On the uniqueness of possibilistic measure of uncertainty and information
type: Item
instance of: scholarly article
title: On the uniqueness of possibilistic measure of uncertainty and information
zbMATH Open document ID: 0632.94039
DOI: 10.1016/0165-0114(87)90090-X
author: George J. Klir
author: Matthew Mariano
published in: Fuzzy Sets and Systems
publication date: 1987-01-01T00:00:00Z
review text: Under a set of axioms, which, except one, are all counterparts of the probabilistic axioms used in defining entropy, the authors prove that the (previously) derived possibilistic measure of uncertainty is unique. The axioms are discussed and some lemmas are derived. However, the necessity of all the axioms is not proved and some of them (U3 plus U4, or U7) seem to be too strong. On the other hand, the proof of uniqueness is done only for finite sets on which the possibilistic measures are defined. It would be interesting to derive a measure of uncertainty with axiom U5 referring to fuzzy topological spaces.
Mathematics Subject Classification ID: 94D05
Mathematics Subject Classification ID: 94A17
zbMATH DE Number: 4029469
zbMATH Keywords: fuzzy measures
zbMATH Keywords: possibility distribution function
zbMATH Keywords: axiomatic development
zbMATH Keywords: possibilistic measure of uncertainty
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4029469