On similarity measures between intuitionistic fuzzy sets

Abstract

In this paper, we first review several popular similarity measures between fuzzy sets and then extend those similarity measures to intuitionistic fuzzy sets. We also propose two new similarity measures between intuitionistic fuzzy sets. These similarity measures have been found to satisfy some similarity measure axioms. Several numerical experiments are performed to assess the performance of these measures. Numerical results clearly indicate these new measures to be superior in performance to the others. Finally, we apply the new measures to evaluate students' answerscripts. The experimental results show the superiority of the proposed measures for students' evaluation. C 2008 Wiley Periodicals, Inc.

Some new similarity measures for intuitionistic fuzzy values and their application in group decision making

“…The same results can be obtained using some existing similarity measures (Mitchell 2003 and a sample is given as: Obviously, the sample B belongs to the pattern 1 A by using the maximum degree of similarity. The same results can be got by some existing similarity measures (Mitchell 2003, Liang & Shi 2003, Huang & Yang 2004, 2008a, 2008b. Example 3 Assume that there are three patterns denoted with IFVs in…”

“…and a sample is given as: It seems that the sample B belongs to the pattern 2 A which is also the result obtained by using some existing similarity measures (Mitchell 2003, Liang & Shi 2003, Huang & Yang 2004, 2008a, 2008b.…”

A novel correlation coefficient of intuitionistic fuzzy sets based on the connection number of set pair analysis and its application

“…In order to compare the performance of the proposed approach with some existing approaches under the IFS environment, we conducted a comparison analysis based on the different approaches as given by the authors in [31,51,[53][54][55][56][57]. The results corresponding to these are summarized as below:…”

“…(b) If we apply the cosine similarity measure CSM (·) as proposed by Ye [53] to the considered problem (for more details, we refer to Ye [53]) then its value corresponding to each pattern is CSM (C 1 , B (f) If we apply the similarity measure S(·), as proposed by Hung and Yang [57], on the considered problem, then we get their respective measure values corresponding to each pattern is S(C 1 , B) = 0.4700, S(C 2 , B) = 0.4700 and S(C 3 , B) = 0.5100 and hence the ranking of these pattern is C 3 C 2 = C 1 . Therefore, the pattern C 3 is classifying with the pattern B.…”

“…From this analysis, it has been concluded that Al suffers from Malaria, Bob from Stomach problems, Joe from Typhoid and Ted from Viral Fever. In order to compare the performance of the proposed approach with some existing approaches under the IFS environment, we conducted a comparison analysis based on the different approaches as given by the authors in [31,51,56,57]. The results corresponding to these are summarized as below:…”