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The category of hesitant $H$-fuzzy sets

전영배|이정곤|허걸|김준희|임평기
기초자연과학연구소 (The Natural Science Institute Wonkwang University)|2019.08|ANNALS OF FUZZY MATHEMATICS AND INFORMATICS|제18권 제1호|pp. 57-74|DOI 10.30948/afmi.2019.18.1.57

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참고문헌

키워드

Cartesian closed categoryTopological universeHesitant $H$-fuzzy spaceTopological category

초록

We redefine the hesitant fuzzy empty set, the hesitant fuzzy whole set, the intersection and the union of two hesitant fuzzy sets, and prove that the family $HS(X)$ of all hesitant fuzzy sets in a set $X$ is a Boolean algebra. Next, we introduce the category ${\bf HSet}(H)$ consisting of hesitant $H$-fuzzy spaces and preserving mappings between them and study the category ${\bf HSet}(H)$ in the sense of a topological universe and prove that it is Cartesian closed over $\bf Set$, where $\bf Set$ denotes the category consisting of ordinary sets and ordinary mappings between them.

Abstract

We redefine the hesitant fuzzy empty set, the hesitant fuzzy whole set, the intersection and the union of two hesitant fuzzy sets, and prove that the family $HS(X)$ of all hesitant fuzzy sets in a set $X$ is a Boolean algebra. Next, we introduce the category ${\bf HSet}(H)$ consisting of hesitant $H$-fuzzy spaces and preserving mappings between them and study the category ${\bf HSet}(H)$ in the sense of a topological universe and prove that it is Cartesian closed over $\bf Set$, where $\bf Set$ denotes the category consisting of ordinary sets and ordinary mappings between them.

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