Abstract: In this paper, we introduce the notion of rough IF-subgroup with respect to an IF-normal subgroup of a group, and give some properties of the lower and the upper approximations in a group.
Abstract: In this paper we aim to introduce the concept of lattice-valued fuzzy frame or L-fuzzy frame, related to traditional frames analogously to how L-fuzzy (resp. L-fuzzifying) topological spaces related to L-topological spaces (resp. traditional topological spaces). Some properties of L-fuzzy frames are introduced.
Abstract: The notions of L-sobriety and L-spatiality are introduced for the category L-BiTop of L-bitopological spaces. Such notions are used to extend the known adjunction between the category L-Top of L-topological spaces and the category Loc of locals to one between the category L-BiTop and BiLoc. Also, the concepts of localic regularity and localic compactness are introduced in the mentioned category.
Abstract: This paper is devoted to the construction of a bicompletion of Lowen fuzzy quasi-uniform spaces (or just [0,1]-fuzzy quasi-uniform spaces in this paper) and the study of that bicompletion, which appears to have a number of properties that one could resonably expect in analogy to the situation in ordinary quasi-uniform spaces, i.e., denseness of the original spaces in its bicompletion, extension property of quasi-uniformly continuous maps.
Abstract: In 1976 Singal and Lal extended the study of nearness between sets to the Nachbin's [1965] topological and order structures. Also, in 1978 Dimitrijevi developed such an idea, in the same manner, with more study of its properties. The aim of this paper is to introduce the idea of order in a fuzzy proximity space (Katsaras, 1979, 1980, 1980) and construct new spaces in the area of fuzzy topological and order structures, the so-called fuzzy proximity ordered spaces. Also, we study some properties of these spaces.
Abstract: Since the fuzzy topological space (X, Ï„) may be considered as a fuzzy topological ordered space when it is realised that the non-empty set X is partially ordered by agreeing that x y in X if and only if x = y. Then the study of the fuzzy topological ordered spaces not only includes the study of the abstract fuzzy topological spaces but also reveals many generalizations of well-known results concerning the abstract fuzzy topological spaces. This paper provides a certain number of separation axioms for fuzzy topological ordered spaces, which we label FTi-order separation axioms (for i = 1,2,3,4). The relationships between some of the FTi-order separation axioms are studied.
Abstract: In an ordered vector space one can consider various fuzzy topologies determined by the order relation. But it is also convenient to consider the case in which, in an ordered vector space, a fuzzy topology is given from the beginning. In this case one requires not only that the fuzzy topology be compatible with the structure of vector space, but also that it be compatible with the order relation, in one sense or another.
Abstract: The study of the relationship between fuzzy topological and order structures was initiated by Katsaras in [J. Math. Anal. Appl. 84 (1981) 44–58]. In [M.Y. Bakier et al. Proc. of Assiut First Intern. Conf., Part VIII (1990) 41–61] some properties of these spaces are studied. In [M.Y. Bakier and K. El-Saady, Fuzzy Sets and Systems 54 (1993) 213–220] is, by similar manner introduced the idea of order in fuzzy topological vector spaces. In another work of A.S. Mashhour et al. the study of the relationship between order and Lowen-fuzzy uniformities is introduced and many results are studied. In this paper, by similar manner, we will introduce the idea of order in both the fuzzy proximity space and the fuzzy syntopogenous space and we study some properties of these spaces.
