This paper is a study about the relationships among topologies and intuitionistic fuzzy topology induced, respectively, by approximation operators and an intuitionistic fuzzy approximation operator associated with an approximation space (X,R), when the relation R on X is precisely reflexive and transitive. In particular, we consider an intuitionistic fuzzy approximation operator on an approxima...

The Constraint Hierarchy (CH) framework is used to tackle multiple criteria selection (MCS), consisting of a set of candidates and a set of, possibly competing, criteria for selecting the \best" candidate(s). In this paper, we identify aspects of the CH framework for further enhancement so as to model and solve MCS problems more accurately. We propose the Fuzzy Constraint Hierarchies framework,...

In this paper, based in the L ukasiewicz logic, the definition offuzzifying soft neighborhood structure and fuzzifying soft continuity areintroduced. Also, the fuzzifying soft proximity spaces which are ageneralizations of the classical soft proximity spaces are given. Severaltheorems on classical soft proximities are special cases of the theorems weprove in this paper.

The aim of this paper is to study the categorical relations betweenmatroids, Goetschel-Voxman’s fuzzy matroids and Shi’s fuzzifying matroids.It is shown that the category of fuzzifying matroids is isomorphic to that ofclosed fuzzy matroids and the latter is concretely coreflective in the categoryof fuzzy matroids. The category of matroids can be embedded in that offuzzifying matroids as a simul...

This remarkable little theorem and related phenomena have been the concern of many authors. Apart from the mysterious appearance of the number 14, the attraction of this theorem is that it is simple to state and can be examined and proved using concepts available after any first encounter with topology. The goal of this article is both to provide an original investigation into variations of the...

A new class of harmonic multivalent functions defined by an integral operator is introduced. Coefficient inequalities, extreme points, distortion bounds, inclusion results and closure under an integral operator for this class are obtained .

In a former paper, the algorithm NextClosures for computing the set of all formal concepts as well as the canonical base for a given formal context has been introduced. Here, this algorithm shall be generalized to a setting where the data-set is described by means of a closure operator in a complete lattice, and furthermore it shall be extended with the possibility to handle constraints that ar...

We define the notion of rational closure in the context of Description Logics extended with a tipicality operator. We start from ALC +T, an extension of ALC with a typicality operator T : intuitively allowing to express concepts of the form T(C), meant to select the “most normal” instances of a concept C. The semantics we consider is based on rational model. But we further restrict the semantic...

Gap-deenability and the gap-closure operator were deened in FFK91]. Few complexity classes were known at that time to be gap-deenable. In this paper, we give simple characterizations of both gap-deenability and the gap-closure operator, and we show that many complexity classes are gap-deenable, including P #P , P #P1] , PSPACE, EXP, NEXP, MP, and BP P. If a class is closed under union, intersec...

In this note, we study the lattice structure on the class of all weak hyper K-ideals of a hyper K-algebra. We first introduce the notion of (left,right) scalar in a hyper K-algebra which help us to characterize the weak hyper K-ideals generated by a subset. In the sequel, using the notion of a closure operator, we study the lattice of all weak hyper K-ideals of ahyper K-algebra, and we prove a ...