Relationships Between Probability and Possibility Theories
Document Type
Book Chapter
Department or Administrative Unit
Computer Science
Publication Date
2-1-2017
Abstract
The goal of a new area of Computing with Words (CWW) is solving computationally tasks formulated in a natural language (NL). The extreme uncertainty of NL is the major challenge to meet this ambitious goal requiring computational approaches to handle NL uncertainties. Attempts to solve various CWW tasks lead to the methodological questions about rigorous and heuristic formulations and solutions of the CWW tasks. These attempts immediately reincarnated the long-time discussion about different methodologies to model uncertainty, namely: Probability Theory, Multi-valued logic, Fuzzy Sets, Fuzzy Logic, and the Possibility theory. The main forum of the recent discussion was an on-line Berkeley Initiative on Soft Computing group in 2014. Zadeh claims that some computing with words tasks are in the province of the fuzzy logic and possibility theory, and probabilistic solutions are not appropriate for these tasks. In this work we propose a useful constructive probabilistic approach for CWW based on sets of specialized K-Measure (Kolmogorov’s measure) probability spaces that differs from the random sets. This work clarifies the relationships between probability and possibility theories in the context of CWW.
Recommended Citation
Kovalerchuk, B. (2017). Relationships Between Probability and Possibility Theories. In V. Kreinovich (Ed.), Uncertainty Modeling (pp. 97–122). Springer. https://doi.org/10.1007/978-3-319-51052-1_7
Rights
© Springer International Publishing AG 2017
Comments
This article was originally published in Uncertainty Modeling: Dedicated to Professor Boris Kovalerchuk on his Anniversary. The full-text article from the publisher can be found here.
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