Counterintuitive Test Problems for Transformed Fuzzy Number-Based Similarity Measures between Intuitionistic Fuzzy Sets

Abstract

This paper analyzes the counterintuitive behaviors of transformed fuzzy number (FN)- based similarity measures between intuitionistic fuzzy sets (IFSs). Among these transformed FN-based similarity measures, Chen and Chang’s similarity measure (2015) is a novel one. An algorithm of computing Chen and Chang’s similarity measure is proposed. We analyze the counterintuitive behaviors of Chen and Chang’s similarity measure for seven general test problems and four test problems with three inclusive IFSs. The results indicate that there are six counterintuitive test problems for Chen and Chang’s similarity measure.

Representations of a Comparison Measure between Two Fuzzy Sets

“…A comparison measure calculates the degree of equality or inequality between two compared FSs. Some related definitions such as similarity, similitude, proximity or resemblance were proposed for the equality measures [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], as well as some other dual definitions such as dissimilarity, dissimilitude, divergence or distance for the inequality measures [6,9,13,[18][19][20][21][22][23]. The inequality measures have received much less attention in the literature.…”

“…The degree of comparison measure is an important tool for cluster analysis [8], decision-making [7,14,21,22], e-waste [2,17,20], image processing [10], medical diagnosis [13], pattern recognition [3,4,9,12] and service quality [11,18]. Recently, many papers [5,9,10,12,15,16,18,[20][21][22] have been dedicated to the comparison measures, and research on this area is still carried out in the literature.…”