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

Abstract

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.

An extension of TOPSIS based on linguistic terms in triangular intuitionistic fuzzy structure

“…Cri3 Cri4 Cri5 Alt 1 (5.67,7.67,9.33), (5,7,8.67), (5.67,7.67,9), (8.33,9.67,10), (3,5,7), (5,7.67,9.67) (4.17,7,9.17) (4.67,7.67,9.33) (7.33,9.67,10) (2,5,8) Alt 2 (6.33,8.33,9.67), (9,10,10), (8.33,9.67,10), (9,10,10), (7,8.67,9.67), (5.5,8.33,9.83) (8,10,10) (7.33,9.67,10) (8,10,10) (6.17.8.67,9.83) Alt 3 (6.33,8,9), (7,8.67,9.67), (7,8.67,9.67), (7,8.67,9.67), (6.33,8.33,9.67), (5.33,8,9.33) (6.17.8.67,9.83) (6.17.8.67,9.83) (6.17.8.67,9.83) (5.5,8.33,9.83) Weight (0.7,0.867,0.967) (0.9,1,1) (0.767,0.933,1) (0.9,1,1) (0.433,0.633,0.833) (0.617,0.867,0.983) (0.8,1,1) (0.67,0.933,1) (0.8,1,1) (0.367,0.633,0.9) Cri 5 Alt1 (0.59,0.79,0.96), (0.5,0.7,0.86), (0.57,0.77,0.9), (0.83,0.97,1), (0.31,0.52,0.72), (0.51,0.65,1) (0.45,0.59,1) (0.5,0.6,1) (0.61,0.64,0.84) (0.25,0.4,1) Alt2 (0.65,0.86,1), (0.9,1,1), (0.83,0.97,1), (0.9,1,1), (0.72,0.89,1), (0.5,0.6,0.9) (0.41,0.41,0.52) (0.46,0.48,0.63) (0.61,0.61,0.77) (0.2,0.23,0.32) Alt3 (0.65,0.83,0.93), (0.7,0.87,0.97), (0.7,0.87,0.97), (0.7,0.87,0.97), (0.65,0.86,1), (0.53,0.62,0.93) (0.42,0.48,0.67) (0.47,0.54,0.76) (0.62,0.71,1) (0.2,0.24,0.36) Step 6: The weighted normalized IF decision matrix can be obtained by (3.6) as shown in Table 7.…”

“…Chu et al [7] has overcome with improvement in Chen's model. Atalik et al ([4], [3]) proposed some rankings among triangular intuitionistic fuzzy numbrers based on gerogonne point and incircle of triangluar intuitionistic fuzzy number. Ghaemi et al [12] applied TOPSIS technique on type-2 fuzzy set.…”

Ranking Triangular Intuitionistic Fuzzy Numbers: A Nagel Point Approach and Applications in Multi-Criteria Decision Making

“…A new ranking based on considering a fuzzy origin and measures distance of each intuitionistic fuzzy number from fuzzy origin in [3] 2017. The method based on the incircle of the membership function and non-membership function of TIFN uses lexicographical order to rank intuitionistic fuzzy numbers was investigated by Atalik et.al in [4] in 2020. A new type-2 intuitionistic exponential triangular fuzzy number was introduced in [5] and some of properties and theorems of this type of fuzzy number with graphical representations have been studied and some examples are given to show the effectiveness of the proposed method.…”

A new ranking method for trapezoidal intuitionistic fuzzy numbers and its application to multi-criteria decision making

“…Rezvani [9] proposed a ranking method according to a crisp value associated with an intuitionistic fuzzy number related to the spread value concept defined. In the following period, many papers addressing this research topic were published ( [19], [16], [3], [24], [26], [1], [13]).…”