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ON FUZZY QUOTIENT BCK-ALGEBRAS

Yıl 2020, Cilt: 10 Sayı: 1, 59 - 68, 01.01.2020

Öz

In this paper, by considering the concept of fuzzy congruence in some alge-braic structures, we specially study fuzzy congruence in BCK-algebras. We prove that there is a bijection between the set of fuzzy ideals and the set of fuzzy congruences in BCK-algebras. Then we show that for each fuzzy ideal , there is an associated algebra X= that is a BCK-algebra. Also, we obtain a congruence relation on a BCK-algebra by fuzzy ideals.

Kaynakça

  • Ahmad, B., (1993), Fuzzy BCI-algebras, Journal of Fuzzy Mathematics, 1, pp. 445-452.
  • Chon, I., (2008), ε-Fuzzy Congruence on Semigroups, Communications of the Korean Mathematical Society, 23, pp. 461-468.
  • Cignoli, R., DOttaviano, M. L. and Mundici, D., (2000), Algebric Foundation of Many-valued Rea- , soning, Kluwer Academic, Dordrecht.
  • Dymek, G., ( 2008), Fuzzy prime ideals of Pseudo-MV-algebras, Soft computing, 12, pp. 365-372.
  • Hoo, C. S., (1994), Fuzzy ideals of BCI and MV-algebras, Fuzzy Sets and Systems, 62, pp. 111-114.
  • Imai, Y. and Is´eki, K. , (1966), On axiom systems of propositional calculi, Proceedings of the Japan Academy, 42, pp. 19-21
  • Jun, Y. B., (1993), Closed fuzzy ideals in BCI-algebras, Mathematica Japonica, 38, pp. 401-405.
  • Kondo, M., (2003), Fuzzy congruence on BCI-algebras, Scientiae Mathematicae Jpnonicae, 57, pp. 191-196.
  • Meng, J. and Jun, Y. B., (1994), BCK-algebras, Kyungmoon Sa Co, Korea.
  • Rashmanlou, H., Samanta, S., Pal, M. and Borzooei, R. A., (2015), A study on bipolar fuzzy graphs, Journal of Intellegent and Fuzzy Systems, 28, pp. 571-580.
  • Rezaei, A. and Borumand Saeid , A., (2012), Fuzzy congruence relations in CI-algebras, Neural Comput and Applic, 21, pp. 319-328.
  • Saidi Goraghani, S., Borzooei, R. A., (2016), Prime ·-Ideals and Fuzzy Prime ·-Ideals in P M V - algebras, Annals of Fuzzy Mathematics and Informatics, 12, pp. 527-538.
  • Tchikapa, C. N., Lele, C., (2012), Relation diagram between fuzzy n-fold filters in BL-algebras, Annals of Fuzzy Mathematics and Informatics, 4, pp. 131-141.
Yıl 2020, Cilt: 10 Sayı: 1, 59 - 68, 01.01.2020

Öz

Kaynakça

  • Ahmad, B., (1993), Fuzzy BCI-algebras, Journal of Fuzzy Mathematics, 1, pp. 445-452.
  • Chon, I., (2008), ε-Fuzzy Congruence on Semigroups, Communications of the Korean Mathematical Society, 23, pp. 461-468.
  • Cignoli, R., DOttaviano, M. L. and Mundici, D., (2000), Algebric Foundation of Many-valued Rea- , soning, Kluwer Academic, Dordrecht.
  • Dymek, G., ( 2008), Fuzzy prime ideals of Pseudo-MV-algebras, Soft computing, 12, pp. 365-372.
  • Hoo, C. S., (1994), Fuzzy ideals of BCI and MV-algebras, Fuzzy Sets and Systems, 62, pp. 111-114.
  • Imai, Y. and Is´eki, K. , (1966), On axiom systems of propositional calculi, Proceedings of the Japan Academy, 42, pp. 19-21
  • Jun, Y. B., (1993), Closed fuzzy ideals in BCI-algebras, Mathematica Japonica, 38, pp. 401-405.
  • Kondo, M., (2003), Fuzzy congruence on BCI-algebras, Scientiae Mathematicae Jpnonicae, 57, pp. 191-196.
  • Meng, J. and Jun, Y. B., (1994), BCK-algebras, Kyungmoon Sa Co, Korea.
  • Rashmanlou, H., Samanta, S., Pal, M. and Borzooei, R. A., (2015), A study on bipolar fuzzy graphs, Journal of Intellegent and Fuzzy Systems, 28, pp. 571-580.
  • Rezaei, A. and Borumand Saeid , A., (2012), Fuzzy congruence relations in CI-algebras, Neural Comput and Applic, 21, pp. 319-328.
  • Saidi Goraghani, S., Borzooei, R. A., (2016), Prime ·-Ideals and Fuzzy Prime ·-Ideals in P M V - algebras, Annals of Fuzzy Mathematics and Informatics, 12, pp. 527-538.
  • Tchikapa, C. N., Lele, C., (2012), Relation diagram between fuzzy n-fold filters in BL-algebras, Annals of Fuzzy Mathematics and Informatics, 4, pp. 131-141.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

S. S. Goraghani Bu kişi benim

Yayımlanma Tarihi 1 Ocak 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 10 Sayı: 1

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