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Keywords:
MV-algebra; GMV-algebra; rough set; approximation space; normal ideal; congruence
MV-algebra; GMV-algebra; rough set; approximation space; normal ideal; congruence
Summary:
Generalized MV-algebras (= GMV-algebras) are non-commutative generalizations of MV-algebras. They are an algebraic counterpart of the non-commutative Łukasiewicz infinite valued fuzzy logic. The paper investigates approximation spaces in GMV-algebras based on their normal ideals.
References:
[1] Biswas, R., Nanda, S.: Rough groups and rough subgroups. Bull. Polish Acad. Sci., Math. 42 (1994), 251–254. MR 1811855 | Zbl 0834.68102
[2] Burris, S., Sankapanavar, H. P.: A Course in Universal Algebra. Springer-Verlag, New York, Heidelberg, Berlin, 1981. MR 0648287
[3] Cataneo, G., Ciucci, D.: Algebraic structures for rough sets. Lect. Notes Comput. Sci. 3135 (2004), 208–252. DOI 10.1007/978-3-540-27778-1_12
[4] Cignoli, R. L. O., D’Ottaviano, I. M. L., Mundici, D.: Algebraic Foundation of Many-valued Reasoning. Kluwer Acad. Publ., Dordrecht, Boston, London, 2000. MR 1786097
[5] Ciucci, D.: On the axioms of residuated structures independence dependencies and rough approximations. Fundam. Inform. 69 (2006), 359–387. MR 2350921 | Zbl 1100.06011
[6] Ciucci, D.: A unifying abstract approach for rough models. In: C., Wang, et al: RSKT 2008, 5009, Springer-Verlag, Heidelberg, 2008, 371–378.
[7] Davvaz, B.: Roughness in rings. Inform. Sci. 164 (2004), 147–163. DOI 10.1016/j.ins.2003.10.001 | MR 2076574 | Zbl 1072.16042
[8] Davvaz, B.: Roughness based on fuzzy ideals. Inform. Sci. 176 (2006), 2417–2437. DOI 10.1016/j.ins.2005.10.001 | MR 2247407 | Zbl 1112.03049
[9] Estaji, A. A., Khodaii, S., Bahrami, S.: On rough set and fuzzy sublattice. Inform. Sci. 181 (2011), 3981–3994. DOI 10.1016/j.ins.2011.04.043 | MR 2818650 | Zbl 1242.06008
[10] Georgescu, G., Iorgulescu, A.: Pseudo MV-algebras. Multi. Val. Logic 6 (2001), 95–135. MR 1817439 | Zbl 1014.06008
[11] Kondo, M., M.: Algebraic approach to generalized rough sets. In: D., Slezak, et al: RSFDGrC 2005, LNAI, 5009, Springer-Verlag, Berlin, Heidelberg, 2005, 132–140. MR 2167787 | Zbl 1134.68509
[12] Kuroki, N.: Rough ideals in semigroups. Inform. Sci. 100 (1997), 139–163. DOI 10.1016/S0020-0255(96)00274-5 | MR 1446627 | Zbl 0916.20046
[13] Leoreanu-Fotea, V., Davvaz, B.: Roughness in n-ary hypergroups. Inform. Sci. 178 (2008), 4114–4124. DOI 10.1016/j.ins.2008.06.019 | MR 2454652 | Zbl 1187.20071
[14] Leuştean, I.: Non-commutative Łukasiewicz propositional logic. Arch. Math. Logic 45 (2006), 191–213. DOI 10.1007/s00153-005-0297-8 | MR 2209743 | Zbl 1096.03020
[15] Li, T. J., Leung, Y., Zhang, W. X.: Generalized fuzzy rough approximation operators based on fuzzy coverings. Int. J. Approx. Reason. 48 (2008), 836–856. DOI 10.1016/j.ijar.2008.01.006 | MR 2437954 | Zbl 1186.68464
[16] Li, X., Liu, S.: Matroidal approaches to rough sets via closure operators. Inter. J. Approx. Reason. 53 (2012), 513–527. MR 2903082 | Zbl 1246.68233
[17] Liu, G. L., Zhu, W.: The algebraic structures of generalized rough set theory. Inform. Sci. 178 (2008), 4105–4113. DOI 10.1016/j.ins.2008.06.021 | MR 2454651 | Zbl 1162.68667
[18] Pawlak, Z.: Rough sets. Inter. J. Inf. Comput. Sci. 11 (1982), 341–356. MR 0703291 | Zbl 0525.04005
[19] Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. System Theory, Knowledge Engineering and Problem Solving 9, Kluwer Academic Publ., Dordrecht, 1991. Zbl 0758.68054
[20] Pawlak, Z., Skowron, A.: Rudiments of rough sets. Inform. Sci. 177 (2007), 3–27. DOI 10.1016/j.ins.2006.06.003 | MR 2272732 | Zbl 1142.68549
[21] Pawlak, Z., Skowron, A.: Rough sets: some extensions. Inform. Sci. 177 (2007), 28–40. DOI 10.1016/j.ins.2006.06.006 | MR 2272733 | Zbl 1142.68550
[22] Pawlak, Z., Skowron, A.: Rough sets and Boolean reasoning. Inform. Sci. 177 (2007), 41–73. DOI 10.1016/j.ins.2006.06.007 | MR 2272734 | Zbl 1142.68551
[23] Pei, D.: On definable concepts of rough set models. Inform. Sci. 177 (2007), 4230–4239. DOI 10.1016/j.ins.2007.01.020 | MR 2346788 | Zbl 1126.68076
[24] Rachůnek, J.: A non-commutative generalization of MV-algebras. Czechoslovak Math. J. 52 (2002), 255–273. DOI 10.1023/A:1021766309509 | MR 1905434 | Zbl 1012.06012
[25] Radzikowska, A. M., Kerre, E. E.: Fuzzy rough sets based on residuated lattices. In: Transactions on Rough Sets II, Lecture Notes in Computer Sciences, 3135, Springer-Verlag, Berlin, Heidelberg, 2004, 278–296. Zbl 1109.68118
[26] Rasouli, S., Davvaz, B.: Roughness in MV-algebras. Inform. Sci. 180 (2010), 737–747. DOI 10.1016/j.ins.2009.11.008 | MR 2574551 | Zbl 1194.06009
[27] She, Y. H., Wang, G. J.: An approximatic approach of fuzzy rough sets based on residuated lattices. Comput. Math. Appl. 58 (2009), 189–201. DOI 10.1016/j.camwa.2009.03.100 | MR 2535981
[28] Xiao, Q. M., Zhang, Z. L.: Rough prime ideals and rough fuzzy prime ideals in semigroups. Inform. Sci. 176 (2006), 725–733. DOI 10.1016/j.ins.2004.12.010 | MR 2201320 | Zbl 1088.20041
[29] Yang, L., Xu, L.: Algebraic aspects of generalized approximation spaces. Int. J. Approx. Reason. 51 (2009), 151–161. DOI 10.1016/j.ijar.2009.10.001 | MR 2565213 | Zbl 1200.06004
[30] Zhu, P.: Covering rough sets based on neighborhoods: An approach without using neighborhoods. Int. J. Approx. Reason. 52 (2011), 461–472. DOI 10.1016/j.ijar.2010.10.005 | MR 2771972 | Zbl 1229.03047
[31] Zhu, W.: Relationship between generalized rough set based on binary relation and covering. Inform. Sci. 179 (2009), 210–225. DOI 10.1016/j.ins.2008.09.015 | MR 2473013
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