Soft Convolution Algebra

In the dissertation, the definitions of soft intersection semigroups, soft intersection Clifford semigroups, soft intersection sub-Clifford semigroups, soft convolution algebra, soft convolution restricted sub-algebra are given. Some of their related properties and principle of judgment are discussed. In addition, some equivalent conditions of idempotent soft convolution algebra are investigated. The dissertation is organized as follows:In Chapter 3, the definitions of soft intersection semigroups, soft intersection Clifford semigroups, soft intersection sub-Clifford semigroups are given and several related properties are discussed. Further more, the judgment theorems of soft intersection Clifford semigroups are investigated.In Chapter 4, the definitions of soft convolution algebra, soft convolution restricted sub-algebra are given and we also get the equivalent conditions of the exchange properties of soft convolution algebra. The operation properties of soft convolution algebra in terms of the associative and distributive laws are investigated. Finally, the judgment theorems of identity element in soft convolution algebra are given.In Chapter 5, the transitivity of soft convolution algebra on the base of the binary relation“? ” is investigated and its some properties are discussed.In addition, some equivalent conditions of soft convolution algebras and soft convolution restricted sub-algebra in different operations on exchange and idempotent are given and some relevant conclusions are also obtained.