×

Decision systems in rough set theory: a set operatorial perspective. (English) Zbl 1411.68155


MSC:

68T37 Reasoning under uncertainty in the context of artificial intelligence
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Adaricheva, K. V.; Gorbunov, V. A.; Tumanov, V. I., Join-semidistributive lattices and convex geometries, Adv. Math., 173, 1-49, (2003) · Zbl 1059.06003
[2] Andrews, G. E., Euler’s De Partitio numerorum, Bull. Amer. Math. Soc., 44, 4, 561-573, (2007) · Zbl 1172.11031
[3] Baker, M.; Norine, S., Riemann-Roch and Abel-Jacobi theory on a finite graph, Adv. Math., 215, 2, 766-788, (2007) · Zbl 1124.05049
[4] Bayley, R. A., Association Schemes: Designed Experiments, Algebra and Combinatorics, 387, (2004), Cambridge University Press: Cambridge University Press, Cambridge · Zbl 1051.05001
[5] Bayley, R. A., Orthogonal partitions in designed experiments, Designs, Codes Crypt., 8, 3, 45-77, (1996) · Zbl 0877.05006
[6] Berge, C., Hypergraphs: Combinatorics of Finite Sets, (1984), Elsevier: Elsevier, Amsterdam
[7] Biacino, L., Generated envelopes, J. Math. Anal. Appl., 172, 179-190, (1993) · Zbl 0777.60004
[8] Biacino, L.; Gerla, G., An extension principle for closure operators, J. Math. Anal. Appl., 198, 1-24, (1996) · Zbl 0855.54007
[9] Birkhoff, G., Lattice Theory, (1967), American Mathematical Society: American Mathematical Society, Providence, Rhode Island · Zbl 0126.03801
[10] Bisi, C.; Chiaselotti, G., A class of lattices and boolean functions related to the Manickam-Miklös-Singhi conjecture, Adv. Geom., 13, 1, 1-27, (2013) · Zbl 1259.05178
[11] Bisi, C.; Chiaselotti, G.; Marino, G.; Oliverio, P. A., A natural extension of the Young partition lattice, Adv. Geom., 15, 3, 263-280, (2015) · Zbl 1317.05018
[12] Bisi, C.; Chiaselotti, G.; Gentile, T.; Oliverio, P. A., Dominance order on signed partitions, Adv. Geom., 17, 1, 5-29, (2017) · Zbl 1383.05020
[13] Cameron, P. J.; Gadoleau, M.; Soren, R., Combinatorial representations, J. Combin. Theory Ser. A, 120, 3, 671-682, (2013) · Zbl 1259.05033
[14] Cattaneo, G.; Ciucci, D.; Peter, J. F.; Skowron, A., Special Issue on Foundations of Rough Sets, 3135, Algebraic structures for rough sets, 208-252, (2004), Springer-Verlag
[15] Cattaneo, G.; Ciucci, D.; Peter, J. F.; Skowron, A., Special Issue on Foundations of Rough Sets, 5656, Lattices with interior and closure operators and abstract approximation spaces, 67-116, (2009), Springer-Verlag
[16] Cattaneo, G., An investigation about rough set theory: Some foundational and mathematical aspects, Fund. Inf., 108, 197-221, (2011) · Zbl 1241.03060
[17] Cattaneo, G.; Chiaselotti, G.; Oliverio, P. A.; Stumbo, F., A new discrete dynamical system of signed integer partitions, European J. Combin., 55, 119-143, (2016) · Zbl 1333.05026
[18] Chartrand, G.; Eroh, L.; Johnson, M. A.; Oellermann, O. R., Resolvability in graphs and the metric dimension of a graph, Discrete Appl. Math., 105, 99-113, (2000) · Zbl 0958.05042
[19] Chiaselotti, G.; Keith, W.; Oliverio, P. A., Two self-dual lattices of signed integer partitions, Appl. Math. Inf. Sci., 8, 3191-3199, (2014)
[20] Chiaselotti, G.; Ciucci, D.; Gentile, T.; Infusino, F., Rough set theory applied to simple undirected graphs, Proc. RSKT 2015, 9436, 423-434, (2015), Springer
[21] Chiaselotti, G.; Ciucci, D.; Gentile, T.; Infusino, F., Preclusivity and simple graphs, Proc. RSFDGrC 2015, 9437, 127-137, (2015), Springer
[22] Chiaselotti, G.; Ciucci, D.; Gentile, T.; Infusino, F., Preclusivity and simple graphs: The \(n\)-cycle and \(n\)-path cases, Proc. RSFDGrC 2015, 9437, 138-148, (2015), Springer
[23] Chiaselotti, G.; Ciucci, D.; Gentile, T.; Infusino, F., Generalizations of rough set tools inspired by graph theory, Fund. Inf., 148, 207-227, (2016) · Zbl 1388.03045
[24] Chiaselotti, G.; Gentile, T., Intersection properties of maximal directed cuts in digraphs, Disc. Math., 340, 3171-3175, (2017) · Zbl 1347.05083
[25] Chiaselotti, G.; Ciucci, D.; Gentile, T.; Infusino, F., Rough set theory and digraphs, Fund. Inf., 153, 291-325, (2017) · Zbl 1400.05193
[26] Chiaselotti, G.; Gentile, T.; Infusino, F.; Oliverio, P. A., The adjacency matrix of a graph as a data table. A geometric perspective, Ann. Mat. Pur. Appl., 196, 3, 1073-1112, (2017) · Zbl 1366.05029
[27] Chiaselotti, G.; Gentile, T.; Infusino, F., Knowledge pairing systems in granular computing, Knowl. Based Syst., 124, 144-163, (2017)
[28] Chiaselotti, G.; Gentile, T.; Infusino, F., Simplicial complexes and closure systems induced by indistinguishability relations, C. R. Acad. Sci. Paris, Ser. I, 355, 991-1021, (2017) · Zbl 1371.05327
[29] Chiaselotti, G.; Gentile, T.; Infusino, F.; Oliverio, P. A., Dependency and accuracy measures for directed graphs, Appl. Math. Comput., 320, 781-794, (2018)
[30] Ciucci, D. E., Temporal dynamics in information tables, Fund. Inf., 115, 1, 57-74, (2012) · Zbl 1237.68212
[31] Doust, I.; Weston, A., Enhanced negative type for finite metric trees, J. Funct. Anal., 254, 9, 2336-2364, (2008) · Zbl 1148.46012
[32] Eiter, T.; Gottlob, G., Identifying the minimal transversals of a hypergraph and related problems, SIAM J. Comput., 24, 1278-1304, (1995) · Zbl 0842.05070
[33] Elbassioni, K., On the complexity of monotone dualization and generating minimal hypergraph transversals, Discr. Appl. Math., 32, 2, 171-187, (2008)
[34] Frolik, Z.; Katetov, M.; Ptak, V., General topology and its relations to modern analysis and algebra II, Proc. Second Prague Topological Symp., (1966), Academic Press: Academic Press, New York
[35] Gutev, V., Selections and topological convexity, Topology Appl., 155, 814-823, (2008) · Zbl 1144.54010
[36] Gyárfás, A.; Lehel, J., Hypergraph families with bounded edge cover or transversal number, Combinatorica, 3, 3-4, 351-358, (1983) · Zbl 0534.05052
[37] Hagen, M., Lower bounds for three algorithms for transversal hypergraph generation, Discr. Appl. Math., 157, 1460-1469, (2009) · Zbl 1177.05116
[38] Harley, P. W. III, Metric and symmetric spaces, Proc. Amer. Math. Soc., 43, 2, 428-430, (1974) · Zbl 0288.54031
[39] Hjorth, P.; Lisonek, P.; Markvorsen, S.; Thomassen, C., Finite metric spaces of strictly negative type, Linear Algebra Appl., 270, 255-273, (1998) · Zbl 0894.51003
[40] Keith, W. J., A bijective toolkit for signed partitions, Ann. Combin., 15, 95-117, (2011) · Zbl 1233.05031
[41] Martin, H. W., Metrization of symmetric spaces and regular maps, Proc. Amer. Math. Soc., 35, 269-274, (1972) · Zbl 0264.54023
[42] Magner, A.; Janson, S.; Kollias, G.; Szpankowski, W., On symmetry of uniform and preferential attachment graphs, Electronic J. Combin., 21, 3, (2014) · Zbl 1331.05197
[43] Michael, E., Convex structures and continuous selections, Canadian J. Math., 11, 556-575, (1959) · Zbl 0093.36603
[44] Pagliani, P.; Chakraborty, M. K., Formal Topology and Information Systems, Transactions on Rough Sets VI, 4374, 253-297, (2007), Springer-Verlag · Zbl 1186.68453
[45] Pagliani, P.; Chakraborty, M. K., A Geometry of Approximation, Rough Set Theory: Logic, Algebra and Topology of Conceptual Patterns, (2008), Springer · Zbl 1213.03002
[46] Z. Pawlak, Rough Sets — Theoretical Aspects of Reasoning about Data (Kluwer Academic Publishers, Dordrecht, 1991). · Zbl 0758.68054
[47] Pawlak, Z.; Skowron, A., Rudiments of rough sets, Inf. Sci., 177, 3-27, (2007) · Zbl 1142.68549
[48] Pawlak, Z.; Skowron, A., Rough sets: Some extensions, Inf. Sci., 177, 28-40, (2007) · Zbl 1142.68550
[49] Pawlak, Z.; Skowron, A., Rough sets and Boolean reasoning, Inf. Sci., 177, 41-73, (2007) · Zbl 1142.68551
[50] Pfaltz, J. L., Convexity in directed graphs, J. Combin. Theory, 10, 143-162, (1971) · Zbl 0174.26803
[51] Poonen, B., Union-closed families, J. Combin. Theory Ser. A, 59, 253-268, (1992) · Zbl 0758.05096
[52] Rota, G., On the foundations of combinatorial theory I. Theory of Möbius Functions, Z. Wahrs., 2, 340-368, (1964) · Zbl 0121.02406
[53] Sanahuja, S. M., New rough approximations for \(n\)-cycles and \(n\)-paths, Appl. Math. Comput., 276, 96-108, (2016) · Zbl 1410.68355
[54] Sánchez, S., On the supremal p-negative type of finite metric spaces, J. Math. Anal. Appl., 389, 98-107, (2012) · Zbl 1236.46018
[55] Ślezak, D., On generalized decision functions: Reducts, networks and ensembles, RSFDGrC, 13-23, (2015)
[56] Stawicki, S.; Ślezak, D.; Janusz, A.; Widz, S., Decision bireducts and decision reducts — a comparison, Int. J. Appr. Reas., 84, 75-109, (2017) · Zbl 1419.68178
[57] Tanga, J.; Shea, K.; Min, F.; Zhu, W., A matroidal approach to rough set theory, Theor. Comput. Sci., 471, 3, 1-11, (2013) · Zbl 1258.05022
[58] Wang, S.; Zhu, W.; Zhu, Q.; Min, F., Four matroidal structures of covering and their relationships with rough sets, Int. J. Appr. Reas., 54, 9, 1361-1372, (2013) · Zbl 1316.05025
[59] Wild, M., A theory of finite closure spaces based on implications, Adv. Math., 108, 118-139, (1994) · Zbl 0863.54002
[60] Wild, M., Computations with Finite Closure Systems and Implications, 959, 111-120, (1995), Springer
[61] Wild, M., Base exchange properties of graphic matroids, Discr. Math., 148, 1-3, 253-264, (1996) · Zbl 0846.05014
[62] Wild, M., Optimal implicational bases for finite modular lattices, Quaes. Math., 23, 153-161, (2000) · Zbl 0963.06006
[63] Wild, M., On rank functions of lattices, Order, 22, 4, 357-370, (2005) · Zbl 1105.06007
[64] Wild, M., Theoretical Computer Science, 658, The joy of implications, aka pure Horn formulas: Mainly a survey, 264-292, (2017), Springer · Zbl 1418.03144
[65] Wolf, R., On the gap of finite metric spaces of \(p\)-negative type, Linear Algebra Appl., 436, 1246-1257, (2012) · Zbl 1241.46014
[66] Xiang, S. W.; Xia, S., A further characteristic of abstract convexity structures on topological spaces, J. Math. Anal. Appl., 335, 716-723, (2007) · Zbl 1131.54034
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.