Interval-Valued Intuitionistic Fuzzy Subalgebras/Ideals of Hilbert Algebras

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Aiyared Iampan, V. Vijaya Bharathi, M. Vanishree, N. Rajesh


In this paper, the concept of interval-valued intuitionistic fuzzy sets to subalgebras and ideals of Hilbert algebras is introduced. The inverse image of interval-valued intuitionistic fuzzy subalgebras and interval-valued intuitionistic fuzzy ideals of Hilbert algebras is studied and some related properties are investigated. Equivalence relations on interval-valued intuitionistic fuzzy ideals are discussed.

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  1. B. Ahmad, A. Kharal, On Fuzzy Soft Sets, Adv. Fuzzy Syst. 2009 (2009), 586507.
  2. K.T. Atanassov, Intuitionistic Fuzzy Sets, Fuzzy Sets Syst. 20 (1986), 87–96.
  3. M. Atef, M.I. Ali, T.M. Al-shami, Fuzzy Soft Covering-Based Multi-Granulation Fuzzy Rough Sets and Their Applications, Comput. Appl. Math. 40 (2021), 115.
  4. N. Cagman, S. Enginoglu, F. Citak, Fuzzy Soft Set Theory and Its Application, Iran. J. Fuzzy Syst. 8 (2011), 137-147.
  5. W.A. Dudek, Y.B. Jun, On Fuzzy Ideals in Hilbert Algebra, Novi Sad J. Math. 29 (1999), 193-207.
  6. H. Garg, S. Singh, A Novel Triangular Interval Type-2 Intuitionistic Fuzzy Sets and Their Aggregation Operators, Iran. J. Fuzzy Syst. 15 (2018), 69-93.
  7. H. Garg, K. Kumar, An Advanced Study on the Similarity Measures of Intuitionistic Fuzzy Sets Based on the Set Pair Analysis Theory and Their Application in Decision Making, Soft Comput. 22 (2018), 4959–4970.
  8. H. Garg, K. Kumar, Distance Measures for Connection Number Sets Based on Set Pair Analysis and Its Applications to Decision-Making Process, Appl Intell. 48 (2018), 3346–3359.
  9. D. Busneag, A Note on Deductive Systems of a Hilbert Algebra, Kobe J. Math. 2 (1985), 29-35.
  10. D. Busneag, Hilbert Algebras of Fractions and Maximal Hilbert Algebras of Quotients, Kobe J. Math. 5 (1988), 161-172.
  11. A. Diego, Sur les algébres de Hilbert, Collection de Logique Math. Ser. A (Ed. Hermann, Paris) 21 (1966), 1-52.
  12. W.A. Dudek, On Fuzzification in Hilbert Algebras, Contrib. Gen. Algebra. 11 (1999), 77-83.
  13. Y.B. Jun, Deductive systems of Hilbert algebras, Math. Japon. 43 (1996), 51-54.
  14. I. Chajda, R. Halas, Congruences and Ideals in Hilbert Algebras, Kyungpook Math. J. 39 (1999), 429-429.
  15. L.A. Zadeh, Fuzzy sets, Inf. Control. 8 (1965), 338-353.