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Measure based representation of uncertain information

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Abstract

We discuss the use of monotonic set measures for the representation of uncertain information. We look at some important examples of measure-based uncertainty, specifically probability and possibility and necessity. Others types of uncertainty such as cardinality based and quasi-additive measures are discussed. We consider the problem of determining the representative value of a variable whose uncertain value is formalized using a monotonic set measure. We note the central role that averaging and particularly weighted averaging operations play in obtaining these representative values. We investigate the use of various integrals such as the Choquet and Sugeno for obtaining these required averages. We suggest ways of extending a measure defined on a set to the case of fuzzy sets and the power sets of the original set. We briefly consider the problem of question answering under uncertain knowledge.

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Authors and Affiliations

  1. Iona College, Machine Intelligence Institute, New Rochelle, NY, 10801, USA

    Ronald R. Yager

  2. King Saud University, Riyadh, Saudi Arabia

    Ronald R. Yager

  3. ALISR Laboratory, College of Computer and Information Sciences, King Saud University, Riyadh, Saudi Arabia

    Naif Alajlan

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  1. Ronald R. Yager
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  2. Naif Alajlan
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Correspondence to Ronald R. Yager.

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Yager, R.R., Alajlan, N. Measure based representation of uncertain information. Fuzzy Optim Decis Making 11, 363–385 (2012). https://doi.org/10.1007/s10700-012-9127-8

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