Some constructions of the join of fuzzy subgroups and certain lattices of fuzzy subgroups with sup property

  • Authors:

  • Naseem Ajmal;Aparna Jain

  • Affiliations:

  • Department of Mathematics, Zakir Hussain College, University of Delhi, J.L. Nehru Marg, New Delhi, India;Department of Mathematics, Shivaji College, University of Delhi, Ring Road, Raja Garden, New Delhi, India

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2009

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Abstract

In this paper, some new lattices of fuzzy substructures are constructed. For a given fuzzy set @m in a group G, a fuzzy subgroup S(@m) generated by @m is defined which helps to establish that the set L"s 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 L"s"""t,L"s"""n,L"s"""n"""""""t, etc. are also obtained. The notion of infimum is used to construct a fuzzy subgroup i(@m) generated by a given fuzzy set @m, in contrast to the usual practice of using supremum. In the process a new fuzzy subgroup i(@m)^* is defined which we shall call a shadow fuzzy subgroup of @m. It is established that if @m has inf property, then i(@m)^* also has this property.