پیوندهای مفید
آمار
| تعداد نشریات | 31 |
| تعداد شمارهها | 484 |
| تعداد مقالات | 4,286 |
| تعداد مشاهده مقاله | 7,298,678 |
| تعداد دریافت فایل اصل مقاله | 4,896,188 |
Graph based on residuated lattices | ||
| Journal of Hyperstructures | ||
| دوره 3، شماره 1، شهریور 2014، صفحه 27-39 اصل مقاله (358.11 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2014.2571 | ||
| نویسندگان | ||
| L. Torkzadeh* 1؛ A. Ahadpanh2؛ M. Behzadi3 | ||
| 1Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran | ||
| 2Department of Mathematics, Kerman Science and Research Branch, Islamic Azad University, Kerman, Iran | ||
| 3Department of Mathematics,Kerman Science and Research Branch, Islamic Azad University, Kerman, Iran | ||
| چکیده | ||
| In this paper, the residuated graph of residuated lattices will be studied. To do so, the notion of zero divisors of a nonempty subset of a residuated lattice is first introduced and some related properties are investigated. By means of the set of all zerodivisors of an element of a residuated lattice L, the residuated graph Γ(L) is defined and several examples are given. This graph is connected and also some necessary conditions for the residuated graph to be a star graph are found. Finally, the relation between a residuated lattice L and the residuated graph Γ(L) are studied. | ||
| کلیدواژهها | ||
| Residuated lattice؛ Graph؛ zero divisors؛ Residuated graph | ||
| مراجع | ||
|
[1] T. Kowalski and H. Ono, Residuated lattices: an algebraic glimpse at logic without contraction, 2001 [2] P. Hajek, Metamathematics of Fuzzy Logic, Kluwer Academic Publishers, 1998. [3] R. Cingnoli, I.M.L. D’Ottaviano and D. Mundici , Algebraic Foundations of Many-valued Reasoning, Kluwer Academic publ., Dordrecht, 2000. [4] F. Esteva and L. Godo, Monoidal t-norm based logic, towards a logic for left-continuous t-norm, Fuzzy sets and systems, 124 (2001), 271-288. [5] M. Ward and R. P. Dilworth, Residueted Lattices, Trans. Am. Math. Soc. 45(1939), 335-354. [6] T. S. Blyth and M. F. Janowitz, Residuation Theory , Pergamon press, Oxford,New York, 1972. [7] G. Gratzer, Lattice Theory, First Concepts and Distributive Lattices, A Series of Books in Mathematics, San Francisco: W. H. Freeman and Company 1972. [8] U. Hohle, Commutative, residuated l-monoids, in: U. Hohle, E.P. Klement (Eds.), Non-Classical Logics and Their Applications to Fuzzy Subsets, Kluwer Academic Publishers, Boston, Dordrecht, 1995, 53-106. [9] I. Beck, Coloring of commutative rings, J. Algebra 116 (1988), no. 1, 208-226. [10] Y. B. Jun and K. J. Lee, Graphs based on BCK/BCI-algebras, Interna-tional Journal of Mathematices and Mathematical Sciences, vol.2011, Article ID 616981, 8 pages, 2011. [11] R. Diestel, Graph Theory, Springer-Verlag, New York, 1997. [12] A. Iorgulescu: Classes of BCK algebras-Part III, Preprint Series of The Institute of Mathematics of the Romanian Academy, preprint nr.3 (2004), 1-37. [13] A. Iorgulescu, On BCK-algebras - Part III: Classes of examples of proper MV - algebras, BL-algebras and divisible bounded residuated lattices, with or without condition (WNM), submitted. | ||
|
آمار تعداد مشاهده مقاله: 249 تعداد دریافت فایل اصل مقاله: 274 |
||