Products of fuzzy subgroups

✍ Scribed by Howard Sherwood

• Publisher: Elsevier Science
• Year: 1983
• Tongue: English
• Weight: 603 KB
• Volume: 11
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(83)80070-0

✦ Synopsis

Fuzzy subgroups are different from ordinary subgroups in that one cannot tell with certainty which group elements belong and which do not. Of course this requires an appropriate modification of the closure property which takes the form of an inequality. In this paper a study of products of fuzzy subgroups is begun. Some results are expected: the product of fuzzy subgroups is a fuzzy subgroup, products with the same but permuted factors are isomorphic, and there is a natural isomorphism from any factor into the product. Functions called t-norms are used to construct products of fuzzy subgroups, different r-norms yielding different products. Since a fuzzy subgroup must satisfy an inequality (generalizing closure) and the strength of that inequality is important, some results relate the t-norm, used in forming the product, to the strength of the ensuing inequality. When can complicated fuzzy subgroups be expressed as products of simple ones? This question is addressed for fuzzy subgroups of finite abelian groups.