Abstract
The features of fuzzy lattices valued by lattices can be observed in the light of more general results from fuzzy algebraic and fuzzy relational structures. By approaching directly the problem of defining the notion of a fuzzy lattice, several directions can be taken. In this paper we present an idea and two of its variations to define what is referred to as L M fuzzy lattices. The idea is to fuzzify the membership functions of elements of the carrier of an ordinary, crisp, lattice. L M1 fuzzy lattices require for the cuts of the structure to be sublattices of the lattice whose carrier’s membership function has been the subject of fuzzification. More generally, L M2 fuzzy lattices require that the cuts are lattices themselves, not insisting on being substructures of the crisp lattice. The structure of the famines of cuts in both cases are presented, as well as an algorithm to construct L M fuzzy lattice with a given set of cuts. Alternative approaches to defining fuzzy lattices are discussed at the end of the paper.
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Trajkovski, G., Čukić, B. (1999). On Two Types of L M Fuzzy Lattices. In: Reusch, B. (eds) Computational Intelligence. Fuzzy Days 1999. Lecture Notes in Computer Science, vol 1625. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48774-3_32
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DOI: https://doi.org/10.1007/3-540-48774-3_32
Publisher Name: Springer, Berlin, Heidelberg
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