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SOME QUOTIENTS ON A BCK-ALGEBRA GENERATED BY A FUZZY SET | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 4، دوره 1، شماره 2، دی 2004، صفحه 33-43 اصل مقاله (186.89 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2004.503 | ||
| نویسندگان | ||
| Abbas Hasankhani* 1؛ Hamid Saadat2 | ||
| 1Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran | ||
| 2Islamic Azad University Science and Research Campus, Kerman, Iran | ||
| چکیده | ||
| First we show that the cosets of a fuzzy ideal μ in a BCK-algebra X form another BCK-algebra X/μ (called the fuzzy quotient BCK-algebra of X by μ). Also we show that X/μ is a fuzzy partition of X and we prove several some isomorphism theorems. Moreover we prove that if the associated fuzzy similarity relation of a fuzzy partition P of a commutative BCK-algebra is compatible, then P is a fuzzy quotient BCK-algebra. Finally we define the notion of a coset of a fuzzy ideal and an element of a BCK-algebra and prove related theorems. | ||
| کلیدواژهها | ||
| Fuzzy similarity relations؛ Fuzzy partitions؛ Fuzzy quotient؛ Fuzzy ideal؛ Cosets؛ Quotient algebra | ||
| مراجع | ||
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[1] A. Hasankhani, F-Spectrum of a BCK-algebra, J. Fuzzy Math. Vol. 8, No. 1 (2000), 1-11. [2] V. Hohle, Quotients with respect to similarity relations, Fuzzy sets and systems 27 (1988), 31-44. [3] C. S. Hoo, Fuzzy ideal of BCI and MV-algebra, Fuzzy sets and Systems 62 (1994), 111-114. [4] Y. Imai and K. Iseki, On axiom systems of propositional calculi, XIV. Proc. Jopan Academy, 42 (1966), 19-22. [5] K. Iseki, On ideals in BCK-algebra, Math. Seminar Notes, 3 (1975), Kobe University. [6] K. Iseki, Some properties of BCK-algebra, 2 (1975), xxxv, these notes. [7] K. Iseki and S. Tanaka, Ideal theory of BCK-algebra, Math. Japonica, 21 (1976), 351-366. [8] K. Iseki and S. Tanaka, An introduction to the theory of BCK-algrba, Math. Japonica, 23 (1978), 1-26. [9] W. J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy sets and Systems 8 (1982), 133-139. [10] S. Ovchinnikov, Similarity relations, fuzzy partitions, and fuzzy ordering, Fuzzy sets and system, 40 (1991), 107-126. [11] O. Xi, Fuzzy BCK-algebra, Math. Japonica, 36 (1991), 935-942. [12] L. A. Zadeh, Similarity relations and fuzzy ordering, Inform. Sci. 3 (1971), 177-200. [13] L. A. Zadeh, Fuzzy sets, Information and control, 8 (1965), 338-353. | ||
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