A natural interpretation of fuzzy sets and fuzzy relations
type: Item
instance of: scholarly article
title: A natural interpretation of fuzzy sets and fuzzy relations
zbMATH Open document ID: 1007.03047
DOI: 10.1016/S0165-0114(01)00135-X
author: Mamoru Shimoda
published in: Fuzzy Sets and Systems
publication date: 2002-09-30T00:00:00Z
review text: The author presents a new interpretation of fuzzy sets and fuzzy relations (such as reflexive, symmetric, transitive, etc.) in a cumulative Heyting-valued model for intuitionistic set theory. This interpretation is claimed to be natural, since the definitions and basic properties are almost the same as those concerning crisp sets. The canonical embedding of the class of all sets into the model becomes one of the key issues. In view of this, the author distinguishes between generalized fuzzy sets, fuzzy subsets of crisp sets, and membership functions of fuzzy sets on crisp sets.
reviewed by: Ilya S. Molchanov
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 1809952
zbMATH Keywords: fuzzy sets
zbMATH Keywords: fuzzy relations
zbMATH Keywords: Heyting-valued model
zbMATH Keywords: intuitionistic set theory
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1809952