A Theory of Lattice Interval Valued Fuzzy Sets and Fuzzy Maps Between Different Lattice Interval Valued Fuzzy Sets
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Abstract
The aim of this paper is 1. to introduce the notions of, an interval valued f-set with truth values in a complete lattice of closed intervals or a simply a cloci over an arbitrary a complete lattice ,L called an L-interval valued f-set or simply an L-ivf-set, an L-interval valued f-subset and to introduce an interval valued f-map between an L-interval valued f-set and an M-interval valued f-set where the complete lattice L may possibly be different from the complete lattice ,M an M-interval valued f-image of an L-interval valued f-subset under an interval valued f-map and an L-interval valued f-inverse image of an M-interval valued f-subset under an interval valued f-map, and 2. to study the standard (lattice) algebraic properties of, all L-interval valued f-subsets of an L-interval valued f-set, all M-interval valued f-images of L-interval valued f-subsets under an interval valued f-map and of all L-interval valued f-inverse images of M-interval valued f-subsets under an interval valued f-map, generalizing the Theory of f-Sets. Keywords: Fuzzy Set, Fuzzy Image, Fuzzy Inverse Image, Complete Lattice of Closed Intervals, L-Interval Valued Fuzzy Set
Subjclass: Primary 94D05; Secondary 04A72, 03E72, 03B50, 20N25, 54A40
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