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

• Published in: Fuzzy sets and systems Vol. 137; no. 1; pp. 151 - 175
• Main Authors: Inuiguchi, Masahiro, Greco, Salvatore, Słowinski, Roman, Tanino, Tetsuzo
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Amsterdam Elsevier B.V 01.07.2003; Elsevier
• Subjects: Applied sciences; Conjunction function; Decision theory. Utility theory; Exact sciences and technology; General logic; Implication function; Logic and foundations; Mathematical logic, foundations, set theory; Mathematics; Modifier function; Necessity measure; Operational research and scientific management; Operational research. Management science; Possibility measure; Sciences and techniques of general use; Set theory; Modifier function; Necessity measure; Conjunction function; Implication function; Possibility measure; Possibility theory; Decision making; Reasoning; Preference theory; Fuzzy set; Modeling
• ISSN: 0165-0114; 1872-6801
• DOI: 10.1016/S0165-0114(02)00438-4

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.