in this note by considering a complete lattice l, we define thenotion of an l-fuzzy hyperrelation on a given non-empty set x. then wedefine the concepts of (pom)l-fuzzy graph, hypergraph and subhypergroupand obtain some related results. in particular we construct the categories ofthe above mentioned notions, and give a (full and faithful) functor form thecategory of (pom)l-fuzzy subhypergroups ...

We provide fuzzy quasi-metric versions of a fixed point theorem ofGregori and Sapena for fuzzy contractive mappings in G-complete fuzzy metricspaces and apply the results to obtain fixed points for contractive mappingsin the domain of words.

The concepts of L-fuzzy ideal generated by a L-fuzzy subset, L-fuzzy prime and completely prime ideal where L is a complete lattice are considered and some results are proved

The notion of absorbent ordered filters in implicative semigroupsis introduced, and its fuzzification is considered. Relations among (fuzzy) orderedfilters, (fuzzy) absorbent ordered filters, and (fuzzy) positive implicativeordered filters are stated. The extensionproperty for (fuzzy) absorbent orderedfilters is established. Conditions for (fuzzy) ordered filters to be (fuzzy)absorbent ordered ...

Given a reference lattice (X,⊑), we define fuzzy intervals to be the fuzzy sets such that their pcuts are crisp closed intervals of (X,⊑). We show that: given a complete lattice (X,⊑) the collection of its fuzzy intervals is a complete lattice. Furthermore we show that: if (X,⊑) is completely distributive then the lattice of its fuzzy intervals is distributive.

In this paper we investigate various properties of equivalence classes of fuzzy equivalence relations over a complete residuated lattice. We give certain characterizations of fuzzy semipartitions and fuzzy partitions over a complete residuated lattice, as well as over a linearly ordered complete Heyting algebra. In the latter case, for a fuzzy equivalence relation over a linearly ordered comple...