An Innovative Approach towards Possibility Fuzzy Soft Ordered Semigroups for Ideals and Its Application

The objective of this paper is put forward the novel concept of possibility fuzzy soft ideals and the possibility of fuzzy soft interior ideals. The various results in the form of the theorems with these notions are presented and further validated by suitable examples. In modern life decision-making problems, there is a wide applicability of the possibility fuzzy soft ordered semigroup which has also been constructed in the paper to solve the decision-making process. Elementary and fundamental concepts including regular, intra-regular and simple ordered semigroups in terms of possibility fuzzy soft ordered semigroup are presented. Later, the concept of left (resp. right) regular and left (resp. right) simple in terms of possibility fuzzy soft ordered semigroups are delivered. Finally, the notion of possibility fuzzy soft semiprime ideals in an ordered semigroup is defined and illustrated by theorems and example.