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.

In this paper, we utilized triangular conorms (S-norm). The essence of using S-norm is that the similarity order does not change using different norms. In fact we are investigating for a new conception for calculating the similarity of two Fermatean fuzzy sets. For this purpose, utilizing an S-norm, we first present a formula for calculating the similarity of two Fermatean fuzzy values, so that they are truthful in similarity properties. Following that, we generalize a formula for calculating the similarity of the two Fermatean fuzzy sets which prove truthful in similarity conditions. Finally, various numerical examples have been presented to elaborate the said method.

In this paper, we introduce the concepts of (α, β)-fuzzy interior ideals and $(\bar \beta ,\bar \alpha )$ -fuzzy interior ideals of ordered semigroups, where α, β ∈ {ε _gg , qδ, ε _γ ∨ qδ, ε _γ ∧ qδ}, and $\bar \alpha ,\bar \beta \in \{ \overline {\varepsilon _\gamma } ,\overline {q\delta } ,\overline {\varepsilon _\gamma } \vee \overline {q_\delta } ,\overline {\varepsilon _\gamma } \wedge \overline {q_\delta } \} ,\alpha \ne \varepsilon _\gamma \wedge q_\delta $ and $\bar \beta \ne \overline {\varepsilon _\gamma } \wedge \overline {q_\delta } $ , and some related properties are investigated. Special concentration is paid to (ε _γ , ε _γ ∨ qδ)-fuzzy interior ideals and ( $\overline {\varepsilon _\gamma } ,\overline {\varepsilon _\gamma } \vee \overline {q_\delta } $ )-fuzzy interior ideals.