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Computational and Applied Mathematics

, Volume 37, Issue 4, pp 5013–5033 | Cite as

Generalized roughness in fuzzy filters and fuzzy ideals with thresholds in ordered semigroups

  • Tahir Mahmood
  • Muhammad Irfan Ali
  • Azmat Hussain
Article

Abstract

In the present paper, concept of roughness for fuzzy filters with thresholds \(\left( u_{1},u_{2}\right) \) in ordered semigroups is introduced. Then, this concept is extended to fuzzy bi-filters with thresholds and fuzzy quasi-filters with thresholds. Further approximations of fuzzy ideals with thresholds, fuzzy bi-ideals with thresholds, and fuzzy interior ideals with thresholds are studied. Moreover, this concept is applied to study approximations of fuzzy quasi-ideals with thresholds and semiprime fuzzy quasi-ideals with thresholds.

Keywords

Rough sets Fuzzy set Ordered Semigroups Approximation of fuzzy filters with thresholds Approximation of fuzzy ideals with thresholds 

Mathematics Subject Classification

08A72 34C41 06F05 

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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Statistics, Faculty of Basic and Applied SciencesInternational Islamic UniversityIslamabadPakistan
  2. 2.Department of MathematicsIslamabad Model College for GirlsIslamabadPakistan

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