Relationship between entropy and subsethood measure for hesitant fuzzy sets

DOI: 10.5176/2251-1938_ORS18.37

Authors: Jin Han Park, Min Jee Kim, Jong Jin Seo,Young Chel Kwun, Nam Ju Kim, Ja Hong Koo

Abstract:

The purpose of this paper is to establish a unified formulation of subsethood, entropy, and similarity for hesitant fuzzy elements. We present an axiomatic skeleton for subsethood measures in the hesitant fuzzy setting, in order to subsethood to reduce an entropy measure. Moreover, the entropy-subsethood theorem in the hesitant fuzzy setting is stated and algebraically proved, which generalize the works of Kosko [Fuzzy entropy and conditioning, Inform. Sci. 40 (1986) 165-174] for fuzzy sets. Finally, we investigate the relationship between hesitant fuzzy subsethood and hesitant similarity measures.

Keywords: Hesitant fuzzy sets; subsethood measure; entropy; similarity measure.