Notes on triangular intuitionistic fuzzy numbers

Seikh, Mijanur Rahaman; Nayak, Prasun Kumar; Pal, Madhumangal

doi:10.1504/ijmor.2013.054730

Cited by 30 publications

(25 citation statements)

References 13 publications

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“…Definition 1 [14]. A triangular intuitionistic fuzzy number ( , , ); , a b c u v is a special IFS on a real number set R, whose membership function and non-membership function are defined as follows:…”

Section: Basic Concepts Of Tifnsmentioning

confidence: 99%

“…Definition 5 [14]. A -cut set of a TIFN (( , , ); , ) a a a a b c u is a crisp subset of R, which is defined as…”

Section: Basic Concepts Of Tifnsmentioning

confidence: 99%

“…(14), the overall evaluations of each provider are calculated as follows: Step 3: Using Eqs. (9) and (10), the value of membership and non-membership functions of 1 2 3 , , S S S can be achieved as follows:…”

Section: A Cloud Service Provider Selection Problemmentioning

confidence: 99%

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Multiple attribute decision making with triangular intuitionistic fuzzy numbers and application to cloud service provider selection

Zheng

Jia

2014

Proceedings of 2nd International Conference on Information Technology and Electronic Commerce

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The notion of Triangular intuitionistic fuzzy numbers (TIFNs) is very useful and interesting in MultipleAttribute Decision Making (MADM) problems for quantifying uncertainty and subjectivity, but the ranking of TIFNs is not an easy problem. The aim of this paper is to propose a new approach to rank TIFNs. The concepts and operational laws of TIFNs are introduced. Then a new approach is developed to rank TIFNs by determining intersection value of diagonals. And the ranking method is applied to MADM problems, in which the attribute preference values take the form of TIFNs. In addition, a cloud computing service provision example is also provided to illustrate the procedure of the proposed method, and the results of experiments verify that the method is effective and feasible.

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Section: Basic Concepts Of Tifnsmentioning

confidence: 99%

“…Definition 5 [14]. A -cut set of a TIFN (( , , ); , ) a a a a b c u is a crisp subset of R, which is defined as…”

Section: Basic Concepts Of Tifnsmentioning

confidence: 99%

See 1 more Smart Citation

Multiple attribute decision making with triangular intuitionistic fuzzy numbers and application to cloud service provider selection

Zheng

Jia

2014

Proceedings of 2nd International Conference on Information Technology and Electronic Commerce

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“…Parvathi and Malathi [17] [18] worked on the intuitionistic fuzzy decisive set method which, is a combination of bisection method and phase one of the simplex method to obtain a feasible solution. In [19], the authors described a method to approximate a TIFN to a nearly approximated interval number. The average ranking index is also introduced here to find out order relations between two TIFNs.…”

Section: Introductionmentioning

confidence: 99%

Solving Intuitionistic Fuzzy Linear Programming Problem

Kabiraj¹,

Nayak²,

Raha³

2019

IJIS

Self Cite

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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.

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“…The basic arithmetic operations of generalized triangular intuitionistic fuzzy numbers (GTIFNs) and the notion of (a,b)-cut sets were defined by Seikh et al [24]. Also a nearest interval approximation method is described to approximate a GTIFN to a nearest interval number.…”

Section: Introductionmentioning

confidence: 99%

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

Prakash¹,

Suresh²,

Vengataasalam³

2016

Math Sci

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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

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Notes on triangular intuitionistic fuzzy numbers

Cited by 30 publications

References 13 publications

Multiple attribute decision making with triangular intuitionistic fuzzy numbers and application to cloud service provider selection

Multiple attribute decision making with triangular intuitionistic fuzzy numbers and application to cloud service provider selection

Solving Intuitionistic Fuzzy Linear Programming Problem

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

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