Abstract
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.
Highlights
As classical mathematical tools are unable to solve the modern uncertain problems, scientists are paying much attention to deriving tools for solving these uncertainties
Fuzzy mathematics is an approach put forwarded by Zadeh that opens up a new direction for scientists in solving such hard problems [1]
This section elaborates some innovative concepts of possibility fuzzy soft left ideals and possibility fuzzy soft interior ideals
Summary
As classical mathematical tools are unable to solve the modern uncertain problems, scientists are paying much attention to deriving tools for solving these uncertainties. In the modern decision-making process, many researchers are studying different approaches of fuzzy soft sets coupling with semigroup theory and relating their possible applications in the field of decision sciences. This progress in the field of fuzzy mathematics motivates the Authors to develop a new direction to solve decision-making problems. This new research had a massive scope in solving decision-making problems in the field of applied sciences. Important relations between regular and intra-regular ordered semigroups with possibility fuzzy soft interior ideals and possibility fuzzy soft left The notion of semi-prime possibility fuzzy soft ideals in ordered semigroups has been defined
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