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
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.
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