Characterization and comparison of sugeno and choquet integrals
Fuzzy Sets and SystemsPublished 1 November 1992
Luis M. de Campos, María Elena Díez Jorge
Citations111
SJR quartileQ1
SJR score0.75
SNIP1.25
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
Two types of fuzzy integrals that can be defined on any kind of fuzzy measure: Sugeno and Choquet integrals are characterized, pointing out their formal similarities and their conceptual differences.
Abstract
Starting from the concept of 'equiordered functions' we characterize two types of fuzzy integrals that can be defined on any kind of fuzzy measure: Sugeno and Choquet integrals. The characterization theorems that we obtain allow us to carry out a comparative study of these two fuzzy integrals, pointing out their formal similarities and their conceptual differences.
Keywords
Decision SciencesMathematicsEngineering
Fuzzy Sets and SystemsFuzzy sets as a basis for a theory of possibility
7,964 Citations1978Lotfi A. Zadeh
Fuzzy Sets and SystemsFuzzy sets as a basis for a theory of possibility
7,280 Citations1999Lotfi A. Zadeh
The theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable.
The Annals of Mathematical StatisticsUpper and Lower Probabilities Induced by a Multivalued Mapping
5,972 Citations1967A. P. Dempster
Studies in fuzziness and soft computingUpper and Lower Probabilities Induced by a Multivalued Mapping
5,299 Citations2008Arthur P. Dempster
A distinctive feature of the present approach is a rule for conditioning, or more generally, arule for combining sources of information, as discussed in Sects.
Fuzzy Sets and SystemsAn interpretation of fuzzy measures and the Choquet integral as an integral with respect to a fuzzy measure
666 Citations1989Toshiaki Murofushi, Michio Sugeno
The non-additivity of Sugeno's fuzzy measures is interpreted in terms of addition and the rationality of the Choquet integral is discussed and it is shown through concrete examples that it is reasonable as an integral with respect to a fuzzy measure.
Theory and decision library. Series C, Game theory, mathematical programming and operations researchAdditive Representations of Preferences
414 Citations1989Peter P. Wakker
Journal of Mathematical Analysis and ApplicationsThe fuzzy integral
367 Citations1980Dan A. Ralescu, Gregory T. Adams
This paper defines the fuzzy integral of a positive, measurable function, with respect to a fuzzy measure, and shows that the monotone convergence theorem and Fatou's lemma are still true in this new setting.
Journal of Mathematical Analysis and Applications⊥-Decomposable measures and integrals for Archimedean t-conorms ⊥
280 Citations1984Siegfried Weber
Fuzzy Sets and SystemsTwo families of fuzzy integrals
168 Citations1986Fermín Suárez García, Pedro Gil Álvarez
It is shown that Sugeno's fuzzy integral is a particular case of them and they are studied to study their principal properties.
Information SciencesThe degree of belief in a fuzzy event
152 Citations1981Philippe Smets
Epistemic probabilities are better described by belief functions and their definition is extended in order to apply them to fuzzy events.
Fuzzy Sets and SystemsTwo integrals and some modified versions — Critical remarks
86 Citations1986Siegfried Weber
Fuzzy Sets and SystemsRepresentation of fuzzy measures through probabilities
78 Citations1989Luis M. de Campos, Manuel Jorge Bolaños Carmona
A method to study fuzzy measures associating certain sets of probabilities to them based on the consideration of one property of a fuzzy integral, called monotone expectation is developed.
Journal of Mathematical Analysis and ApplicationsToward a general theory of fuzzy variables
40 Citations1982Dan A. Ralescu
A general framework for a theory is presented that encompasses both statistical uncertainty and nonstatistical uncertainty, which relates to the concept of a fuzzy set and possibility theory, and the possibility of using this theory in Bayesian estimation with fuzzy prior information.
Fuzzy Sets and SystemsOn medical diagnosis using possibility measures
35 Citations1983M.A. Vila, Miguel Delgado
A model of clinical diagnosis in the context of possibility distributions is presented by using B-optimal membership functions, an expression for automatic diagnosis is formulated for a concrete fuzzy set of symptoms by means of a new formulation of fuzzy integrals for additive fuzzy measures.
Fuzzy Sets and SystemsFuzzy integrals and conditional fuzzy measures
34 Citations1983Rudolf Kruse
A fuzzy integral for fuzzy events with respect to @l-additive fuzzy measures is introduced and a Radon-Nikodym-like theorem is used to give the definition of the conditional fuzziness.
Fuzzy Sets and SystemsNonlinearity of the fuzzy integral
31 Citations1983Erich Peter Klement, Dan A. Ralescu
It is proved that the fuzzy integral has some linearity properties only for small classes of fuzzy measures, and an extension to bounded functions (as proposed by Kandel 2?5) is not well-defined, in general.
Journal of Mathematical Analysis and ApplicationsFuzzy measures and measures of fuzziness
25 Citations1984Wang Zi-Xiao
It is proven that a measure of fuzziness satisfying some conditions can surely be expressed as a fuzzy integral with respect to some fuzzy measure.
Fuzzy Sets and SystemsConvergence properties of the monotone expectation and its application to the extension of fuzzy measures
22 Citations1989Manuel Jorge Bolaños Carmona, Luis M. de Campos +1 more
A functional on fuzzy measures (called monotone expectation) based on Choquet's integral operator is defined, and its convergence properties are studied to extend fuzzy measures to fuzzy subsets.
Journal of Mathematical Analysis and ApplicationsOn a multiplication and a theory of integration for belief and plausibility functions
6 Citations1987Manfred Berres
