On Three Types of Soft Rough Covering-Based Fuzzy Sets

Recently, the concept of a soft rough fuzzy covering (briefly, SRFC) by means of soft neighborhoods was defined and their properties were studied by Zhan’s model. As a generalization of Zhan’s method and in order to increase the lower approximation and decrease the upper approximation, the present work aims to define the complementary soft neighborhood and hence three types of soft rough fuzzy covering models (briefly, 1-SRFC, 2-SRFC, and 3-SRFC) are proposed. We discuss their axiomatic properties. According to these results, we investigate three types of fuzzy soft measure degrees (briefly, 1-SMD, 2-SMD, and 3-SMD). Also, three kinds of ψ -soft rough fuzzy coverings (briefly, 1- ψ -SRFC, 2- ψ -SRFC, and 3- ψ -SRFC) and three kinds of D -soft rough fuzzy coverings (briefly, 1- D -SRFC, 2- D -SRFC, and 3- D -SRFC) are discussed and some of their properties are studied. Finally, the relationships among these three models and Zhan’s model are presented.

Soft bigeneralized topological spaces

In this paper, soft bigeneralized topological spaces are introduced. Besides, we defined soft open set, soft closed set, soft closure set, soft interior set, soft basis and soft neighborhood on the soft bigeneralized topological spaces. Furthermore, some important theorems are proved and interesting examples are given.

A contribution to the study of soft proximity spaces

In this paper we study the soft proximity spaces. First, we investigate the relation between proximity spaces and soft proximity spaces. Also, we define the notion of a soft ?-neighborhood in the soft proximity spaces which offer an alternative approach to the study of soft proximity spaces. Later, we show how a soft proximity space is derived from a soft uniform space. Finally, we obtain the initial soft proximity space determined by a family of soft proximity spaces.