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Bipolar fuzzy a-ideals of BCI-algebras

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The notion of bipolar fuzzy a-ideals of BCI-algebras is introduced, and their properties are investigated. Relations between bipolar fuzzy subalgebras, bipolar fuzzy ideals and bipolar fuzzy a-ideals are discussed. Conditions for a bipolar fuzzy ideal to be a bipolar fuzzy a-ideal are provided. Characterizations of bipolar fuzzy a-ideals are given. Using a finite collection of a-ideals, a bipolar fuzzy a-ideal is established.

Abstract

The notion of bipolar fuzzy a-ideals of BCI-algebras is introduced, and their properties are investigated. Relations between bipolar fuzzy subalgebras, bipolar fuzzy ideals and bipolar fuzzy a-ideals are discussed. Conditions for a bipolar fuzzy ideal to be a bipolar fuzzy a-ideal are provided. Characterizations of bipolar fuzzy a-ideals are given. Using a finite collection of a-ideals, a bipolar fuzzy a-ideal is established.

참고문헌 (9)

  1. D. Dubois, "Fuzzy Sets and Systems" (1980), Academic Press
  2. Young Bae Jun, "BIPOLAR FUZZY TRANSLATIONS IN BCK", BCI-ALGEBRAS, 2009, pp.22(3), 399~408[DOI]
  3. Y. B. Jun, "Subalgebras and closed ideals of BCH-algebras based on bipolar-valued fuzzy sets", Sci. Math. Jpn, 68(2), pp.287~297 (2008)
  4. K. J. Lee, "Bipolar fuzzy subalgerbas and bipolar fuzzy ideals of BCK", BCI-algerbas, 2009, pp.32(3), 361~373
  5. K. M. Lee, "Bipolar-valued fuzzy sets and their operations", Proc. Int. Conf. on Intelligent Technologies, pp.307~312 (2000)
  6. 이건명, "구간값 퍼지집합, Intuitionistic 퍼지집합, Bipolar-valued 퍼지집합의 비교", 한국지능시스템학회 논문지, 14(2), pp.125~129 (2004), 한국지능시스템학회
  7. Y. L. Liu, "q-ideals and a-ideals in BCI-algebras, Southeast Asian Bull", Math, 24(2), pp.243~253 (2000)
  8. L. A. Zadeh, "Fuzzy sets", Information and Control, 8, pp.338~353 (1965)
  9. H.-J. Zimmermann, "Fuzzy Set Theory and its Applications" (1985), Kluwer-Nijhoff Publishing

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