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Relationships Between Probability and Possibility Theories

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Uncertainty Modeling

Part of the book series: Studies in Computational Intelligence ((SCI,volume 683))

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.

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Authors and Affiliations

  1. Department of Computer Science, Central Washington University, 400 E. University Way, Ellensburg, WA, 98926, USA

    Boris Kovalerchuk

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  1. Boris Kovalerchuk
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Correspondence to Boris Kovalerchuk .

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  1. University of Texas at El Paso, Department of Computer Science University of Texas at El Paso, El Paso, TX, USA

    Vladik Kreinovich

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Kovalerchuk, B. (2017). Relationships Between Probability and Possibility Theories. In: Kreinovich, V. (eds) Uncertainty Modeling. Studies in Computational Intelligence, vol 683. Springer, Cham. https://doi.org/10.1007/978-3-319-51052-1_7

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  • DOI: https://doi.org/10.1007/978-3-319-51052-1_7

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