Smooth subgroups and smooth homomorphisms
type: Item
instance of: scholarly article
title: Smooth subgroups and smooth homomorphisms
zbMATH Open document ID: 0977.20059
DOI: 10.1016/S0165-0114(98)00392-3
author: Mustafa Demirci
published in: Fuzzy Sets and Systems
publication date: 2001-10-11T00:00:00Z
review text: This review concerns also the preceding item Zbl 0977.20058. The papers use fuzzy equality relations [cf. e.g. \textit{M. Wygralak}, Fuzzy Sets Syst. 10, 157-168 (1983; Zbl 0517.94025); \textit{M. Demirci}, Fuzzy Sets Syst. 106, No. 2, 239-246 (1999; Zbl 0934.03067)] in a generalization of fuzzy algebra structures. It is a new version of the author's paper [J. Math. Anal. Appl. 230, No. 1, 142-156 (1999; Zbl 0949.20050)] with weakened conditions (in the axioms and results) in the following manner: ``\(\mu>0\)'' instead of ``\(\mu =1\)''; ``\(\mu>0\Rightarrow\nu>0\)'' instead of ``\(\mu\leq\nu\)''. Namely ``smooth'' \(\equiv\) ``weakly vague''. However, the concept introduced here of smooth binary operations is quite different from that known from the papers by \textit{G. Mayor, J. Torrens} [Int. J. Intell. Syst. 8, No. 7, 771-778 (1993; Zbl 0785.68087)] and \textit{J. Fodor} [IEEE Trans. Fuzzy Syst. 8, No. 6, 791-795 (2000)].
Mathematics Subject Classification ID: 20N25
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 1563549
zbMATH Keywords: fuzzy relations
zbMATH Keywords: fuzzy functions
zbMATH Keywords: group axioms
zbMATH Keywords: group homomorphisms
reviewed by: Józef Drewniak
MaRDI profile type: Publication
cites work: Fuzzy functions and their fundamental properties
cites work: Smooth groups
cites work: Q4044675
full work available at URL: s0165-0114(98)00392-3
OpenAlex ID: W2066763967
description: scientific article; zbMATH DE number 1563549