Abstract
In this study, the generalized intersection and union operations of fuzzy soft set (FSS) are established on the basis of traditional FSS operations, which overcome the shortcomings of traditional FSS operations that do not meet De Morgan’s law, and a series of properties of generalized intersection and union operations of FSS are obtained. The fuzzy soft topology under generalized intersection and generalized union operation of FSSs is established. Finally, the topological construction of weak FSS and strong FSS is discussed, and the relationship between them and the topological construction of traditional FSS is obtained.
Highlights
In real life, the data of many complex problems often have uncertainty, randomness, and fuzziness
Probability theory, fuzzy sets [1], intuitionistic fuzzy sets [2], rough sets [3], and so on are the main methods to deal with uncertain data, obtained in various fields of engineering, computer science, economics, medical science, etc., but these theories have their own difficulties, mainly reflected in the lack of parameter tools
In 2001, Liu et al combined the fuzzy set with soft set and proposed the concept of fuzzy soft set (FSS) [11]. en, Das et al redefined the concept of FSS and studied its operation
Summary
The data of many complex problems often have uncertainty, randomness, and fuzziness. Burc Kandemir established the topological structure of fuzzy soft sets based on some basic definitions in the topological space of Munkres point sets and combined with the operational properties of FSSs [13]. In the study of fuzzy soft topological space structure and properties, the intersection, union, and complement operations of FSSs need to satisfy De Morgan’s law. Considering that De Morgan’s law of intersection, union, and complement operations of FSSs is not valid, this paper constructs the generalized intersection and union operations of FSSs on the basis of the existing FSS operations, satisfies De Morgan’s law, and further studies the operation properties of the generalized intersection and union operations and constructs the corresponding fuzzy soft topology. Based on the concepts of weak fuzzy soft set Journal of Mathematics and strong fuzzy soft set proposed by F.B.Hua and Y.P.Wang in [20], the corresponding structures and properties of fuzzy soft topology are studied
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