\((\alpha,\beta)\)-fuzzy mappings
type: Item
instance of: scholarly article
title: \((\alpha,\beta)\)-fuzzy mappings
zbMATH Open document ID: 0797.04007
DOI: 10.1016/0165-0114(93)90188-N
author: Sandeep Kumar Bhakat
author: Phullendu Das
published in: Fuzzy Sets and Systems
publication date: 1994-10-17T00:00:00Z
review text: It is well known that relations, mappings, cardinal numbers and ordinal numbers are the quintessence of set theory. Analogously, these problems, especially fuzzy mappings, are the basic ones followed with interest in fuzzy set theory. Dubois and Prade gave a definition for fuzzy mappings and Liu Yingming gave the concept of fuzzy points. Based on these results, the authors put forward a concept for fuzzy mapping, \((\alpha,\beta)\)-fuzzy mappings, which has its substance by means of the cut sets of fuzzy sets. (It is worth noting that the reviewer has also given a definition of fuzzy mappings by using cut sets [the reviewer, \textit{Luo Chengzhong} and \textit{Wang Peizhuang}, ibid. 55, No. 1, 61-77 (1993; Zbl 0786.04005)]. Then the authors of this paper discuss some properties from their definition, for instance, \((\alpha,\beta)\)-fuzzy injectivity, \((\alpha,\beta)\)-fuzzy surjectivity and an application to fuzzy algebra.
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 496163
zbMATH Keywords: quasi-coincidence
zbMATH Keywords: fuzzy injectivity
zbMATH Keywords: fuzzy surjectivity
zbMATH Keywords: fuzzy set
zbMATH Keywords: fuzzy mappings
zbMATH Keywords: fuzzy points
zbMATH Keywords: cut sets
zbMATH Keywords: fuzzy algebra
reviewed by: Hongxing Li
MaRDI profile type: Publication
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cites work: Q4091811
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full work available at URL: 0165-0114(93)90188-n
OpenAlex ID: W282626618
description: scientific article; zbMATH DE number 496163