Ranking of fuzzy numbers by a new metric

Abstract

In this paper, a new approach for comparison among fuzzy numbers based on new metric distance (D TM ) is proposed. All reasonable properties of ranking function are proved. At first, the distance on the interval numbers based on convex hall of endpoints is proposed. The existing distance measures for interval numbers, (Bardossy and Duckstein in Fuzzy rule-based modeling with applications to geophysical, biological and engineering systems. Diamond and Tanaka Fuzzy regression analysis. In: Slowinski R (ed) Fuzzy sets in decision analysis, operations research and statistics. Kluwer, Boston, pp 349-387, 1998) do not satisfy the properties of a metric distance, while the proposed distance does. It is extended to fuzzy numbers and its properties are proved in detail. Finally, we compare the proposed definition with some of the known ones.

Ranking of Intuitionistic Fuzzy Numbers by New Distance Measure

“…Much identical definition was followed by Allahviranloo and Firozja [1], but application of their proposed distance measure d (p) T M I to intuitionistic fuzzy setting would make the scenario more complex. To make this distance measure more convinient to be applicable in case of intuitionistic fuzzy setting,the authors have defined it in a much more easier way.…”

“…Let a, b, c, d, e, z are real numbers. Propositions given by Allahviranloo and Firozja [1] can be reformulated as follows:…”

Ranking of intuitionistic fuzzy numbers by new distance measure

“…Much identical definition was followed by Allahviranloo and Firozja [1], but application of their proposed distance measure d…”

Comparison Of Fuzzy Numbers With Ranking Fuzzy And Real Number

“…defined the maximal and minimal reference sets of fuzzy numbers to measure LR deviation degree and then the transfer coecient was defined to measure the relative variation of LR deviation degree of fuzzy number and then proposed the ranking method based on the LR deviation degree and relative variation of fuzzy numbers. In [20], Asady proposed a revised method of ranking LR fuzzy number based on deviation degree with Wang , s method. In [21], Wang and Luo presented a ranking approach for fuzzy numbers called area ranking based on positive and negative ideal points, which defined two indices for the purpose of ranking.…”