Geodesic
Fuzzy Sub-Equality Algebras Based on Fuzzy Points
Bulletin of the Section of Logic, Tome 53 (2024) no. 2, pp. 195-222.

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In this paper, by using the notion of fuzzy points and equality algebras, the notions of fuzzy point equality algebra, equality-subalgebra, and ideal were established. Some characterizations of fuzzy subalgebras were provided by using such concepts. We defined the concepts of (∈, ∈) and (∈, ∈∨ q)-fuzzy ideals of equality algebras, discussed some properties, and found some equivalent definitions of them. In addition, we investigated the relation between different kinds of (α,β)-fuzzy subalgebras and (α,β)-fuzzy ideals on equality algebras. Also, by using the notion of (∈, ∈)-fuzzy ideal, we defined two equivalence relations on equality algebras and we introduced an order on classes of X, and we proved that the set of all classes of X by these order is a poset.
Keywords: equality algebra, fuzzy set, fuzzy point, fuzzy ideal, sub-equality algebras, \((\in, \in)\)-fuzzy sub-equality algebras, \((\in, \in\! \vee \, {q})\)-fuzzy sub-equality algebras, \((q, \in\! \vee \, {q})\)-fuzzy sub-equality algebras 
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Kologani, Mona Aaly; Takallo, Mohammad Mohseni; Jun, Young Bae; Borzooei, Rajab Ali. Fuzzy Sub-Equality Algebras Based on Fuzzy Points. Bulletin of the Section of Logic, Tome 53 (2024) no. 2, pp. 195-222. http://geodesic.mathdoc.fr/item/BSL_2024_53_2_a3/

[1] M. Aaly Kologani, M. Mohseni Takallo, R. Borzooei, Y. Jun, Implicative equality algebras and annihilators in equality algebras, Journal of Discrete Mathematical Sciences and Cryptography, (2021), pp. 1–18 | DOI

[2] M. Aaly Kologani, M. Mosheni Takallo, R. A. Borzooei, Y. B. Jun, Right and left mappings in equality algebras, Kragujevac Journal of Mathematics, vol. 46(5) (2022), pp. 815–832 | DOI

[3] M. Aaly Kologani, X. Xin, Y. Jun, M. Mohseni Takallo, Positive implicative equality algebras and equality algebras with some types, Journal of Algebraic Hyperstructures and Logical Algebras, vol. 3(2) (2022), pp. 69–86 | DOI

[4] P. Allen, H. S. Kim, J. Neggers, Smarandache disjoint in BCK/d-algebras, Scientiae Mathematicae Japonicae, vol. 61(3) (2005), pp. 447–450.

[5] P. J. Allen, H. S. Kim, J. Neggers, Companion d-algebras, Mathematica Slovaca, vol. 57(2) (2007), pp. 93–106 | DOI

[6] P. J. Allen, H.-S. Kim, J. Neggers, Deformations of d/BCK-algebras, Bulletin of the Korean Mathematical Society, vol. 48(2) (2011), pp. 315–324 | DOI

[7] R. Borzooei, F. Zebardast, M. Aaly Kologani, Some types of filters in equality algebras, Categories and General Algebraic Structures with Applications, vol. 7 (Special Issue on the Occasion of Banaschewski’s 90th Birthday (II)) (2017), pp. 33–55.

[8] R. A. Borzooei, M. Mohseni Takallo, M. Aaly Kologani, Y. B. Jun, Quotient Structures in Equality Algebras, Journal of Algebraic Systems, vol. 11(2) (2024), pp. 65–82 | DOI

[9] L. C. Ciungu, On pseudo-equality algebras, Archive for Mathematical Logic, vol. 53(5–6) (2014), pp. 561–570 | DOI

[10] A. Dvurečenskij, O. Zahiri, Pseudo equality algebras: revision, Soft Computing, vol. 20 (2016), pp. 2091–2101 | DOI

[11] B. Ganji Saffar, Fuzzy n-fold obstinate and maximal (pre) filters of EQ-algebras, Journal of Algebraic Hyperstructures and Logical Algebras, vol. 2(1) (2021), pp. 83–98 | DOI

[12] S. Jenei, Equality algebras, Studia Logica, vol. 100(6) (2012), pp. 1201–1209 | DOI

[13] S. Jenei, L. Kőrödi, On the variety of equality algebras, [in:] Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology, Atlantis Press (2011), pp. 153–155 | DOI

[14] Y. B. Jun, On (α, β)-fuzzy subalgebras of BCK/BCI-algebras, Bulletin of the Korean Mathematical Society, vol. 42(4) (2005), pp. 703–711 | DOI

[15] V. Novák, B. De Baets, EQ-algebras, Fuzzy Sets and Systems, vol. 160(20) (2009), pp. 2956–2978 | DOI

[16] A. Paad, Ideals in bounded equality algebras, Filomat, vol. 33(7) (2019), pp. 2113–2123 | DOI

[17] M. M. Takallo, M. A. Kologani, MBJ-neutrosophic filters of equality algebras, Journal of Algebraic Hyperstructures and Logical Algebras, vol. 1(2) (2020), pp. 57–75 | DOI

[18] L. A. Zadeh, Fuzzy sets, Information and Control, vol. 8(3) (1965), pp. 338–353 | DOI

[19] F. Zebardast, R. A. Borzooei, M. A. Kologani, Results on equality algebras, Information Sciences, vol. 381 (2017), pp. 270–282 | DOI