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Open AccessArticle

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

1
Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi’an 710072, China
2
School of Mathematics, Thapar Institute of Engineering & Technology, Deemed University, Patiala 147004, India
3
Department of Mathematics and Statistics, University of Swat, Mingora 19130, Pakistan
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1183; https://doi.org/10.3390/math7121183
Received: 6 November 2019 / Revised: 20 November 2019 / Accepted: 23 November 2019 / Published: 3 December 2019
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. View Full-Text
Keywords: soft ordered semigroup; fuzzy soft ideals; possibility fuzzy soft interior ideals; simple possibility fuzzy soft ordered semigroup; possibility fuzzy soft semiprime ideals soft ordered semigroup; fuzzy soft ideals; possibility fuzzy soft interior ideals; simple possibility fuzzy soft ordered semigroup; possibility fuzzy soft semiprime ideals
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Habib, S.; Garg, H.; Nie, Y.; Muhammad Khan, F. An Innovative Approach towards Possibility Fuzzy Soft Ordered Semigroups for Ideals and Its Application. Mathematics 2019, 7, 1183.

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