• Title/Summary/Keyword: union-soft algebra

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UNION-SOFT SETS WITH APPLICATIONS IN BCK/BCI-ALGEBRAS

  • Jun, Young Bae
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.6
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    • pp.1937-1956
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    • 2013
  • The aim of this article is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, the notion of union-soft sets is introduced, and its application to BCK/BCI-algebras is considered. The notions of union-soft algebras, union-soft (commutative) ideals and closed union-soft ideals are introduced, and related properties and relations are investigated. Conditions for a union-soft ideal to be closed are provided. Conditions for a union-soft ideal to be a union-soft commutative ideal are also provided. Characterizations of (closed) union-soft ideals and union-soft commutative ideals are established. Extension property for a union-soft commutative ideal is established.

ON KU-ALGEBRAS CONTAINING (α, β)-US SOFT SETS

  • Ansari, Moin A.;Koam, Ali N.A.;Haider, Azeem
    • Korean Journal of Mathematics
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    • v.28 no.1
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    • pp.89-104
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    • 2020
  • In this paper, we connect (α, β) union soft sets and their ideal related properties with KU-algebras. In particular, we will study (α, β)-union soft sets, (α, β)-union soft ideals, (α, β)-union soft commutative ideals and ideal relations in KU-algebras. Finally, a characterization of ideals in KU-algebras in terms of (α, β)-union soft sets have been provided.

ON SOME PROPERTIES OF SOFT α-IDEALS

  • TOUQEER, M.;ASLAM MALIK, M.
    • Journal of applied mathematics & informatics
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    • v.33 no.5_6
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    • pp.671-686
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    • 2015
  • The notion of soft α-ideals and α-idealistic soft BCI-algebras is introduced and their basic properties are discussed. Relations between soft ideals and soft α-ideals of soft BCI-algebras are provided. Also idealistic soft BCI-algebras and α-idealistic soft BCI-algebras are being related. The restricted intersection, union, restricted union, restricted difference and "AND" operation of soft α-ideals and α-idealistic soft BCI-algebras are established. The characterizations of (fuzzy) α-ideals in BCI-algebras are given by using the concept of soft sets. Relations between fuzzy α-ideals and α-idealistic soft BCI-algebras are discussed.

On Generalized Intuitionistic Soft Equality

  • Park, Jin Han;Kwun, Young Chel
    • Journal of the Korean Institute of Intelligent Systems
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    • v.24 no.5
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    • pp.569-577
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    • 2014
  • Park et al. (2011) introduced the concept of generalized intuitionistic fuzzy soft sets, which can be seen as an effective mathematical tool to deal with uncertainties. In this paper, the concept of generalized intuitionistic fuzzy soft equality is introduced and some related properties are derived. It is proved that generalized intuitionistic fuzzy soft equality is congruence relation with respect to some operations and the generalized intuitionistic fuzzy soft quotient algebra is established.

PYTHAGOREAN FUZZY SOFT SETS OVER UP-ALGEBRAS

  • AKARACHAI SATIRAD;RUKCHART PRASERTPONG;PONGPUN JULATHA;RONNASON CHINRAM;AIYARED IAMPAN
    • Journal of applied mathematics & informatics
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    • v.41 no.3
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    • pp.657-685
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    • 2023
  • This paper aims to apply the concept of Pythagorean fuzzy soft sets (PFSSs) to UP-algebras. Then we introduce five types of PFSSs over UP-algebras, study their generalization, and provide illustrative examples. In addition, we study the results of four operations of two PFSSs over UP-algebras, namely, the union, the restricted union, the intersection, and the extended intersection. Finally, we will also discuss t-level subsets of PFSSs over UP-algebras to study the relationships between PFSSs and special subsets of UP-algebras.