Direct products of bounded fuzzy lattices realized by triangular norm operators without zero divisors

In this note we continue the work of Chon, as well as Mezzomo, Bedregal, and Santiago, by studying direct products of bounded fuzzy lattices arising from fuzzy partially ordered sets. Chon proved that fuzzy lattices are closed under taking direct products defined using the minimum triangular norm operator. Mezzomo, Bedregal, and Santiago extended Chon's result to the case of bounded fuzzy lattices under the same minimum triangular norm product construction. The primary contribution of this study is to strengthen their result by showing that bounded fuzzy lattices are closed under a much more general construction of direct products; namely direct products that are defined using triangular norm operators without zero divisors. Immediate consequences of this result are then investigated within distributive and modular fuzzy lattices

Fuzzy modularity and fuzzy complements in fuzzy lattices

In this paper, we study the concept of fuzzy modularity in fuzzy lattices. We also define a fuzzy Birkhoff lattice and study fuzzy complements in fuzzy lattices. We prove that the notions of a right and a left complement coincide in a fuzzy lattice.Emerging Sources Citation Index (ESCI)MathScinetScopu

Heyting Almost Distributive fuzzy Lattices

In this paper, we introduce the concept of Heyting almost distributive fuzzy lattices (HADFL) using the concepts of Heyting almost distributive lattices (HADL), almost distributive fuzzy lattices, fuzzy partial order relation and fuzzy Heyting algebra. Using the properties of fuzzy Heyting algebra, we also give a necessary and sufficient condition for an HADFL to be fuzzy Heyting algebra (FHA)

‘Del’ relation and parallelism in fuzzy lattices

The notions of ‘del’ relation, a neutral element and parallelism from lattice theory are introduced in a fuzzy lattice and their properties are obtained.Publisher's Versio

Fuzzy Lattice Reasoning for Pattern Classification Using a New Positive Valuation Function

This paper describes an enhancement of fuzzy lattice reasoning (FLR) classifier for pattern classification based on a positive valuation function. Fuzzy lattice reasoning (FLR) was described lately as a lattice data domain extension of fuzzy ARTMAP neural classifier based on a lattice inclusion measure function. In this work, we improve the performance of FLR classifier by defining a new nonlinear positive valuation function. As a consequence, the modified algorithm achieves better classification results. The effectiveness of the modified FLR is demonstrated by examples on several well-known pattern recognition benchmarks

Fuzzy Amicable sets of an Almost Distributive Fuzzy Lattice

In this paper, we introduce the concept of Fuzzy Amicable sets, we prove some properties of Fuzzy Amicable set, too. We also prove that two Fuzzy compatible elements of an Almost distributive Fuzzy Lattice (ADFL) are equal if and only if their corresponding unique Fuzzy amicable elements are equal. We define the homomorphism of two Almost Distributive Fuzzy lattices (ADFL) and finally we observe that any two Fuzzy amicable set in an Almost Distributive Fuzzy Lattice (ADFL) are isomorphic