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T-FUZZY CONGRUENCES AND T-FUZZY FILTERS OF A BL-ALGEBRA | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 6، دوره 6، شماره 4، اسفند 2009، صفحه 37-47 اصل مقاله (196 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2009.533 | ||
| نویسندگان | ||
| Rajab Ali Borzooei* 1؛ Mahmood Bakhshi2 | ||
| 1Department of Mathematics, Shahid Beheshti University, Tehran, Iran | ||
| 2Department of Mathematics, Bojnord University, Bojnord, Iran | ||
| چکیده | ||
| In this note, we introduce the concept of a fuzzy filter of a BLalgebra, with respect to a t-norm briefly, T-fuzzy filters, and give some related results. In particular, we prove Representation Theorem in BL-algebras. Then we generalize the notion of a fuzzy congruence (in a BL-algebra) was defined by Lianzhen et al. to a new fuzzy congruence, specially with respect to a tnorm. We prove that there is a correspondence bijection between the set of all T-fuzzy filters of a BL-algebra and the set of all T-fuzzy congruences in that BL-algebra. Next, we show how T-fuzzy filters induce T-fuzzy congruences, and construct a new BL-algebras, called quotient BL-algebras, and give some homomorphism theorems. | ||
| کلیدواژه‌ها | ||
| T-fuzzy filter؛ T-fuzzy congruence | ||
| مراجع | ||
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[1] M. Bakhshi and R. A. Borzooei, Lattice structure of fuzzy congruence relations on a hypergroupoid, Inform. Sci., 177(16) (2007), 3305-3316. [2] M. Bakhshi, M. Mashinchi and R. A. Borzooei, Representation of fuzzy structures, International Review of Fuzzy Mathematics, 1(1) (2006), 73-87. [3] C. C. Chang, Algebraic analysis of many valued logics, Trans. Amer. Math. Soc., 88 (1958), 467-490. [4] P. H´ajek, Metamathematics of fuzzy logic, Klower Academic Publishers, Dordrecht, 1998. [5] E. P. Klement and R. Mesiar, Logical, algebraic, analytic and probabilistic aspects of triangular norms, Elsevier, Netherlands, 2005. [6] L. Liu and K. Li, Fuzzy filters of BL-algebras, Inform. Sci., 173 (2005), 141-154. [7] L. Liu and K. Li, Fuzzy Boolean and positive implicative filters of BL-algebras, Fuzzy Sets and Systems, 152 (2005), 333-348. [8] V. Murali, Fuzzy congruence relations, Fuzzy Sets and Systems., 29 (1984), 391-394. [9] E. Turunen, BL-algebras and basic fuzzy logic, Mathware and Soft Computing, 6 (1999), 49-61. [10] E. Turunen, Boolean deductive systems of BL-algebras, Arch. Math. Logic, 40 (2001), 467- 473. | ||
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