Remarks on the lattices of fuzzy subsets of a groupoid |
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Authors: | I Bonjak R Madarsz |
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Institution: | aDepartment of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad, Serbia |
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Abstract: | In this paper we give a necessary and sufficient condition for a groupoid D such that the sup-min product is distributive over arbitrary intersection of fuzzy subsets of D, and correct some results from the paper S. Ray, The lattice of all idempotent fuzzy subsets of a groupoid, Fuzzy Sets and Systems 96 (1998) 239–245]. Also, we prove that the set of all idempotent fuzzy sets forms a complete lattice, which is a complete join-sublattice of the lattice of all fuzzy subgroupoids. This result extends the corresponding result from the above mentioned paper. |
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Keywords: | Algebra Groupoid Distributivity Idempotent fuzzy subset Lattice of fuzzy subsets |
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