On fuzzification of some concepts of graphs
type: Item
instance of: scholarly article
title: On fuzzification of some concepts of graphs
zbMATH Open document ID: 0934.05099
DOI: 10.1016/S0165-0114(97)00064-X
author: Assia Alaoui
published in: Fuzzy Sets and Systems
publication date: 2000-04-10T00:00:00Z
review text: The author discusses certain fuzzy sets which generalize the concepts of internally stable set (also known as independent set), externally stable set (also known as dominating set), not externally dominated set (which means a set of vertices such that there is no arc from outside it into it) and kernel. The structure of the fuzzy analogous is studied and it is shown that they are characterized as solutions of certain mathematical programming problems. In some particular cases an exhaustive description of the investigated sets is obtained. The paper is remarkably self-contained. Erratum: On page 366, line 9, \(y\in A\) should be \(y\not\in A\).
reviewed by: Siegfried J. Gottwald
Mathematics Subject Classification ID: 05C69
Mathematics Subject Classification ID: 05C99
zbMATH DE Number: 1340703
zbMATH Keywords: fuzzy sets
zbMATH Keywords: independent set
zbMATH Keywords: dominating set
zbMATH Keywords: programming problems
MaRDI profile type: Publication
cites work: Axiomatic approach to implication for approximate reasoning with fuzzy logic
cites work: Fuzzy power sets and fuzzy implication operators
cites work: Q5617548
cites work: Q5672929
cites work: Q3351098
cites work: Q3848223
cites work: Weighted minimum and maximum operations in fuzzy set theory
cites work: Q4315286
cites work: Fixed points and generators of fuzzy relations
cites work: Q4315285
cites work: Q3779949
cites work: Q5615362
cites work: Decision-making with a fuzzy preference relation
cites work: On formalization of a general fuzzy mathematical problem
cites work: Solutions of irreflexive relations
cites work: Q4138414
cites work: Subsolutions and the Supercore of Cooperative Games
cites work: Q5650538
cites work: Q4841242
cites work: Q5543332
cites work: Q5528483
cites work: Eigen fuzzy sets and fuzzy relations
cites work: Q4041054
cites work: On Kernels of Graphs and Solutions of Games: A Synopsis Based on Relations and Fixpoints
cites work: Fuzzification of set inclusion: Theory and applications
cites work: A lattice-theoretical fixpoint theorem and its applications
cites work: Q5844986
cites work: Q4076804
cites work: Fuzzy sets
full work available at URL: s0165-0114(97)00064-x
OpenAlex ID: W1977339532
Recommended article: Q5268977
Recommended article: Certain fuzzy graph structures
Recommended article: Fuzzy graphs and fuzzy hypergraphs
Recommended article: Q3224717
Recommended article: Fuzzy graph theory
Recommended article: Fuzzy morphisms between graphs
Recommended article: Q3466526
Recommended article: Q4929832
Recommended article: Q4519737
description: scientific article; zbMATH DE number 1340703