Soft Computing

, Volume 22, Issue 11, pp 3675–3683 | Cite as

New types of hesitant fuzzy soft ideals in BCK-algebras

  • H. A. Alshehri
  • H.  A. Abujabal
  • N. O. Alshehri
Foundations
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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.

Keywords

Hesitant fuzzy (implicative–positive implicative and commutative) ideals in BCK-algebras Hesitant fuzzy soft (implicative–positive implicative and commutative) ideals in BCK-algebras 
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Notes

Compliance with ethical standards

Conflict of interest

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

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia
  2. 2.Department of Mathematics, Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia
  3. 3.Department of Natural and Engineering Science, Faculty Applied Studies and Community ServiceKing Saud UniversityRiyadhSaudi Arabia

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