Goguen categories were introduced as a suitable categorical description of L-fuzzy relations, i.e., of relations taking values from an arbitrary complete Brouwerian lattice L instead of the unit interval [0, 1] of the real numbers. In this paper we want to study the algebraic structures derived from Goguen categories by replacing its second-order axiom by some weaker versions.

The goal of this paper is to introduce the notions of , -double fuzzy ideals and , -double fuzzy ideal bases where and are strictly two-sided, commutative quanta and also investigate the relationships between these two structures. Then, we construct a functor from the category of , -double fuzzy ideal spaces to the category of , -double fuzzy cotopological spaces. Furthermore, we show the exist...

The aim of this paper is to introduce monadic L-fuzzy quantifiers of the type 〈1, 1〉 and to investigate some of their semantic properties that are well-known in the generalized quantifier theory. Further, some relations between the semantic properties of generalized quantifiers are also studied for monadic L-fuzzy quantifiers. Finally, a property “to be extensional w.r.t. a given L-permutation ...

It is well known that lattice-valued rough sets are important branches of fuzzy sets. The axiomatic characterization and related topology the main research directions For L=(L,⊛), a complete co-residuated lattice (CCRL), Qiao recently defined an L-fuzzy lower approximation operator (LFLAO) on basis relation. In this article, we give further study Qiao’s LFLAO around induced L-topology. Firstly,...

Interval-valued fuzzy soft sets realize a hybrid soft computing model in a general framework. Both Molodtsov's soft sets and interval-valued fuzzy sets can be seen as special cases of interval-valued fuzzy soft sets. In this study, we first compare four different types of interval-valued fuzzy soft subsets and reveal the relations among them. Then we concentrate on investigating some nonclassic...

it is well known fact that binary relations are generalized mathematical functions. contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. some basic operations on functions such as the inverse and composition are applicable to binary relations as well. depending on the domain or range or both are fuzzy value fuzzy set, i...

in this note, we aim to present some properties of the space of all weakly fuzzy bounded linear operators, with the bag and samanta’s operator norm on felbin’s-type fuzzy normed spaces. in particular, the completeness of this space is studied. by some counterexamples, it is shown that the inverse mapping theorem and the banach-steinhaus’s theorem, are not valid for this fuzzy setting. also...

Closure (interior) operators and closure systems are important tools in many mathematical environments. Considering the logical sense of a complete residuated lattice L, this paper aims to present concepts L-closure (L-interior) by means infimums (supremums) L-families L-subsets show their equivalence categorical sense. Also, two types fuzzy relations between corresponding L-interior proposed, ...

Goguen categories were introduced in [13] as a suitable categorical description of L-fuzzy relations, i.e., of relations taking values from an arbitrary complete Brouwerian lattice L instead of the unit interval [0, 1] of the real numbers. In this paper we want to study operations on morphisms of a Goguen category which are derived from suitable binary functions on the underlying lattice of sca...

This paper is a survey of the theory of Goguen categories which establishes a suitable categorical description of L-fuzzy relations, i.e., of relations taking values from an arbitrary complete Brouwerian lattice L instead of the unit interval [0, 1] of the real numbers. In particular, we concentrate on representability, the existence of crisp versions of several categorical constructions, and o...