
تعداد نشریات | 33 |
تعداد شمارهها | 771 |
تعداد مقالات | 7,477 |
تعداد مشاهده مقاله | 12,474,391 |
تعداد دریافت فایل اصل مقاله | 8,478,599 |
Semi-G-filters, Stonean filters, MTL-filters, divisible filters, BL-filters and regular filters in residuated lattices | ||
Iranian Journal of Fuzzy Systems | ||
مقاله 11، دوره 13، شماره 1، اردیبهشت 2016، صفحه 145-160 اصل مقاله (379.32 K) | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2016.2294 | ||
نویسندگان | ||
D. Busneag* 1؛ D. Piciu2 | ||
1Department of Mathematics, Faculty of Mathematics and Natural Sci- ences, University of Craiova, Craiova, Romania | ||
2Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Craiova, Craiova, Romania | ||
چکیده | ||
At present, the filter theory of $BL$textit{-}algebras has been widely studied, and some important results have been published (see for example cite{4}, cite{5}, cite{xi}, cite{6}, cite{7}). In other works such as cite{BP}, cite{vii}, cite{xiii}, cite{xvi} a study of a filter theory in the more general setting of residuated lattices is done, generalizing that for $BL$textit{-}algebras. Note that filters are also characterized by various types of fuzzy sets. Most of such characterizations is trivial but some are nontrivial, for example characterizations obtained in cite{xm}. Both situation have revealed a rich range of classes of filters: Boolean, implicative, Heyting, positive implicative, fantastic (or MV-filter), etc. In this paper we work in the general cases of residuated lattices and put in evidence new types of filters in a residuated lattice (in the spirit of cite {mvl}): semi-G-filterstextit{, }Stonean filters, divisible filters, BL-filters and regular filters. | ||
کلیدواژهها | ||
residuated lattice؛ Boolean algebra؛ BL-algebra؛ MV-algebra؛ MTL-algebra؛ Divisible residuated lattice؛ Regular residuated lattice؛ Deductive system؛ Filter؛ Boolean filter؛ MTL-filter؛ Divisible filter؛ BL-filter؛ MV-filter؛ Semi-G-filter؛ Stonean filter؛ Regular filter | ||
مراجع | ||
[1] R. Balbes and Ph. Dwinger, Distributive lattices, University of Missouri Press, 1974. [2] W. J. Blok and D. Pigozzi, Algebraizable logics, Memoirs of the American Mathematical Society, Amer. Math. Soc, Providence, 396 (1989). [3] K. Blount and C. Tsinakis, The structure of residuated lattices, Internat. J. Algebra Comput., 13(4) (2003), 437-461. [4] D. Busneag and D. Piciu, Some types of lters in residuated lattices, Soft Comput., 18(5) (2014), 825-837. [5] D. Busneag and D. Piciu, A new approach for classication of lters in residuated lattices, Fuzzy Sets and Systems, 260 (2015), 121-130. [6] D. Busneag, D. Piciu and L. Holdon, Some properties of ideals in Stonean Residuated Lattices, J. Multi-Valued Logic & Soft Computing, 24(5-6) (2015), 529-546. [7] D. Busneag, D. Piciu and J. Paralescu, Divisible and semi-divisible residuated lattices, Ann. St. Univ. Al. I. Cuza, Iasi, Matematica (S.N.), doi:10.2478/aicu-2013-0012, (2013), 14-45. [8] C. C. Chang, Algebraic analysis of many-valued logic, Trans. Amer. Math. Soc., 88 (1958), 467-490. [9] L. Chun-hui and X. Luo-shan, On -Ideals and lattices of -Ideals in regular residuated lattices, In B.-Y. Cao et al. (Eds.): Quantitative Logic and Soft Computing (2010), AISC 82, 425-434. [10] R. Cignoli, I. M. L. D'Ottaviano and D. Mundici, Algebraic foundations of many-valued reasoning, Trends in Logic-Studia Logica Library 7, Dordrecht: Kluwer Academic Publishers (2000). [11] R. P. Dilworth, Non-commutative residuated lattices, Trans. Amer. Math. Soc., 46 (1939), 426-444. [12] P. Hajek, Metamathematics of fuzzy logic, Trends in Logic-Studia Logica Library 4, Dordrecht: Kluwer Academic Publishers (1998). [13] M. Haveshki, A. Borumand Saeid and E. Eslami, Some types of lters in BL-algebras, Soft Comput., 10 (2010), 657-664. [14] U. Hohle, Commutative residuated monoids, In: U. Hohle, P. Klement (eds), Non-classical Logics and Their Aplications to Fuzzy Subsets, Kluwer Academic Publishers, (1995). [15] P. M. Idziak, Lattice operations in BCK-algebras, Math. Japonica, 29 (1984), 839-846. [16] A. Iorgulescu, Algebras of logic as BCK algebras, Ed. ASE, Bucuresti, 2008. [17] M. Kondo and W. A. Dudek, Filter theory of BL-algebras, Soft Comput., 12 (2008), 419-423. [18] W. Krull, Axiomatische Begrundung der allgemeinen Ideal theorie, Sitzungsberichte der physikalisch medizinischen Societad der Erlangen, 56 (1924), 47-63. [19] L. Lianzhen and L. Kaitai, Boolean lters and positive implicative lters of residuated lattices, Inf. Sciences, 177 (2007), 5725-5738. [20] X. Ma, J. Zhan and W. A. Dudek, Some kinds of (; _ q)-fuzzy lters of BL-algebras, Computers and Mathematics with Applications, 58 (2009), 248-256. [21] M. Okada and K. Terui, The nite model property for various fragments of intuitionistic linear logic, Journal of Symbolic Logic, 64 (1999), 790-802. [22] J. Pavelka, On fuzzy logic II. Enriched residuated lattices and semantics of propositional calculi, Zeitschrift fur mathematische Logik und Grundlagen der Mathematik, 25 (1979), 119-134. [23] D. Piciu, Algebras of fuzzy logic, Ed. Universitaria, Craiova (2007). [24] E. Turunen, Boolean deductive systems of BL algebras, Arch. Math. Logic, 40 (2001). [25] E. Turunen, Mathematics behind fuzzy logic, Physica-Verlag (1999). [26] B. Van Gasse, G. Deschrijver, C. Cornelis and E. E. Kerre, Filters of residuated lattices and triangle algebras, Inf. Sciences, 180(16) (2010), 3006-3020. [27] M. Ward, Residuated distributive lattices, Duke Mathematcal Journal, 6 (1940), 641-651. [28] M. Ward and R. P. Dilworth, Residuated lattices, Trans. Amer. Math. Soc., 45 (1939), 335- 354. [29] M. A. Zhenming, MTL -lters and their characterization in residuated lattices, Computer Engineering and Applications, 48(20) (2012), 64-66. [30] Y. Zhu and Y. Xu, On lter theory of residuated lattices, Inf. Sciences, 180 (2010), 3614-3632. | ||
آمار تعداد مشاهده مقاله: 2,185 تعداد دریافت فایل اصل مقاله: 731 |