Relational Contexts and Relational Concepts

• Autorzy: Jiang F. , Sui Y. , Cao C.
• Języki publikacji: EN

Abstrakty

EN

Formal concept analysis (FCA) is a mathematical description and theory of concepts implied in formal contexts. And the current formal contexts of FCA aim to model the binary relations between individuals (objects) and attributes in the real world. In the real world we usually describe each individual by some attributes, which induces the relations between individuals and attributes. But there also exist many relations between individuals, for instance, the parent-children relation in a family. In this paper, to model the relations between individuals in the real world, we propose a new context - relational context for FCA, which contains a set U of objects and a binary relation r on U. Corresponding to the formal concepts in formal contexts, we present different kinds of relational concepts in relational contexts, which are the pairs of sets of objects. First we define the standard relational concepts in relational contexts. Moreover, we discuss the indirect relational concepts and negative relational concepts in relational contexts, which aim to concern the indirection and negativity of the relations in relational contexts, respectively. Finally, we define the hybrid relational concepts in relational contexts, which are the combinations of any two different kinds of relational concepts. In addition, we also discuss the application of relational contexts and relational concepts in the supply chain management field.

Słowa kluczowe

EN

formal concept analysis; FCA; formal contexts; relational contexts; concept lattices; supply chain

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2010
• Tom: Vol. 99, nr 3
• Strony: 293--314
• Opis fizyczny: Bibliogr. 35 poz., tab., wykr.

Twórcy

autor

Jiang F.

autor

Sui Y.

autor

Cao C.

• College of Information Science and Technology, Qingdao University of Science and Technology, 69#, Songling Road, Laoshan District, Qingdao, Shandong, 266061, P. R. China.,

Bibliografia

• [1] Burusco, A., Fuentes-González, R.: The study of L-fuzzy concept lattice. Mathware & Soft Computing, 3, 1994, 209-218.
• [2] Chen, I. J., Paulraj, A.: Towards a theory of supply chain management: the constructs and measurements. Journal of Operations Management, 22, 2004, 119-150.
• [3] Christopher,M. G. (Ed.): Logistics and supply chainmanagement: steategies for reducing costs and improving sevices. London: Pitman Publishing, 1998.
• [4] Danese, P., Romano, P., Vinelli, A.:Managing business processes across supply networks: the role of coordination mechanisms. Journal of Purchasing & Supply Management, 10, 165-177.
• [5] Eklund, P. W., Martin, P.: WWW indexation and document navigation using conceptual structures. In: Proc. of the 2nd IEEE Conference on Intelligent Information Processing Systems (ICIPS '98), IEEE Press (1998) 217-221.
• [6] Ganter, B., Wille, R.: Conceptual scaling. In: Roberts, F., Eds., Applications of combinatorics and graph theory to the biological and social sciences, Springer-Verlag, New York (1989) 139-167.
• [7] Ganter, B., Wille, R.: Formal Concept Analysis: mathematical foundations. Springer-Verlag, Berlin (1999).
• [8] Hendricks, K. B., Singhal, V. R.: Association between supply chain glitches and operating performance. Management Science, 51(5), 2005, 695-711.
• [9] Hu, K. Y., Sui, Y. F., Lu, Y. C., Wang, J. and Shi, C. Y.: Concept approximation in concept lattice. In: Proc. of the 5th Pacific-Asia Conference on Knowledge Discovery and Data Mining, LNAI 2035, Springer Verlag (2001) 167-173.
• [10] Jiang, F., Sui, Y. F. and Cao, C. G.: Rough Contexts and Rough-Valued Contexts. In: Proc. of the first Int. Conf. on Rough Set and Knowledge Technology (RSKT 2006), LNAI 4062, Chongqing, P.R. China, 2006, 176-183.
• [11] Jiang, F., Sui, Y. F. and Cao, C. G.: Formal Concept Analysis in Relational Database and Rough Relational Database. Fundamenta Informaticae, IOS Press, 80(4), 2007, 435-451.
• [12] Jiang, F., Meng, Y. X. and Liu, Y.: Formal Concept Analysis in Relational Contexts. IEEE International Conference On Granular Computing, China, 2008, 326-329.
• [13] Kent, R. E.: Rough Concept Analysis. In: Ziarko, W. (Ed.), Proc. Int. Workshop on Rough Sets, Fuzzy Sets and Knowledge Discovery, Canada, Springer-Verlag (1994) 248-255.
• [14] Kent, R. E.: Rough concept analysis: a synthesis of rough sets and formal concept analysis. Fundamenta Informaticae, 27(2), 1996, 169-181.
• [15] Pagliani, P.: From concept lattices to approximation spaces: algebraic structures of some spaces of partial objects, Fundamenta Informaticae, 18, 1-25, 1993.
• [16] Pagliani, P.: Modalizing Relations by means of Relations: a general framework for two basic approaches to Knowledge Discovery in Database. In: M. Gevers (Ed.), Proc. of the 7th Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU '98), Paris, France (1998) 1175-1182.
• [17] Pagliani, P.: Transforming Information Systems. In: Proc. of the Tenth International Conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, University of Regina, Canada, 2005, 660-670.
• [18] Pagliani, P. and Chakraborty,M. K.: Information quanta and approximation spaces. I: non-classical approximation operators, Proceedings of IEEE International Conference on Granular Computing, 2005, 605-610.
• [19] Pagliani, P. and Chakraborty, M. K.: Information quanta and approximation spaces. II: generalised approximation spaces, Proceedings of IEEE International Conference on Granular Computing, 2005, 611-616.
• [20] Pasquier, N., Bastide, Y., Taouil, T., Lakhal, L.: Efficient Mining of Association Rules Using Closed Itemset Lattices. Information Systems, 24(1) (1999) 25-46.
• [21] Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences, 11 (5) (1982) 341-356
• [22] Pawlak, Z.: Rough sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht (1991).
• [23] Pawlak, Z., Grzymala-Busse, J. W., Slowinski, R., Ziarko, W.: Rough sets. Communications of the ACM, 38(11) (1995) 89-95.
• [24] Saquer, J. and Deogun, J.: Concept approximations based on rough sets and similarity measures. International Journal of Applied Mathematics and Computer Science, 11(3), 2001, 655-674.
• [25] Skowron, A. and Rauszer, C.: The discernibilty and functions in information systems. In: Slowinski, R., Eds., Intelligent Decision Support: Handbook of Applications and Advances of the Rough set Theory, Kluwer Academic Publishers, Dordrecht (1992) 331-362
• [26] Skowron, A., Stepaniuk, J.: Approximation of Relations. In: Ziarko, W. (Ed.), Rough Sets, Fuzzy Sets and Knowledge Discovery, Springer-Verlag (1994) 161-166.
• [27] Tonella, P.: Concept analysis for module restructuring. IEEE Transactions on Software Engineering, 27(4) (2001) 351-363.
• [28] Valtchev, P., Hacene, M. R., Huchard, M., Roume, C.: Extracting Formal Concepts out of Relational Data. In: Proc. of the 4th Intl. Conf. Journes de l'Informatique Messine (JIM'03), Metz, France (2003) 37-49.
• [29] Wille, R.: Restructuring Lattice theory: An Approach Based on Hierarchies of Concepts. Ordered Sets, Reidtel, D., Dordrecht (1982) 445-470.
• [30] Wille, R.: Conceptual structures of multi-contexts. In: Eklund, P., et al., Eds., Conceptual Structures: Knowledge Representation as Interlingua, LNAI 1114, Springer (1996) 23-39.
• [31] Yao, Y. Y.: A Comparative Study of Formal Concept Analysis and Rough Set Theory in Data Analysis. In: Tsumoto, S., et al. Eds., Proc. of the 4th International Conference on Rough Sets and Current Trends in Computing (RSCTC'2004), LNAI 3066, Springer-Verlag, Uppsala, Sweden (2004) 59-68.
• [32] Yao, Y. Y.: Concept Lattices in Rough Set Theory. In: Dick, S., et al. Eds., Proc. of 2004 Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS 2004), Banff, Alberta, Canada (2004) 796-801.
• [33] Yao, Y. Y., Chen, Y. H.: Rough Set Approximations in Formal Concept Analysis. Transactions on rough sets, V, LNCS 4100, 2006, 285-305.
• [34] Zadeh, L. A.: Fuzzy Sets. Journal of Information and Control, Vol. 8. 1965, 338-353.
• [35] Zeng,M., Chen, X. P.: Achieving cooperation in multiparty alliances: A social dilemma approach to partnership management. Academy of Management Review, 28(4), 2003, 587-605.