Fuzzy relations and fuzzy groups |
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| Authors: | Prabir Bhattacharya N.P. Mukherjee |
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| Affiliation: | Department of Mathematics, Kuwait University, P.O. Box 5969, Kuwait;School of Computer & System Sciences, Jawaharlal Nehru University, New Delhi 110 067, India |
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| Abstract: | Given a group S, we consider fuzzy relations on S, that is, maps from S × S into [0,1]. Of particular interest is to investigate conditions under which the fuzzy relation becomes a fuzzy subgroup on S × S. We prove that if σ is a fuzzy subset of S and μσ is the strongest fuzzy relation on S that is a fuzzy relation on σ, then μσ is a fuzzy subgroup if and only if σ is a fuzzy subgroup. A number of other results are obtained about the interrelationships between fuzzy relations on S (including the weakest fuzzy relation) and fuzzy subgroups on S × S. |
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