A MATHEMATICAL ANALYSIS OF INFORMATION-PRESERVING TRANSFORMATIONS BETWEEN PROBABILISTIC AND POSSIBILISTIC FORMULATIONS OF UNCERTAINTY

DOI10.1080/03081079208945024zbMath0743.94029OpenAlexW1983583104MaRDI QIDQ3989287

George J. Klir, James F. Geer

Publication date: 28 June 1992

Published in: International Journal of General Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03081079208945024

zbMATH Keywords

discorduncertaintypossibility theoryprobability theoryShannon entropynonspecificityinterval scalesinformation preserving transformationslog-interval scales

Mathematics Subject Classification ID

Probabilistic measure theory (60A10) Measures of information, entropy (94A17) Fuzzy sets and logic (in connection with information, communication, or circuits theory) (94D05)

Related Items (17)

ON THE PROBABILITY/POSSIBILITY TRANSFORMATIONS:A COMPARATIVE ANALYSIS ⋮ Fuzziness and randomness in investment project risk appraisal ⋮ On the weighted Gini-Simpson index: estimating feasible weights using the optimal point and discussing a link with possibility theory ⋮ A new transformation of continuous unimodal asymmetric probability distributions into possibility distributions ⋮ Uncertainty measures for general type-2 fuzzy sets ⋮ Application of prediction models using fuzzy sets: a Bayesian inspired approach ⋮ Characterizations of the possibility-probability transformations and some applications ⋮ Likelihood-fuzzy analysis: from data, through statistics, to interpretable fuzzy classifiers ⋮ Uncertainty measures for interval type-2 fuzzy sets ⋮ ON INFORMATION-PRESERVING TRANSFORMATIONS ⋮ MEASUREMENT OF POSSIBILITY DISTRIBUTIONS ⋮ PROBABILITY-POSSIBILITY TRANSFORMATIONS: A COMPARISON ⋮ FURTHER RESULTS ON POSSIBILITY-PROBABILITY CONVERSION VIA RELATIVE INFORMATION AND INFORMATIONAL INVARIANCE ⋮ Possibility theory and statistical reasoning ⋮ Transforming probability distributions into membership functions of fuzzy classes: a hypothesis test approach ⋮ On the normalization of subnormal possibility distributions: New investigations ⋮ Expert Systems and Fuzzy Systems: A New Approach via Possibility‐Probability Conversion

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• IS THERE MORE TO UNCERTAINTY THAN SOME PROBABILITY THEORISTS MIGHT HAVE US BELIEVE?*
• An algorithm for region filling using two-dimensional grammars
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