Possibility and necessity measure specification using modifiers for decision making under fuzziness

Authors:
Masahiro Inuiguchi;Salvatore Greco;Roman Słowinski;Tetsuzo Tanino
Affiliations:
Department of Electronics and Information Systems, Graduate School of Engineering, Osaka University, 2-1, Yamada-Oka, Suita, Osaka 565-0871, Japan;Faculty of Economics, University of Catania, Corso Italia, 55, 95129 Catania, Italy;Institute of Computing Science, Poznan University of Technology, 60-965 Poznan, Poland;Department of Electronics and Information Systems, Graduate School of Engineering, Osaka University, 2-1, Yamada-Oka, Suita, Osaka 565-0871, Japan
Venue:
Fuzzy Sets and Systems - Special issue: Preference modelling and applications
Year:
2003

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Abstract

In this paper, we propose an approach to possibility and necessity measure specification. This approach is more adequate to human reasoning than direct specification of conjunction and implication functions. Using the proposed approach, a possibility measure is specified by two modifier functions and a strong negation while a necessity measure is specified by two modifier functions only. It is demonstrated that many possibility and necessity measures defined by famous conjunction and implication functions are obtained by the proposed approach. Conditions for specified measures to have good properties are also given. Finally, a simple example of application of possibility and necessity measures to a decision problem is given.