A Study On Hybrid Soft Set Models Of Semigroups,Soft Covering Models And Applications In Decision-Making

The paper is focused on researching in the theories of soft rough semigroups,Z-soft rough fuzzy semigroups and soft coverings based rough sets.By combining rough sets,fuzzy sets and soft sets to apply on semigroups,the structure and properties of soft rough semigroups and Z-soft rough semigroups are studied,and decision-making methods for soft rough regular semigroups and soft rough semigroups are given.At the same time,by means of the notions of soft neighborhoods,soft complementary neighborhoods,soft adhesions and soft covering,we introduce corresponding properties of soft coverings based rough sets and propose corresponding decision-makings.The main work of this paper is as follows:In the first chapter,the development background and research status of the related subject are introduced,and the main work and some preliminary knowledge which are used in this paper are also given.In the second chapter,by putting forward the definitions of C-soft sets and CC-soft sets over semigroups,the notions of soft rough semigroups and soft rough ideals are proposed,and some important conclusions are obtained.Based on this view,we propose two different decision-making application methods,and give corresponding examples to illustrate them.In the third chapter,based on the definitions of C-soft sets and CC-soft sets over semigroups in the second chapter,we introduce the definition of Z-soft rough fuzzy semigroups and discuss its related properties.Finally,the decision-making algorithm of Z-soft rough fuzzy sets is given.Especially,the advantages and disadvantages of the three algorithms are analyzed by comparing with the decision-making algorithms about Feng-soft rough fuzzy set and Meng-soft rough fuzzy set.In the fourth chapter,we propose the definitions of soft neighborhoods,soft complementary neighborhoods and soft adhesions over soft coverings.And based on this,we establish different types of soft coverings based rough sets and study their properties and measures,and compare the relationships between soft rough sets and soft coverings based rough sets.Finally,we raise two kinds of decision-making methods and give the corresponding examples to illustrate the two algorithms.