تعداد نشریات | 26 |
تعداد شمارهها | 553 |
تعداد مقالات | 5,713 |
تعداد مشاهده مقاله | 7,977,052 |
تعداد دریافت فایل اصل مقاله | 5,358,454 |
FUZZY EQUATIONAL CLASSES ARE FUZZY VARIETIES | ||
Iranian Journal of Fuzzy Systems | ||
مقاله 2، دوره 10، شماره 4، پاییز 2013، صفحه 1-18 اصل مقاله (440.06 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2013.1044 | ||
نویسندگان | ||
Branka Budimirovic1؛ Vjekoslav Budimirovic2؛ Branimir Seselja3؛ Andreja Tepavcevic ![]() | ||
1College for professional studies for teachers, Sabac, Serbia | ||
2College for professional studies for teachers,Sabac, Mega- trend University, Beograd, Serbia | ||
3Department of Mathematics and Informatics, University of Novi Sad, Novi Sad, Serbia | ||
چکیده | ||
In the framework of fuzzy algebras with fuzzy equalities and a complete lattice as a structure of membership values, we investigate fuzzy equational classes. They consist of special fuzzy algebras fullling the same fuzzy identities, dened with respect to fuzzy equalities. We introduce basic notions and the corresponding operators of universal algebra: construction of fuzzy subalgebras, homomorphisms and direct products. We prove that every fuzzy equational class is closed under these three operators, which means that such a class is a fuzzy variety. | ||
کلیدواژهها | ||
fuzzy algebra؛ Fuzzy identity؛ Fuzzy equality؛ Fuzzy homomorphism؛ Fuzzy direct product؛ Fuzzy equational class؛ Fuzzy variety | ||
مراجع | ||
[1] R. Belohlavek, Fuzzy relational systems: foundations and principles, Kluwer Academic/ Plenum Publishers, New York, 2002. [2] R. Belohlavek and V. Vychodil, Fuzzy equational logic, Studies in Fuzziness and Soft Computing, Springer 2005, 186 (2005). [3] R. Belohlavek and V. Vychodil, Algebras with fuzzy equalities, Fuzzy Sets and Systems, 157 (2006), 161-201. [4] A. Borumand Saeid, Interval-valued fuzzy B-algebras, Iranian Journal of Fuzzy Systems, 3(2) (2006), 63{73. [5] R. A. Borzooei and M. Bakhshi, Some properties of T-fuzzy generalized subgroups, Iranian Journal of Fuzzy Systems, 6(4) (2009), 73{87. [6] B. Budimirovic, V. Budimirovic, B. Seselja and A. Tepavcevic, Compatible fuzzy equalities and fuzzy identities, preprint. [7] B. Budimirovic, V. Budimirovic and A. Tepavcevic, Fuzzy "-subgroups, Information Sciences, 180 (2010), 4006-4014. [8] S. Burris and H. P. Sankappanavar, A course in universal algebra, Springer-Verlag, N. Y., 1981. [9] A. B. Chakraborty and S. S. Khare, Fuzzy homomorphism and algebraic structures, Fuzzy Sets and Systems, 59 (1993), 211{221. [10] P. S. Das, Fuzzy groups and level subgroups, J. Math. Anal. Appl., 84 (1981), 264-269. [11] M. Demirci, Vague groups, J. Math. Anal. Appl., 230 (1999), 142-156. [12] M. Demirci, Foundations of fuzzy functions and vague algebra based on many-valued equiva- lence relations part I: fuzzy functions and their applications, part II: vague algebraic notions, part III: constructions of vague algebraic notions and vague arithmetic operations, Int. J. General Systems, 32(3) (2003), 123-155, 157-175, 177-201. [13] A. Di Nola and G. Gerla, Lattice valued algebras, Stochastica, 11 (1987), 137-150. [14] L. Filep, Study of fuzzy algebras and relations from a general viewpoint, Acta Math. Acad. Paedagog. Nyhazi, 14 (1998), 49{55. [15] U. Hohle, Quotients with respect to similarity relations, Fuzzy Sets and Systems, 27 (1988), 31-44. [16] T. Kuraoka and N. Y. Suzuki, Lattice of fuzzy subalgebras in universal algebra, Algebra universalis, 47 (2002), 223{237. [17] X. Luo and J. Fang, Fuzzifying Closure Systems And Closure Operators, Iranian Journal of Fuzzy Systems, 8(1) (2011), 77{94. [18] J. N. Malik, D.S. Mordeson and N. Kuroki, Fuzzy Semigroups, Springer, 2003. [19] V. Murali, Fuzzy congruence relations, Fuzzy Sets and Systems, 41(1991), 359{369. [20] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 36 (1971), 512{517. [21] B. Seselja, Characterization of fuzzy equivalence relations and of fuzzy congruence relations on algebras, Review of Research Faculty of Science { University of Novi Sad, 11 (1981), 153{ 160. [22] B. Seselja, Homomorphisms of poset-valued algebras, Fuzzy Sets and Systems, 121 (2001), 333{340. [23] B. Seselja and A. Tepavcevic, Fuzzy Boolean algebras, Automated Reasoning, IFIP Transactions A-19, (1992), 83{88. [24] B. Seselja and A. Tepavcevic, Partially ordered and relational valued algebras and congru- ences, Review of Research, Faculty of Science, Mathematical Series, 23 (1993), 273{287. [25] B. Seselja and A. Tepavcevic, On generalizations of fuzzy algebras and congruences, Fuzzy Sets and Systems, 65 (1994), 85{94. [26] B. Seselja and A. Tepavcevic, Fuzzy groups and collections of subgroups, Fuzzy Sets and Systems, 83 (1996), 85{91. [27] B. Seselja and A. Tepavcevic, A note on fuzzy groups, YUJOR, 7(1) (1997), 49{54. [28] B. Seselja and A. Tepavcevic, Fuzzy identities, Proc. of the 2009 IEEE International Conference on Fuzzy Systems, 1660{1664. [29] A. P. Sostak, On a fuzzy topological structure, Frolk, Z., Soucek, V. and Vinarek, J. eds.: Proceedings of the 13th Winter School on Abstract Analysis. Section of Topology, Palermo, (1985), 89{103. [30] R. T. Yeh and S. Y. Bang, Fuzzy relations, fuzzy graphs, and their application to clyster- ing analysis, L. A. Zadeh, K. S. Fu, K. Tanaka, M. Shimura, eds.: Fuzzy Sets and Their Applications to Cognitive and Decision Processes, Academic Press, Inc., (1975), 125{149. | ||
آمار تعداد مشاهده مقاله: 2,905 تعداد دریافت فایل اصل مقاله: 1,441 |