A Ranking Method of Triangular Intuitionistic Fuzzy Numbers and Application to Decision Making

Abstract

Ranking of triangular intuitionistic fuzzy numbers (TIFNs) is an important problem, which is solved by the value and ambiguity based ranking method developed in this paper. Firstly, the concept of TIFNs is introduced. Arithmetic operations and cut sets over TIFNs are investigated. Then, the values and ambiguities of the membership degree and the non-membership degree for TIFNs are defined as well as the value-index and ambiguity-index. Finally, a value and ambiguity based ranking method is developed and applied to solve multiattribute decision making problems in which the ratings of alternatives on attributes are expressed using TIFNs. A numerical example is examined to demonstrate the implementation process and applicability of the method proposed in this paper. Furthermore, comparison analysis of the proposed method is conducted to show its advantages over other similar methods.

Proposed Model for Evaluating Information Systems Quality Based on Single Valued Triangular Neutrosophic Numbers

“…Ye [26] proposed the concept of expected value method for intuitionistic trapezoidal fuzzy and applied it to multi-criteria decision-making problems. Deli and Şubaş [6] adapted and generalized Li et al [14] method to SVN-numbers and the results show that this method is effective and feasible. Prakash et al [21] introduced a ranking method for both trapezoidal intuitionistic fuzzy numbers and triangular intuitionistic fuzzy numbers using the centroid concept and showed the proposed method is flexible and effective.…”

“…Li [13] provides ratio ranking method for TIFNs and cut sets of intuitionistic trapezoidal fuzzy numbers. Li et al [14] introduced a ranking method of triangular intuitionistic fuzzy numbers that depend on value index and ambiguity index for solving multi criteria decision-making problems. Liang et al [15] proposed a ranking method based on the expected values, the score function and the accuracy function of triangular intuitionistic fuzzy number.…”

Multivariate Least Squares Regression using Interval-Valued Fuzzy Data and based on Extended Yao-Wu Signed Distance

“…This distance is an extended version of the Yao-Wu signed distance 46 . It should be mentioned that the distance between IVF sets introduced by some other authors, for instance, Atanassov 31 , Grzegorzewski 43 , Hung and Yang 38 , Guha and Chakraborty 44 and Li et al 47 .…”

A Note on Solving a Fully Intuitionistic Fuzzy Linear Programming Problem based on Sign Distance

“…Further, since these problems of intuitionistic fuzzy optimization contain the imprecise parameters as intuitionistic fuzzy numbers, their quantitative comparison need the ranking methods. There are several ranking methods for intuitionistic fuzzy numbers and are available in literature such as Szmidt and Kacprzyk [16], Wang and Xin [17], Nayagam et at [18], [20], Li [6], Li Nan, Zhang [19], Wei and Tang [21], Nehi [22], De and Das [23]. A distance based ranking of intuitionistic fuzzy numbers was developed by Guha and Chakrborty [25], Esmailzadeh [26], Zhang and Xu [24].…”