Uncertainty balance principle

Migdat Hodzic


The objective of this paper is to present new and simple mathematical approach to deal with uncertainty transformation for fuzzy to random or random to fuzzy data. In particular we present a method to describe fuzzy (possibilistic) distribution in terms of a pair (or more) of related random (probabilistic) events, both fixed and variable. Our approach uses basic properties of both fuzzy and random distributions, and it assumes data is both possibilistic and probabilistic. We show that the data fuzziness can be viewed as a non uniqueness of related random events, and prove our Uncertainty Balance Principle. We also show how Zadeh’s fuzzy-random Consistency Principle can be given precise mathematical meaning. Various types of fuzzy distributions are examined and several numerical examples presented.


Fuzzy Distributions; Cumulative Distributions; Fuzzy to Random Transformation; Random to Fuzzy Transformation; Uncertainty Balance Principle; Uncertainty Change Law

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DOI: http://dx.doi.org/10.21533/pen.v4i2.61


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ISSN: 2303-4521

Digital Object Identifier DOI: 10.21533/pen

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License