Fuzzy generators and fuzzy direct sums of Abelian groups

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

Research output: Contribution to journalArticle

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

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All Science Journal Classification (ASJC) codes

  • Logic
  • Artificial Intelligence

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