The starting point of this paper is the introduction of a new measure of inclusion of fuzzy set A in fuzzy set B. Previously used inclusion measures take values in the interval [0,1]; the inclusion measure proposed here takes values in a Boolean lattice. In other words, inclusion is viewed as an Lfuzzy valued relation between fuzzy sets. This relation is reflexive, antisymmetric and transitive,...

The starting point of this paper is the introduction of a new measure of inclusion of fuzzy set A in fuzzy set B. Previously used inclusion measures take values in the interval [0,1]; the inclusion measure proposed here takes values in a Boolean lattice. In other words, inclusion is viewed as an Lfuzzy valued relation between fuzzy sets. This relation is reflexive, antisymmetric and transitive,...

After the introduction of fuzzy set by Zadeh in 1965 [1], there have been a number of generalizations of this fundamental concept. In 1967, Goguen [2] proposed the concept of L-fuzzy set. The idea of interval valued fuzzy set is given by Zadeh in 1975 [3]. Type 2 fuzzy sets were poposed by Zadeh in [4]. Attanasove introduced intuitionistic fuzzy sets in 1986 [5]. Interval valued intuitionistic ...

In mathematical morphology (MM), images are viewed as L-fuzzy sets, where the symbol L stands for a complete lattice. In particular, fuzzy MM arises by considering L = [0, 1]. Mathematical morphology provides the theoretical basis for certain lattice computing models called morphological neural networks (MNNs) including morphological associative memories (MAMs) that are the focus of this paper....

Gupta and Ray (Fuzzy Sets and Systems 54 (1993) 191) introduced the notion of fuzzy projective planes. We show that an old theorem of Dembowski classi$es all $nite fuzzy projective planes, that the examples in Gupta and Ray (Fuzzy Sets and Systems 54 (1993) 191) arise from ordinary projective planes and have much easier descriptions that can easily be generalized, and that there exist fuzzy pro...

In this paper, we investigate the properties of join and meet preserving maps in complete residuated lattice using Zhang’s the fuzzy complete lattice which is defined by join and meet on fuzzy posets. We define L-upper (resp. L-lower) approximation operators as a generalization of fuzzy rough sets in complete residuated lattices. Moreover, we investigate the relations between L-upper (resp. L-l...

An orthogonal approach to the fuzzification of both multisets and hybrid sets is presented. In particular, we introduce L-multi-fuzzy and L-fuzzy hybrid sets, which are general enough and in spirit with the basic concepts of fuzzy set theory. In addition, we study the properties of these structures. Also, the usefulness of these structures is examined in the framework of mechanical multiset pro...