Distance and Dissimilarity Measure of Picture Fuzzy Sets

Abstract

To measure the difference of two fuzzy sets/intuitionistic sets, we can use the distance measure and dissimilarity measure between fuzzy sets. Characterization of distance/dissimilarity measure between fuzzy sets/intuitionistic fuzzy set is important as it has application in different areas: pattern recognition, image segmentation, and decision making. Picture fuzzy set is a generalization of fuzzy set and intuitionistic set, so that it have many application. In this paper, we introduce concepts: difference between PFS-sets, distance measure and dissimilarity measure between picture fuzzy sets. We also provide the formulas for determining these values.

New Dissimilarity Measures on Picture Fuzzy Sets and Applications

“…In this paper, we introduce some new dissimilarity measures on picture fuzzy sets. These new measures overcome the limitations of the previous dissimilarity measures on picture fuzzy sets in [7,34]. After that, we apply the proposed dissimilarity measures in the pattern recognition.…”

“…Definition 3. [7,34] Let U = {u 1 , u 2 , ..., u n } be a universe set. Given two picture fuzzy sets A, B ∈ P F S(U ).…”

“…The cross-entropy and similarity measures on picture fuzzy sets were studied by Wei and applied in MCDM [38,41,39,40]. As opposed to the similarity measures, the dissimilarity measures on picture fuzzy sets were first introduced by Dinh et al in 2017 [7,34]. But these dissimilarity measures have certain restrictions (detail in Example 1, Section 3).…”

A Novel Multi-Criteria Decision Making Method for Evaluating Water Reuse Applications under Uncertainty

“…Dinh et al (2015) introduced the picture fuzzy database and examples of using the picture fuzzy database. Dinh et al (2017) investigated distance measures and dissimilarity measures on picture fuzzy sets and applied them in pattern recognition. But these dissimilarity measures of Dinh et al (2017) have a restriction that is further explored in the next section.…”

“…In this paper, we propose a new dissimilarity measure of picture fuzzy sets. This measure overcomes the restriction of the four dissimilarity measures of picture fuzzy sets introduced by Dinh et al (2017). We then propose a MCDM based on the new dissimilarity measure and apply it for evaluating the water reuse applications under uncertainty.…”