-fuzzy lattices: an introduction

A Novel Definition of L‐Fuzzy Lattice Based on Fuzzy Set

“…In [1], the author gave an L -valued fuzzy lattice. From the following analysis we can see that L -valued fuzzy lattice is a special case of bifuzzy lattices in fact.…”

“…The concept of fuzzy lattice was also introduced by Tepav$\stackrel{normal˘}{\text{c}}$ević and Trajkovski [1]. But the authors in [1] defined an L -fuzzy lattice based on a fuzzy set of a crisp lattice, so the scope is very limited, and they gave its characterizations by only one kind of its cut sets. To overcome this shortcoming, in this paper we try to present a new definition of an L -fuzzy lattice in an L -fuzzy subset of a general set in terms of an L -poset.…”

Lattice-valued fuzzy frames

“…In this section the author aims to use the definition of L-fuzzy lattice [17] to define the concept of lattice-valued fuzzy frame (or L-fuzzy sub-frame in this paper) of a given ordinary frame. is an L-fuzzy semiframe, since all p-cuts (p 2 L) are sub-semiframes of P(A), which are given as follows:…”

“…This approach not only gives new description of previously known type of sober spaces, but it also leads naturally to a new type of sober spaces not previously documented in the literature. In this paper the author aims to use the definition of L-fuzzy lattice [17] to define the concept of L-fuzzy sub-frames of a given ordinary frame related to traditional frames analogously to how L-fuzzy (resp. L-fuzzifying) topological spaces related to L-topological spaces (resp.…”

Some remarks on the lattice of fuzzy intervals

“…A fuzzy lattice is a fuzzy set such that its cuts are sublattices of a ''reference lattice" (X, v). Relatively little has been published on fuzzy lattices; Yuan and Wu introduced the concept [42] and Ajmal has studied it in greater detail [1][2][3]; Swamy and Raju [39] and, more recently, Tepavcevska and Trajkovski [41] have studied L-fuzzy lattices. Also fuzzy hyperalgebras have been studied in the past [10][11][12]14,15], especially fuzzy hypergroups [13,16,48,49], fuzzy hyperrings [47] etc.…”