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Interval-valued relations and their application to category theory

한상현|백종일|허걸|정민석
기초자연과학연구소 (The Natural Science Institute Wonkwang University)|2022.12|ANNALS OF FUZZY MATHEMATICS AND INFORMATICS|제24권 제3호|pp. 281-299|DOI 10.30948/afmi.2022.24.3.281

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키워드

Interval-valued setInterval-valued (vanishing) pointInterval-valued relationInterval-valued partitionInterval-valued relational spaceTopological (cotopological) categoryCartesian closed categoryTopological universe

초록

In this paper, we define an interval-valued relation and an interval-valued partition, and study some of their properties. Also we define interval-valued relational spaces and obtain some properties of the category (denoted by IVRel), which is class of interval-valued relational spaces and the morphisms between them. Furthermore, we prove that the full subcategory IVRelR of the category IVRel is a topological universe over Set}.

Abstract

In this paper, we define an interval-valued relation and an interval-valued partition, and study some of their properties. Also we define interval-valued relational spaces and obtain some properties of the category (denoted by IVRel), which is class of interval-valued relational spaces and the morphisms between them. Furthermore, we prove that the full subcategory IVRelR of the category IVRel is a topological universe over Set}.

참고문헌 (21)

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  21. H. Herrlich, "Category Theory" (1973), Allyn and Bacon

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