Generalized Bags, Bag Relations, and Applications to Data Analysis and Decision Making
- 635 Downloads
Bags alias multisets have long been studied in computer science, but recently more attention is paid on bags. In this paper we consider generalized bags which include real-valued bags, fuzzy bags, and a region-valued bags. Basic definitions as well as their properties are established; advanced operations such as s-norms, t-norms, and their duality are also studied. Moreover bag relations are discussed which has max-plus and max-min algebras as special cases. The reason why generalized bags are useful in applications is described. As two applications, bag-based data analysis and decision making based on convex function optimization related to bags are discussed.
KeywordsGeneralized bag s-norm bag relation data analysis decision making convex function
Unable to display preview. Download preview PDF.
- 4.Dubois, D., Prade, H.: Toll sets. In: IFSA 1991 Brussels, Artificial Intelligence, pp. 21–24 (1991)Google Scholar
- 6.Knuth, D.E.: The Art of Computer Programming, Seminumerical Algorithms, vol. 2. Addison-Wesley, Reading (1969)Google Scholar
- 9.Lusternik, L.A., Sobolev, V.J.: Elements of Functional Analysis. Hindustan Publishing (1961)Google Scholar
- 10.Manna, Z., Waldinger, R.: The Logical Basis for Computer Programming, Deductive Reasoning, vol. 1. Addison-Wesley, Reading (1985)Google Scholar
- 15.Miyamoto, S.: Fuzzy multisets with infinite collections of memberships. In: Proc. of the 7th International Fuzzy Systems Association World Congress (IFSA 1997), Prague, Czech, June 25-30, vol. 1, pp. 61–66 (1997)Google Scholar
- 16.Miyamoto, S., Kim, K.S.: An image of fuzzy multisets by one variable function and its application. J. Japan Society for Fuzzy Theory and Systems 10(1), 157–167 (1998) (in Japanese)Google Scholar
- 17.Miyamoto, S., Kim, K.S.: Multiset-valued images of fuzzy sets. In: Proceedings of the Third Asian Fuzzy Systems Symposium, Masan, Korea, June 18-21, pp. 543–548 (1998)Google Scholar
- 21.Miyamoto, S., Kawasaki, Y.: Text Analysis Based on Bag Neighborhood Model and Application to Incident Reports. In: Da Ruan, et al. (eds.) Computational Intelligence in Decision and Control, Proc. of the 8th Intern. FLINS Conf., Madrid, Spain, September 21-24, pp. 1015–1020 (2008)Google Scholar
- 22.Miyamoto, S.: Operations for Real-Valued Bags and Bag Relations. In: Proc. of IFSA (to appear, 2009)Google Scholar
- 26.Ramer, A., Wang, C.-C.: Fuzzy multisets. In: Proc. of 1996 Asian Fuzzy Systems Symposium, Kenting, Taiwan, December 11-14, pp. 429–434 (1996)Google Scholar
- 30.Schölkopf, B., Smola, A.J.: Learning with Kernels. The MIT Press, Cambridge (2002)Google Scholar