Fuzzy generators and fuzzy direct sums of Abelian groups

Davender S. Malik, John N. Mordeson, P. S. Nair

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We define the concept of a fuzzy generating set and describe the fuzzy subgroup which it generates. We introduce the notion of a minimal fuzzy generating set and we show that any fuzzy subgroup whose support is cyclic has a minimal fuzzy generating set. We show by examples that this result breaks down if the support of A is a direct sum of two or more cyclic groups. These examples also show that a fuzzy subgroup of a group G need not be a fuzzy direct sum of subgroups whose supports are cyclic even if G is a direct sum of cyclic groups. We show that every fuzzy subgroup is a fuzzy direct sum of p-primary fuzzy subgroups.

Original languageEnglish
Pages (from-to)193-199
Number of pages7
JournalFuzzy Sets and Systems
Volume50
Issue number2
DOIs
StatePublished - Sep 10 1992

Fingerprint

Fuzzy Subgroup
Fuzzy sets
Direct Sum
Abelian group
Generator
Generating Set
Fuzzy Sets
Cyclic group
Breakdown
Subgroup

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Computer Science Applications
  • Computer Vision and Pattern Recognition
  • Information Systems and Management
  • Statistics, Probability and Uncertainty
  • Electrical and Electronic Engineering
  • Statistics and Probability

Cite this

Fuzzy generators and fuzzy direct sums of Abelian groups. / Malik, Davender S.; Mordeson, John N.; Nair, P. S.

In: Fuzzy Sets and Systems, Vol. 50, No. 2, 10.09.1992, p. 193-199.

Research output: Contribution to journalArticle

Malik, Davender S. ; Mordeson, John N. ; Nair, P. S. / Fuzzy generators and fuzzy direct sums of Abelian groups. In: Fuzzy Sets and Systems. 1992 ; Vol. 50, No. 2. pp. 193-199.
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