JACIII Vol.18 No.6 pp. 929-936
doi: 10.20965/jaciii.2014.p0929


Crisp and Fuzzy Granular Hierarchical Structures Generated from a Free Monoid

Tetsuya Murai*1, Sadaaki Miyamoto*2, Masahiro Inuiguchi*3,
Yasuo Kudo*4, and Seiki Akama*5

*1Graduate School of Information Science and Technologies, Hokkaido University, Kita 14, Nishi 9, Kita-ku, Sapporo, Hokkaido 060-0814, Japan
*2Graduate School of Systems and Information Engineering, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japan
*3Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan
*4College of Information and Systems, Graduate School of Engineering, Muroran Institute of Technology
27-1 Miumoto, Muroran, Hokkaido 050-8585, Japan
*51-20-1 Higashi-Yurigaoka, Asoh-ku, Kawasaki, Kanagawa 215-0012, Japan

January 31, 2014
April 15, 2014
Online released:
November 20, 2014
November 20, 2014
crisp and fuzzy granular hierarchical structures, free monoids, fuzzy sets, fuzzy multisets

The granular hierarchical structure that we propose has the limitation that the set of truth values is not described explicitly. By regarding “sets of putting” as a special class of direct sets, we introduce crisp and fuzzy granular hierarchical structures. We found that there are two kinds of different preextensions between Yager’s fuzzy multisets and Zadeh’s fuzzy sets.

  1. [1] T. Murai, S. Miyamoto, M. Inuiguchi, and S. Akama, “Granular hierarchical structures of finite subsets and multisets,” Int. J. Reasoning-based Intelligent Systems, Vol.4, pp. 118-128, 2012.
  2. [2] T. Murai, S. Miyamoto, M. Inuiguchi, Y. Kudo, and S. Akama, “Fuzzy multisets in granular hierarchical structures generated from free monoids,” V. Torra et al. (eds.), MDAI2013, LNAI 8234, Springer, pp. 248-259, 2013.
  3. [3] R. R. Yager, “On the theory of bags,” Int. J. General Systems, Vol.13, pp. 23-37, 1986.
  4. [4] S. Miyamoto, “Generalizations of multisets and rough approximations,” Int. J. of Intelligent Systems, Vol.19, pp. 639-652, 2004.
  5. [5] S. Miyamoto, “Different generalizations of bags,” Annals of Operations Research, Vol.195, pp. 221-236, 2012.
  6. [6] L. A. Zadeh, “Fuzzy sets,” Information and Control, Vol.8, No.3, pp. 338-353, 1965.
  7. [7] Z. Pawlak, “Rough Sets: Theoretical Aspects of Reasoning about Data,” Kluwer Academic Publishers, 1991.

*This site is desgined based on HTML5 and CSS3 for modern browsers, e.g. Chrome, Firefox, Safari, Edge, IE9,10,11, Opera.

Last updated on Mar. 28, 2017