Particle lattices and fuzzy particle lattices
type: Item
instance of: scholarly article
title: Particle lattices and fuzzy particle lattices
zbMATH Open document ID: 0679.06005
DOI: 10.1016/0165-0114(89)90208-X
published in: Fuzzy Sets and Systems
publication date: 1989-01-01T00:00:00Z
review text: Let L be a lattice with at least two elements. A non-zero element p in L is called irreducible if \(p\leq B\vee C\) implies \(p\leq B\) or \(p\leq C\). In the paper under review, irreducible elements are called particles. The author considers the lattices generated by particles. The paper establishes representation theorems for such lattices; several relations with well-known lattice theoretic concepts are also given.
Mathematics Subject Classification ID: 06D99
Mathematics Subject Classification ID: 06D10
Mathematics Subject Classification ID: 06B15
zbMATH DE Number: 4112663
zbMATH Keywords: closed set-lattice
zbMATH Keywords: involution
zbMATH Keywords: fuzzy lattice
zbMATH Keywords: irreducible elements
zbMATH Keywords: representation theorems
author: Xiao-Dong Zhao
reviewed by: Yingming Liu
MaRDI profile type: Publication
cites work: Products of fuzzy topological spaces
cites work: Normality in fuzzy topological spaces
cites work: Uniformities on fuzzy topological spaces
cites work: Separation axioms in fuzzy topological spaces
cites work: Q3684804
cites work: Order-homomorphisms on fuzzes
cites work: Fuzzy addition in the L-fuzzy real line
cites work: A categorical accommodation of various notions of fuzzy topology
cites work: Compactness in fuzzy topological spaces
cites work: Local property, normality, and uniformity in fuzzy topological spaces
cites work: Connectedness on fuzzy topological spaces
cites work: Representation theorem of fuzzy lattices and its applications in fuzzy topology
cites work: Q3791853
cites work: On fuzzy topological spaces
cites work: Fuzzy topology. I: Neighborhood structure of a fuzzy point and Moore-Smith convergence
cites work: Fuzzy topology. II: Product and quotient spaces
cites work: Fuzzy path and fuzzy connectedness
cites work: On induced fuzzy topological spaces
cites work: A comparison of different compactness notions in fuzzy topological spaces
cites work: Fuzzy points and local properties of fuzzy topology
cites work: L-fuzzy sets
cites work: Fuzzy topological spaces
cites work: Q3898534
cites work: Q5567903
full work available at URL: 0165-0114(89)90208-x
OpenAlex ID: W2077949285
description: scientific article; zbMATH DE number 4112663