- Volume 29 Issue 3
After the introduction of fuzzy sets by Zadeh, there have been a number of generalizations of this fundamental concept. The notion of intuitionistic fuzzy sets introduced by Aranassov is one among them. In this paper, we apply the concept of an intuitionistic fuzzy set to implicative ideals in BCK-algebras. The notion of an intuitionistic fuzzy implicative ideal of a BCK-algebra is introduced, and some related properties are investigated. An extension property for intuitionistic fuzzy implicative ideals is established. Characterizations of an intuitionistic fuzzy implicative ideal are given. Conditions for an intuitionistic fuzzy ideal to be an intuitionistic fuzzy implicative ideal are given. Using a collection of implicative ideals, intuitionistic fuzzy implicative ideals are established.
(Implicative) ideal;intuitionistic fuzzy (implicative) ideal
- K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986), 87-96. https://doi.org/10.1016/S0165-0114(86)80034-3
- K. T. Atanassov, New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems 61 (1994), 137-142. https://doi.org/10.1016/0165-0114(94)90229-1
- K. T. Atanassov, Intuitionistic fuzzy sets. Theory and applications, Studies in Fuzziness and Soft Computing, 35. Heidelberg; Physica-Verlag 1999.
- D. W. Borns, J. M. Mack, An Algebraic Introduction to Mathematical Logic, Springer, Berlin, 1975.
B. Davvaz, W. A. Dudek and Y. B. Jun, Intuitionistic fuzzy
$H_v-submodules,$Inform. Sci. 176 (2006), 285-300. https://doi.org/10.1016/j.ins.2004.10.009
- E. Coskun, Systems on intuitionistic fuzzy special sets and intuitionistic fuzzy special measures, Inform. Sci. 128 (2000), 105-118. https://doi.org/10.1016/S0020-0255(00)00046-3
- Y. B. Jun and K. H. Kim, Intuitionistic fuzzy ideals of BCK -algebras, Internat. J. Math. & Math. Sci. 24(12) (2000), 839-849. https://doi.org/10.1155/S0161171200004610
- L. A. Zadeh, Fuzzy sets, Inform. and Control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
- L. A. Zadeh, Toward a generalized theory of uncertainty (GTU) - an outline, Inform. Sci. 172 (2005) 1-40. https://doi.org/10.1016/j.ins.2005.01.017