PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2015 | 13 | 1 |
Tytuł artykułu

Generalized co-annihilator of BL-algebras

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In BL-algebras we introduce the concept of generalized co-annihilators as a generalization of coannihilator and the set of the form x-1F where F is a filter, and study basic properties of generalized co-annihilators. We also introduce the notion of involutory filters relative to a filter F and prove that the set of all involutory filters relative to a filter with respect to the suit operations is a complete Boolean lattice and BL-algebra. We use the technology of generalized co-annihilators to give characterizations of prime filters and minimal prime filters, respectively. In particular, we give a representation of co-annihilators in the quotient algebra of a BL-algebra L via a filter F by means of generalized co-annihilators relative to F in L:
Wydawca
Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
otrzymano
2014-11-26
zaakceptowano
2015-09-15
online
2015-10-19
Twórcy
  • Department of Mathematics, Northwest University, Xi’an, P.R.China and College of Science,
    Xi’an University of Science and Technology, Xi’an, P.R.China
  • mengbl_100@139.com
    Xiao Long Xin:
Bibliografia
  • [1] Cignoli R., Esteva F., Godo L., Torrens A., Basic Fuzzy Logic is the Logic of Continuous T -norm and Their Residua, SoftComput., 2000, 12, 106-112.[Crossref]
  • [2] Dvure´censkij A., State on PseudoMV -algebras, Stud Log., 2001a , 68, 301-327.
  • [3] Dvure´censkij A., On PseudoMV -algebras, Soft Comput., 2001b, 5, 347-354.[Crossref]
  • [4] Dvure´censkij A., Every liner Pseudo BL-algebra admits a state, Soft Comput., 2007, 11, 347-354.[WoS]
  • [5] Flonder P., Georgescu G., Iorgulescu A., Psedo t-norms and Pseudo BL-algebras, Soft Comput., 2001, 5, 355-371.[WoS][Crossref]
  • [6] Georgescu G., Iorgulescu A., Pseudo BL-algebras, Mult Valued Log., 2001, 6, 95-135.
  • [7] Georgescu G., Leustean L., Some class of Pseudo BL-algebras, J. Aust Math Soc., 2002, 73, 127-153.[Crossref]
  • [8] HKajek P., Metamathematics of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht, 1998.
  • [9] Haveshki M., Saeid A B., Eslami E., Some types of filters in BL-algebras, Soft Computing, 2006, 10, 657-664.[WoS][Crossref]
  • [10] Iorgulescu A., Iséki algebras, Connection with BL-algebras, Soft Computing, 2004, 8, 449-463.[Crossref][WoS]
  • [11] Nola A D., Georgescu G., Iorgulescu A., Boolean products of BL-algebras, J. Math Anal Appl, 2000, 251, 106-131.
  • [12] Nola A D., Georgescu G., Iorgulescu A., Pseudo BL-algebras: Part I,II, Mult Valued Log., 2002, 8, 673-714, 715-750.
  • [13] Nola A D., Leustean L., Compact representations of BL-algebras, Arch Math Log., 2003, 42, 737-761.[Crossref]
  • [14] Kondo M., Dudek W A., Filter Theory in BL-algebras, Soft Comput., 2008, 12, 419-423.[WoS][Crossref]
  • [15] Leu¸stean L., Representations of Many-valued Algebras Ph.D. Thesis, University of Bucharest, Faculty of Mathematics andComputer Science, Roumania, 2003.
  • [16] Saeid A B., Motamed S., Normal Filters in BL-Algebras, World Applied Sciences Journal (Special Issue for Applied Math), 2009,7, 70-76.
  • [17] Saeid A B., Ahadpanah A., Torkzadeh L., Smarandache BL-Algebras, J. Applied Logic, 2010, 8, 253-261.
  • [18] Turunen E., Mathematics behind Fuzzy Logic, Advances in Soft Computing, Heidelberg: Physica-Verlag, 1999.
  • [19] Turunen E., BL-algebras of Basic Fuzzy Logic, Mathware & Soft Comp., 1999, 6, 49-61.
  • [20] Turunen E., Boolean Deductive Systems of BL-algebras, Arch Math Logic, 2001, 40, 467-473.[Crossref]
  • [21] Turunen E., Sessa S., Local BL-algebras, Mult-Valued Logic, 2001, 6, 229-249.
  • [22] Zhang X H., Jun Y B., Doh M I., On Fuzzy Filters and Fuzzy Ideals of BL-algebras, Fuzzy Systems & Math, 2006, 20, 8-20.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2015-0060
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.