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

Author

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  • Sana Habib

    (Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi’an 710072, China)

  • Harish Garg

    (School of Mathematics, Thapar Institute of Engineering & Technology, Deemed University, Patiala 147004, India)

  • Yufeng Nie

    (Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi’an 710072, China)

  • Faiz Muhammad Khan

    (Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi’an 710072, China
    Department of Mathematics and Statistics, University of Swat, Mingora 19130, Pakistan)

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.

Suggested Citation

  • Sana Habib & Harish Garg & Yufeng Nie & Faiz Muhammad Khan, 2019. "An Innovative Approach towards Possibility Fuzzy Soft Ordered Semigroups for Ideals and Its Application," Mathematics, MDPI, vol. 7(12), pages 1-16, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1183-:d:293730
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    References listed on IDEAS

    as
    1. Faiz Muhammad Khan & Nor Haniza Sarmin & Asghar Khan & Hidayat Ullah Khan, 2017. "New Types of Fuzzy Interior Ideals of Ordered Semigroups Based on Fuzzy Points," Matrix Science Mathematic (MSMK), Zibeline International Publishing, vol. 1(1), pages 25-33, January.
    2. M. Shabir & A. Khan, 2008. "Characterizations Of Ordered Semigroups By The Properties Of Their Fuzzy Generalized Bi-Ideals," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 4(02), pages 237-250.
    3. Sabu Sebastian & T. V. Ramakrishnan, 2011. "Multi-fuzzy sets: An extension of fuzzy sets," Fuzzy Information and Engineering, Springer, vol. 3(1), pages 35-43, March.
    Full references (including those not matched with items on IDEAS)

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