Model of non-additive H-measure

Владимир Александрович Касьянов

Abstract


The article suggests a model of a non-additive H-measure, where uncertainty is related to the entropy of preference or subjective probabilities. The model of the H-measure is well linked with the Jaynes principle of maximum of entropy, as well as with the principle of maximum of subjective entropy. It is proposed to use the H-measure in tasks of subjective analysis, which studies the genesis of the distributions of preferences, and is its natural development. In the article we propose the model of the non-additive measure similar to the measure of Sugeno, but as it seems to the author, more natural, as it is directly related to the measure of uncertainty in the distribution of preferences, namely, the entropy of preferences. In addition, this measure (called H-measure) is well linked with the Jaynes principle of maximum of entropy, originally formulated for probability distributions, therefore, in the frameworks of the theory of the additive probability measure. The measure of Sugeno seems rather artificial. You never know how the additional term reflects the uncertainty of the situation. On the other hand, the measure of uncertainty is the entropy, in this case the entropy of preferences, which is called the subjective entropy of preferences, and the corresponding variation principle – the principle of maximum of subjective entropy. In the fuzzy set theory there is uncertainty in the choice of fuzzy distributions. The theory does not give direct selection algorithms of these distributions, which are of heuristic nature.


Keywords


H-measure; measure of Sugeno; non-additive measure; subjective entropy; Jaynes maximum entropy principle; principle of maximum of subjective entropy; subjective analysis

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ISSN (print) 1729-3774, ISSN (on-line) 1729-4061