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New types of hesitant fuzzy soft ideals in BCK-algebras

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Abstract

Molodtsov (Comput Math Appl 37:19–31, 1999) introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. As a link between classical soft sets and hesitant fuzzy sets, the notion of hesitant fuzzy soft sets is introduced by Babitha and John (J New Results Sci 3:98–107, 2013). The aim of this paper is to apply notion of hesitant fuzzy soft set for dealing with several kinds of theories in BCK-algebras. The notions of hesitant fuzzy soft implicative ideal, hesitant fuzzy soft positive implicative ideal and hesitant fuzzy soft commutative ideal in BCK-algebras are introduced and related properties are investigated. Relations between a hesitant fuzzy soft subalgebra (ideal) and hesitant fuzzy soft (implicative, positive implicative and commutative) ideals are discussed. Conditions for a hesitant fuzzy soft ideal to be a hesitant fuzzy soft implicative ideal (positive implicative and commutative) are given and provided. Application of hesitant fuzzy soft sets in decision making is investigated.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

    H. A. Alshehri & H. A. Abujabal

  2. Department of Mathematics, Faculty of Science, King Abdulaziz University, Al-Faisaliah Campus, Jeddah, Saudi Arabia

    N. O. Alshehri

  3. Department of Natural and Engineering Science, Faculty Applied Studies and Community Service, King Saud University, Riyadh, Saudi Arabia

    H. A. Alshehri

Authors
  1. H. A. Alshehri
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  2. H. A. Abujabal
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  3. N. O. Alshehri
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Correspondence to H. A. Alshehri.

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The authors declare that there is no conflict of interest regarding the publication of this paper.

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Communicated by A. Di Nola.

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Alshehri, H.A., Abujabal, H.A. & Alshehri, N.O. New types of hesitant fuzzy soft ideals in BCK-algebras. Soft Comput 22, 3675–3683 (2018). https://doi.org/10.1007/s00500-018-3009-0

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