Order-homomorphisms on fuzzes
type: Item
instance of: scholarly article
title: Order-homomorphisms on fuzzes
zbMATH Open document ID: 0553.06015
DOI: 10.1016/0165-0114(84)90074-5
published in: Fuzzy Sets and Systems
publication date: 1984-01-01T00:00:00Z
review text: Suppose that \(L_ 1\) and \(L_ 2\) are fuzzes, i.e. completely distributive lattices with order-reserving involutions. A map \(f: L_ 1\to L_ 2\) is called an order-homomorphism if f is union-preserving and its inverse \(f^{-1}\) is involution-preserving. If the fuzzes \(L_ 1\) and \(L_ 2\) are replaced by fuzzes \(L^ X\) and \(L^ Y\) in the above definition, we get a fuzz function \(f: L^ X\to L^ Y\). In the paper under review, the author studies basic properties of order-homomorphisms. Among others, a condition for a fuzz function to be a function of Zadeh's type (i.e. a fuzz function induced by an ordinary map from X to Y) is obtained (Theorem 2.1). This result is interesting, but the requirement that \(f_ x\) satisfies \((H_ 3)\) may be omitted.
Mathematics Subject Classification ID: 06D10
Mathematics Subject Classification ID: 03E20
Mathematics Subject Classification ID: 06B15
zbMATH DE Number: 3880777
zbMATH Keywords: fuzzes
zbMATH Keywords: completely distributive lattices
zbMATH Keywords: involutions
zbMATH Keywords: order- homomorphisms
zbMATH Keywords: fuzz function
zbMATH Keywords: function of Zadeh's type
author: Guojun Wang
MaRDI profile type: Publication
full work available at URL: 0165-0114(84)90074-5
OpenAlex ID: W1972077758
cites work: Functions, equivalence relations, quotient spaces and subsets in fuzzy set theory
cites work: Uniformities on fuzzy topological spaces
cites work: Q3219439
description: scientific article; zbMATH DE number 3880777