Where do we stand on measures of uncertainty, ambiguity, fuzziness, and the like?
type: Item
instance of: scholarly article
title: Where do we stand on measures of uncertainty, ambiguity, fuzziness, and the like?
zbMATH Open document ID: 0633.94026
DOI: 10.1016/0165-0114(87)90087-X
author: George J. Klir
published in: Fuzzy Sets and Systems
publication date: 1987-01-01T00:00:00Z
review text: The paper gives an extensive exposure of two alternative ways of developing fuzzy set theory. They reflect two fundamentally different types of uncertainty involved, namely vagueness and ambiguity. Vagueness refers to concepts which do not possess sharp boundaries. A concept of fuzzy set specified by its membership function introduced by Zadeh lies in this area of interest. Ambiguity is associated with one-to-many relations, viz. situations in which a choice between some alternatives is left unspecified. It refers to fuzzy measure defined in the power set P(X) of all sets in X (the fuzzy measure \(g:P(X)\to [0,1]\) satisfies properties of (i) \(g(\emptyset)=0,\) \(g(X)=1,\) (ii) monotonicity \(g(A)\leq g(B)\) for \(A\subset B,\) \((iii)\quad g(\lim_{n\to \infty}A_ n)=\lim_{n\to \infty}g(A_ n)\) for any monotonic sequence of sets \(A_ 1\), \(A_ 2\),..., \(A_ n\),....). A list of measures of vagueness (called measures of fuzziness) is studied. Afterwards measures of ambiguity attached to belief and plausibility measures as nonspecifity, dissonance and confusion are investigated. In sequel links existing between uncertainty, information and system complexity are indicated.
Mathematics Subject Classification ID: 94D05
zbMATH DE Number: 4031584
zbMATH Keywords: fuzzy set theory
zbMATH Keywords: uncertainty
zbMATH Keywords: vagueness
zbMATH Keywords: ambiguity
zbMATH Keywords: fuzzy measure
zbMATH Keywords: belief and plausibility measures
zbMATH Keywords: nonspecifity
zbMATH Keywords: dissonance
zbMATH Keywords: confusion
zbMATH Keywords: system complexity
MaRDI profile type: Publication
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Where do we stand on measures of uncertainty, ambiguity, fuzziness, and the like? (full work available at URL)
full work available at URL: 0165-0114(87)90087-x

Where do we stand on measures of uncertainty, ambiguity, fuzziness, and the like? (OpenAlex ID)
OpenAlex ID: W2080087838