

Section: A a A A A A B A M B M B B B B B B A Bmentioning

confidence: 99%

“…3) Peng's method [26] for an optimistic decision maker ( 1)   gives: A A A  . This ranking order is similar to Peng's method [26] for an optimistic decision maker   1   .…”

Section: A a A A   mentioning

confidence: 99%

“…Peng and Chen[26], in order to rank the canonical IFNs, proposed a new method based on the concepts of center index and radius index of canonical intuitionistic fuzzy numbers. According to this method, let…”

mentioning

confidence: 99%

See 2 more Smart Citations

Operations and Ranking Methods for Intuitionistic Fuzzy Numbers, a Review and New Methods

Keikha¹,

Nehi²

2016

IJISA

View full text Add to dashboard Cite

Intuitionistic Fuzzy Numbers (IFNs) transfer more information than fuzzy numbers do in uncertain situations. It is caused that many others tried to define methods for ranking of IFNs and arithmetic operations on them, which are used in practical applications of IFNs such as decision making. Arithmetic operators on IFNs changed membership and non-membership degrees. The resulted degrees have important interpretations in real application of IFNs. In this paper, we will first review the existing methods for ranking and arithmetic operations on several representations of IFNs. Then, we will propose a new method based on arithmetic mean and geometric mean to compute membership and non-membership degrees of resulted IFN from arithmetic operations on IFNs. It is caused that the resulted degrees don't change monotonousness and be closer to reality. Furthermore, a new method for ranking of IFNs will be proposed. Finally, the proposed methods are used in the numerical examples, compared to some other existing methods.

show abstract

Section: A a A A A A B A M B M B B B B B B A Bmentioning

confidence: 99%

Section: A a A A   mentioning

confidence: 99%

See 1 more Smart Citation

Operations and Ranking Methods for Intuitionistic Fuzzy Numbers, a Review and New Methods

Keikha¹,

Nehi²

2016

IJISA

View full text Add to dashboard Cite

show abstract

“…In Peng et al [17], defined the concepts of canonical intuitionistic fuzzy numbers and fuzzy cut sets, and the relation between generalized fuzzy numbers and canonical intuitionistic fuzzy numbers were studied. Next, the concept of center index and radius index of canonical intuitionistic fuzzy numbers, based on fuzzy cut sets are introduced, and the ranking index with the degree of optimism of the decision maker for canonical intuitionistic fuzzy numbers is defined.…”

Section: Introductionmentioning

confidence: 99%

A new approach for ranking of intuitionistic fuzzy numbers using a centroid concept

Prakash¹,

Suresh²,

Vengataasalam³

2016

Math Sci

View full text Add to dashboard Cite

Ranking of intuitionistic fuzzy numbers is a difficult task. Many methods have been proposed for ranking of intuitionistic fuzzy numbers. In this paper we have ranked both trapezoidal intuitionistic fuzzy numbers and triangular intuitionistic fuzzy numbers using the centroid concept. Some of the properties of the ranking function have been studied. Also, comparative examples are given to show the effectiveness of the proposed method.Keywords Intuitionistic fuzzy set Á Trapezoidal intuitionistic fuzzy number Á Triangular intuitionistic fuzzy number Á Ranking of trapezoidal intuitionistic fuzzy number Á Centroid of an intuitionistic fuzzy number

show abstract

A noval ranking approach based on incircle of triangular intuitionistic fuzzy numbers

Atalik

Şentürk

2020

IFS

View full text Add to dashboard Cite

Since proposed by Zadeh in 1965, ordinary fuzzy sets help us to model uncertainty and developed many types such as type 2 fuzzy, intuitionistic fuzzy, hesitant fuzzy etc. Intuitionistic fuzzy sets include both membership and non-membership functions for their each element. Ranking of a number is to identify a relationship of scalar quantity between these numbers. Ranking of fuzzy numbers play an important role in modeling problems such as fuzzy decision making, fuzzy linear programming problems. In this study, a new ranking method for triangular intuitionistic fuzzy numbers is proposed. The method based on the incircle of the membership function and non-membership function of TIFN uses lexicographical order to rank intuitionistic fuzzy numbers. Two examples are provided to illustrate the applicability of the method. Also, a comparative study is performed to demonstrate the validity of the proposed method. The results indicate that proposed method is consistent with other methods in the literature. Also, the method overcomes the problems such as numbers being very small or close to each other.

show abstract

A New Method for Ranking Canonical Intuitionistic Fuzzy Numbers

Cited by 4 publications

References 9 publications

Operations and Ranking Methods for Intuitionistic Fuzzy Numbers, a Review and New Methods

Operations and Ranking Methods for Intuitionistic Fuzzy Numbers, a Review and New Methods

A new approach for ranking of intuitionistic fuzzy numbers using a centroid concept

A noval ranking approach based on incircle of triangular intuitionistic fuzzy numbers

Contact Info

Product

Resources

About