A Family of Polymodal Systems and its Application to Generalized Possibility Measures and Multi-Rough Sets
Sadaaki Miyamoto*, Tetsuya Murai**, and Yasuo Kudo***
*Department of Risk Engineering, School of Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennodai, Ibaraki 305-8573, Japan
**Graduate School of Information Science and Technology, Hokkaido University, Kita 14, Nishi 9, Kita-Ku, Sapporo 060-0814, Japan
***Department of Computer Science and Systems Engineering, Muroran Institute of Technology, 27-1 Mizumoto, Muroran 050-8585, Japan
Polymodal systems generally have large areas of applications to theoretical computer science including the theory of programming, while other applications are not yet fully explored. In this paper we consider a family of polymodal systems with the structure of lattices on the polymodal indices. After investigating theory of the polymodal systems such as the completeness, we study two applications. One is generalized possibility measures in which lattice-valued measures are proposed and relations with the ordinary possibility and necessity measures are uncovered. Second application is consideration of an information system as a table such as the one in the relational database. It is known that rough sets are used to discover regularities from such information tables. Applying polymodal logic concept, we generalize rough sets which are called multi-rough sets here. Our consideration is mainly to establish theoretical frameworks in these two application areas and hence no real examples are shown here.
-  B. F. Chellas, “Modal Logic,” Cambridge University Press, 1980.
-  D. Dubois and H. Prade, “Possibility Theory: An Approach to Computerized Processing of Uncertainty,” Plenum, 1988.
-  D. Dubois and H. Prade, “Rough fuzzy sets and fuzzy rough sets,” Int. J. General Systems, 17, pp. 191-209, 1990.
-  J. A. Goguen, “L-fuzzy sets,” J. of Math. Anal. and Appl., 18, pp. 145-174, 1967.
-  S. MacLane and G. Birkoff, “Algebra, 2nd ed.,” Macmillan, 1979.
-  Z. Pawlak, “Rough sets,” International Journal of Computer and Information Sciences, 11, pp. 341-356, 1982.
-  Z. Pawlak, “Rough Sets,” Kluwer Academic Publishers, Dordrecht, 1991.
-  S. Popkorn, “First Steps in Modal Logic,” Cambridge University Press, 1994.
-  J. D. Ullman, “Database and Knowledge-base Systems, Vol.I,” Computer Science Press, Rockville, Maryland, 1988.
-  L. A. Zadeh, “Fuzzy sets,” Information and Control, 8, pp. 338-353, 1965.
-  L. A. Zadeh, “Fuzzy sets as a basis for a theory of possibility,” Fuzzy Sets and Systems, 1, pp. 3-28, 1978.
This article is published under a Creative Commons Attribution-NoDerivatives 4.0 International License.