In 1965 L. A Zadeh [11] introduced fuzzy sets as a generalization of ordinary sets. After that C. L. Chang [2] introduced fuzzy topology and that led to the discussion of various aspects of L-topology by many authors. The Čech closure spaces introduced by Čech E. [1] is a generalization of the topological spaces. The theory of fuzzy closure spaces has been established by Mashhour and Ghanim [4]...

A definition of L-fuzzy bags is introduced and studied. In this approach, according to the concept given by M. Delgado et al. (2009), each bag has two parts: function and summary information. Then, the definition of L-fuzzy bag expected value is introduced. In the case L = [0, 1], several integral-based fuzzy bag expected values are prepared. By some examples, the new concepts are illustrated.

The aim of this paper is to study the concept of -induced L-fuzzy topological spaces. Some properties of the functions (namely Scott-continuous function) are studied. The Scott-continuous functions turn out to be the natural tool for studying the -induced L-fuzzy topological space. We also discuss the connections between some separations, countability and covering properties of an ordinary topo...

We show here some of our results on intuitionistic fuzzy topological spaces. In 1983, K.T. Atanassov proposed a generalization of the notion of fuzzy set: the concept of intuitionistic fuzzy set [1]. Some basic results on intuitionistic fuzzy sets were publised in [2,3], and the book [4] provides a comprehensive coverage of virtually all results until 1999 in the area of the theory and applicat...

In this paper, a new definition of locally convex L-topological vector spaces is given. The relationship between this new definition and the previous definition of locally convex L-topological vector spaces given by Yan and Fang in 1999 is investigated. Moreover, the concept of generalized L-fuzzy semi-norm is introduced. By using a family of generalized L-fuzzy semi-norms, a characterization o...

In this paper, we introduce the concept of the generalized topological molecular lattices as a generalization of Wang's topological molecular lattices,  topological spaces, fuzzy topological spaces, L-fuzzy topological spaces and soft topological spaces. Topological molecular lattices were defined by closed elements, but in this new structure we present the concept of the open elements and defi...

D. Molodtsov (1999) introduced the concept of a soft set as a new approach for modeling uncertainties. The aim of this work is to define special kinds of soft sets, namely soft, L-fuzzifying soft, L-soft, and L-fuzzy soft neighborhood sets and to use them in order to give an alternative characterization of categories related to topology: crisp topological, L-topological, L-fuzzifying topologica...

In this paper, we study countably compact fuzzy sets using the definition of C. K. Wong [10] and obtain its several properties. 1. Introduction The concept of fuzzy set and fuzzy set operations were first introduced by L. A. Zadeh [11] in1965. Several other mathematicians studied fuzzy sets in various areas in mathematics. Firstly, C. L. Chang [2] in 1968 developed the theory of fuzzy topologic...

In some cases, the relationship between an object set X and an attribute set Y is set up by means of a fuzzy context sequence. A particular case of this situation appears when we want to study the evolution in time of a fuzzy context. In this work, we deepen in the study of these situations. First we recover the fuzzy context sequence definition and the main results. After that, with the aid of...

Two definitions of fuzzy sets with Boolean-valued membership functions, introduced by Drossos and Markakis and called by them external and internal Boolean fuzzy sets, are compared with a third, classical definition descending more directly from the original Zadeh's and Goguen's ideas. Under some rather general conditions, internal and classical Boolean fuzzy sets are proved to be equivalent in...