Fuzzy ideals of pseudo-BCK algebras

• Autorzy: Dymek G. , Walendziak A.
• Języki publikacji: EN

Abstrakty

EN

Characterizations of fuzzy ideals of a pseudo-BCK algebra are established. Conditions for a fuzzy set to be a fuzzy ideal are given. Given a fuzzy set ž, the least fuzzy ideal containing ž is constructed. The homomorphic properties of fuzzy ideals of a pseudo-BCK algebra are provided. Finally, characterizations of Noetherian pseudo-BCK algebras and Artinian pseudo-BCK algebras in terms of fuzzy ideals are given.

Słowa kluczowe

EN

pseudo-BCK algebra; fuzzy ideal; Noetherian (Artinian) pseudo-BCK algebra

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2012
• Tom: Vol. 45, nr 1
• Strony: 1--15
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Dymek G.

autor

Walendziak A.

• Faculty of Mathematics and Natural Sciences The John Paul II Catholic University Of Lublin Konstantynów 1H 20-708, Lublin, Poland,

Bibliografia

• [1] C.C. Chang, Algebraic analysis of many valued logics Trans.Amer.Math.Soc.88 (1958),467 –490.
• [2] G.Georgescu, A.Iorgulescu, Pseudo-MV algebras: a noncommutative extension of MV algebras The Proc. of the Fourth International Symp. on Economic Informatics, Bucharest, Romania, May 1999, 961–968.
• [3] G.Georgescu ,A.Iorgulescu, Pseudo-BL algebras: a noncommutative extension of BL algebras Abstracts of the Fifth International Conference FSTA 2000, Slovakia, February 2000, 90–92.
• [4] G.Georgescu, A.Iorgulescu, Pseudo-BCK algebras: an extension of BCK algebras Proc. of DMTCS’01: Combinatorics, Computability and Logic, Springer, London, 2001, 97–114.
• [5] P.Hájek, Metamathematics of fuzzy logic Inst. of Comp. Science, Academy of Science of Czech Rep., Technical report 682 (1996).
• [6] P.Hájek, Metamathematics of Fuzzy Logic Kluwer Acad. Publ., Dordrecht, 1998.
• [7] R.Halaš, J.Kühr, Deductive systems and annihilators of pseudo-BCK algebras Ital. J.Pure Appl.Math.25 (2009).
• [8] Y.Imai, K.Iséki, On axiom systems of propositional calculi XIV Proc. Japan Acad. 42 (1966), 19–22.
• [9] A.Iorgulescu, Classes of pseudo-BCK algebras Part I ,J.Mult. Valued Logic Soft Comput.12 (2006), 71–130.
• [10] A.Iorgulescu, Classes of pseudo-BCK algebras Part II, J.Mult. Valued Logic Soft Comput.12 (2006), 575–629.
• [11] Y.B.Jun, Characterizations of Noetherian BCK-algebras via fuzzy ideals Fuzzy Sets and Systems 108 (1999), 231–234.
• [12] Y.B.Jun, Characterizations of pseudo-BCK algebras Sci.Math.Jpn.57 (2003), 265–270.
• [13] Y.B.Jun, H.S.Kim, J.Neggers, On pseudo-BCI ideals of pseudo BCI-algebras Mat. Vesnik 58 (2006), 39–46.
• [14] J.Meng, X.Guo, On fuzzy ideals in BCK/BCI-algebras Fuzzy Sets and Systems 149 (2005), 509–525.
• [15] J.Rachůnek, A non-commutative generalization of MV algebras Czechoslovak Math. J.52 (2002), 255–273.
• [16] O.G.Xi,Fuzzy BCK-algebras Math.Japon.36 (1991),935 –942.
• [17] A.Walendziak, Nontrivial BCK/BCI-algebras do not satisfy the fuzzy ascending chain condition Fuzzy Sets and Systems 158 (2007), 922–923.