Some constructions of the join of fuzzy subgroups and certain lattices of fuzzy subgroups with sup property |
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Authors: | Naseem Ajmal |
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Affiliation: | a Department of Mathematics, Zakir Hussain College, University of Delhi, J.L. Nehru Marg, New Delhi, India b Department of Mathematics, Shivaji College, University of Delhi, Ring Road, Raja Garden, New Delhi, India |
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Abstract: | In this paper, some new lattices of fuzzy substructures are constructed. For a given fuzzy set μ in a group G, a fuzzy subgroup S(μ) generated by μ is defined which helps to establish that the set Ls of all fuzzy subgroups with sup property constitutes a lattice. Consequently, many other sublattices of the lattice L of all fuzzy subgroups of G like , etc. are also obtained. The notion of infimum is used to construct a fuzzy subgroup i(μ) generated by a given fuzzy set μ, in contrast to the usual practice of using supremum. In the process a new fuzzy subgroup i(μ)∗ is defined which we shall call a shadow fuzzy subgroup of μ. It is established that if μ has inf property, then i(μ)∗ also has this property. |
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Keywords: | Fuzzy subgroup Generated fuzzy subgroup sup property inf property Lattice Shadow fuzzy subgroup |
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