A Study On Soft Sets And Rough Sets Of N-ary Semigroups And Their Decision Making

The paper mainly studies some theories of fuzzy sets, soft sets and rough sets based on n-ary semigroups. By means of the notions of idealistic soft n-ary semigroups, soft congruence relations, t-level relations of fuzzy ideals, we introduce some structures and properties of n-ary semigroups. At the same time, two kinds of decision making methods for rough soft sets on n-ary semigroups are established.The whole paper is divided into four chapters.The first chapter briefly introduces the development background and research status about n-ary semigroups, fuzzy sets, rough sets and soft sets, and briefly introduces the main work and some preliminary knowledge of this paper.In the second chapter, by using idealistic soft n-ary semigroups, we give the characterization of the regular n-ary semigroups. The relationships between regular n-ary semigroups and soft regular n-ary semigroups are also discussed. Finally, we introduce quotient n-ary semigroups via soft congruence relations and establish some homomorphisms and related properties.In the third chapter, based on the fuzzy ideals of n-ary semigroups, the congruence relation on the n-ary semigroup is defined, and the concept of the rough n-ary semigroup is established, and its operation properties and structure are studied.In the fourth chapter, based on the congruence relations in the third chapter, the rough sets and soft set theory combined with the n-ary semigroup theory, we discuss properties of upper and lower rough approximations of rough soft n-ary semigroup.Furthermore, we study rough soft ideals(prime ideals). Finally, two kinds of decision making methods for rough soft n-ary semigroups are investigated and the corresponding algebraic examples are given to illustrate.