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Certain information granule system as a result of sets approximation by fuzzy context. (English) Zbl 1460.68107
Summary: This paper presents the application of abstraction methods in creating concepts that allow to describe and solve more complex problems of knowledge representation in semantic networks. In the Semantic Web, knowledge is represented by the attributive language AL. There are many information granules theories formulated in different theories such as set theory, probability theory, possible data sets in the evidence systems, shadowed sets, fuzzy set theory, and rough set theory. In order to equally interpret AL language expressions in different information granules theories within the Semantic Web, it is assumed that AL language expressions are interpreted in the chosen relational system called a granule system. This paper formally describes information granule system and shows the example how to formulate such granule system in the theory of the contextual rough sets [E. Bryniarski and U. Wybraniec-Skardowska, J. Appl. Non-Class. Log. 8, No. 1–2, 9–26 (1998; Zbl 0957.03052)] which describes inclusions of fuzzy context relations with some error. Defined granule system allows to interpret AL languages. It is shown that there is such subsystem of this granule system that is adequate i.e. it is homomorphic within some ordered set algebra.

MSC:
68T37 Reasoning under uncertainty in the context of artificial intelligence
68T30 Knowledge representation
Software:
PR-OWL
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[1] (Baader, F.; Calvanese, D.; McGuinness, D.; Nardi, D.; Patel-Schneider, P., The Description Logic. Handbook Theory, Implementation and Application (2003), Cambridge University Press: Cambridge University Press Cambridge) · Zbl 1058.68107
[2] Blass, A. C.; Childs, D. L., Axioms and Models for an Extended Set Theory (2011), University of Michigan
[3] Blizard, W. D., Multiset Theory, Notre Dame J. Form. Log., 30, 1, 36-66 (1989) · Zbl 0668.03027
[4] Bobillo, F.; Straccia, U., Fuzzy Description Logics with general t-norms and datatypes, Fuzzy Sets Syst., 160, 23, 3382-3402 (2009) · Zbl 1192.68659
[5] Bobillo, F.; Laskey, K. J.; Martin, T.; Nickles, M., Uncertainty reasoning for the Web, Int. J. Approx. Reason., 93, 327-329 (2018) · Zbl 1412.00033
[6] Bonikowski, Z.; Bryniarski, E.; Wybraniec-Skardowska, U., Rough pragmatic description logic, (Skowron, A.; Suraj, Z., Rough Sets and Intelligent Systems - Professor Zdzisław Pawlak in Memoriam, vol. 2 (2013), Springer: Springer Berlin, Heidelberg, New York), 157-184 · Zbl 1327.68246
[7] Bryniarska, A., The paradox of the fuzzy disambiguation in the information retrieval, (IJARAI) Int. J. Adv. Res. Art. Intell., 2, 9, 55-58 (2013)
[8] Bryniarska, A., The model of possible web data retrieval, (Proceedings of 2nd IEEE International Conference on Cybernetics. Proceedings of 2nd IEEE International Conference on Cybernetics, CYBCONF 2015 (2015)), 348-353
[9] Bryniarska, A.; Bryniarski, E., Rough search of vague knowledge, (Wang, G.; Skowron, A.; Yao, Y.; Slezak, D.; Polkowski, L., Thriving Rough Sets-10th Anniversary - Honoring Professor Zdzislaw Pawlak’s Life and Legacy & 35 years of Rough Sets, Studies in Computational Intelligence (2017), Springer: Springer Berlin, Heidelberg ,New York), 283-310
[10] Bryniarska, A., Autodiagnosis of information retrieval on the web as a simulation of selected processes of consciousness in the human brain, (Hunek, W. P.; Paszkiel, S., Biomedical Engineering and Neuroscience. Biomedical Engineering and Neuroscience, Advances in Intelligent Systems and Computing, vol. 720 (2018), Springer), 111-120
[11] Bryniarski, E., A calculus of rough sets of the first order, Bull. Pol. Acad., Math., 37, 109-136 (1989)
[12] Bryniarski, E., Formal conception of rough sets, Fundam. Inform., 27, 2-3, 103-108 (1996) · Zbl 0863.03028
[13] Bryniarski, E.; Wybraniec-Skardowska, U., Genaralized rough sets in contextual spaces, (Lin, T. Y.; Part, I. V., Rought Sets on Data Mining, Part IV. Chapter 17 (1997), Kluwer Academic Publisher), 335-360
[14] Bryniarski, E.; Wybraniec-Skardowska, U., Calculus of contextual rough sets in contextual spaces, J. Appl. Non-Class. Log., 8, 9-26 (1998) · Zbl 0957.03052
[15] Carvalho, R. N.; Laskey, K. B.; Costa, P. C.G., PR-OWL - a language for defining probabilistic ontologies, Int. J. Approx. Reason., 91, 56-79 (2017) · Zbl 1419.68141
[16] Moore, R., Interval Analysis (1966), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0176.13301
[17] Lai, H.; Zhang, D., Concept lattices of fuzzy contexts: formal concept analysis vs. rough set theory, Int. J. Approx. Reason., 50, 695-707 (2009) · Zbl 1191.68658
[18] Li, J.; Kumar Cherukuri, Aswani; Mei, Changlin; Wang, Xizhao, Comparison of reduction in formal decision contexts, Int. J. Approx. Reason., 80, 100-122 (2017) · Zbl 1400.68208
[19] Li, J.; Mei, C.; Lv, Y., Incomplete decision contexts: approximate concept construction, rule acquisition and knowledge reduction, Int. J. Approx. Reason., 54, 1, 149-165 (2013) · Zbl 1266.68172
[20] Li, J.; Mei, C.; Xu, W.; Qian, Y., Concept learning via granular computing: a cognitive viewpoint, Inf. Sci., 298, 447-467 (2015) · Zbl 1360.68688
[21] Li, J.; Huang, C.; Qi, J.; Qian, Y.; Liu, W., Three-way cognitive concept learning via multi-granularity, Inf. Sci., 378, 244-263 (2017)
[22] Pawlak, Z., Rough sets, Int. J. Comput. Inf. Sci., 11, 341-356 (1982) · Zbl 0501.68053
[23] Pawlak, Z., Rough Sets. Theoretical Aspects of Reasoning About. Data (1991), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0758.68054
[24] Pawlak, Z.; Skowron, A., Rudiments of rough sets, Inf. Sci., 177, 1, 3-27 (2007) · Zbl 1142.68549
[25] Pawlak, Z.; Skowron, A., Rough sets and Boolean reasoning, Inf. Sci., 177, 1, 41-73 (2007) · Zbl 1142.68551
[26] Pedrycz, W., Shadowed sets: representing and processing fuzzy sets, IEEE Trans. Syst. Man Cybern., Part B, 28, 103-109 (1998)
[27] Pedrycz, W., Knowledge-Based Clustering: From Data to Information Granules (2005), J. Wiley: J. Wiley Hoboken, NJ · Zbl 1100.68096
[28] Pedrycz, W., Allocation of information granularity in optimization and decision-making models: towards building the foundations of Granular Computing, Eur. J. Oper. Res., 232, 1, 137-145 (2014)
[29] Schoenfisch, J.; Stuckenschmidt, H., Analyzing real-world SPARQL queries and ontology-based data access in the context of probabilistic data, Int. J. Approx. Reason., 90, 374-388 (2017) · Zbl 1419.68147
[30] Tsichritzis, D. C.; Lochovsky, F., Data Models (1982), Published by Prentice Hall, Inc.: Published by Prentice Hall, Inc. Englewood Cliffs, New Jersey, USA · Zbl 0327.68050
[31] Vopěnka, P., Mathematics in the Alternative Set Theory (1979), Teubner: Teubner Leipzig · Zbl 0499.03042
[32] Wille, R., Restructuring lattice theory: an approach based on hierarchies of concepts, (Rival, I., Ordered Sets (1982), Reidel: Reidel Dordrecht-Boston), 445-470
[33] Yao, Y. Y., Interval sets and three-way concept analysis in incomplete contexts, Int. J. Mach. Learn. Cybern., 8, 1, 3-20 (2017)
[34] Yao, Y. Y., Rough-set concept analysis: interpreting RS-definable concepts based on ideas from formal concept analysis, Inf. Sci., 346-347, 442-462 (2016) · Zbl 1398.68524
[35] Zadeh, L. A., Fuzzy sets, Inf. Control, 8, 3, 338-353 (1965) · Zbl 0139.24606
[36] Zadeh, L. A., Towards a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic, Fuzzy Sets Syst., 90, 111-117 (1997) · Zbl 0988.03040
[37] Zadeh, L. A., Toward a generalized theory of uncertainty (GTU) - an outline, Inf. Sci., 172, 1-40 (2005) · Zbl 1074.94021
[38] Zhi, H.; Li, J., Granule description based on formal concept analysis, Knowl.-Based Syst., 104, 62-73 (2016)
[39] Zhi, H.; Li, J., Granule description based on positive and negative attributes, Granular Comput. (2018)
[40] Ziarko, W., Variable precision rough set model, J. Comput. Syst. Sci., 46, 39-59 (1993) · Zbl 0764.68162
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