Paper:
Language: English:

Hybrid Probabilistic Models of Fuzzy and Rough Events

Rolly Intan^*,**, Masao Mukaidono^*, and Hung T. Nguyen^***

Department of Computer Science, Meiji University, Kawasaki-shi, Kanagawa-ken, Japan
Petra Christian University, Siwalankerto 121-131, Surabaya, Indonesia 60236
New Mexico State University, Las Cruces, NM 88003-8001, USA

Received: June 30, 2003

Accepted: August 26, 2003

Keywords: probability of fuzzy event, probability of rough event, evidence theory, generalized fuzzy-rough event

Journal ref: Journal of Advanced Computational Intelligence and Intelligent Informatics, Vol.7, No.3 pp. 322-329, 2003

Abstract

This paper discusses the relationship between probability and fuzziness based on the process of perception. As a generalization of the crisp set, the fuzzy set is used to model fuzzy events as proposed by Zadeh. Similarly, we may consider the rough set to represent a rough event in terms of probability measures. Special attention will be given to conditional probability of fuzzy events as well as the conditional probability of rough events. Several combinations of formulation and properties are examined. In the relation to evidence theory, the probability of a rough event may be considered as a connecting bridge between belief-plausibility measures and the probability measures. Moreover, a generalized fuzzy-rough event is introduced to generalize both fuzzy and rough events.

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