The application of fuzzy integrals in multicriteria decision making
European Journal of Operational ResearchPublished 1 March 1996
Michel Grabisch
Citations995
SJR quartileQ1
SJR score2.24
SNIP2.62
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
It is shown that fuzzy integrals are able to model interaction between criteria in a flexible way and is one of the aims of this review to disseminate this emerging technology in many industrial fields.
Abstract
This paper presents a synthesis on the application of fuzzy integrals as an innovative tool for criteria aggregation in decision problems. The main point is that fuzzy integrals are able to model interaction between criteria in a flexible way. The methodology has been elaborated mainly in Japan, and has been applied there successfully in various fields such as design, reliability, evaluation of goods, etc. It seems however that this technique is still very little known in Europe. It is one of the aims of this review to disseminate this emerging technology in many industrial fields.
Keywords
Decision SciencesMathematicsEngineering
IEEE Transactions on Systems Man and CyberneticsOn ordered weighted averaging aggregation operators in multicriteria decisionmaking
7,125 Citations1988Ronald R. Yager
A type of operator for aggregation called an ordered weighted aggregation (OWA) operator is introduced and its performance is found to be between those obtained using the AND operator and the OR operator.
Cambridge University Press eBooksA value for <i>n</i>-person games
5,046 Citations1988Lloyd S. Shapley
Journal of the Franklin InstituteContributions to the theory of games.
1,842 Citations1960Kuhn, H W, Tucker, A W +1 more
Elsevier eBooksOn Ordered Weighted Averaging Aggregation Operators in Multicriteria Decisionmaking
1,060 Citations1993Ronald R. Yager
Information SciencesA review of fuzzy set aggregation connectives
925 Citations1985Didier Dubois, Henri Prade
An extensive survey on fuzzy set-theoretic operations is provided, and the relevance of the theory of functional equations in the axiomatical construction of classes of such operations and the derivation of functional representations is emphasized.
Elsevier eBooksFUZZY MEASURES AND FUZZY INTEGRALS—A SURVEY
764 Citations1993Michio Sugeno
The concept of fuzzy sets (precisely speaking, fuzzy subsets of an ordinary set) is nothing but an extended concept of ordinary sets, and the concept of probabilities is absolutely different from that of sets.
Fuzzy Sets and SystemsFuzzy integral in multicriteria decision making
668 Citations1995Michel Grabisch
A synthesis on the use of fuzzy integral as an aggregation operator in multicriteria decision making and compared to those of usual aggregation operators is presented.
Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference
575 Citations1995Michel Grabisch, Hung T. Nguyen +1 more
The aim of this book is to provide a rigorous background for uncertainty calculi, with an emphasis on fuzziness, and to give a complete background on uncertainty measures and integrals, especially in a fuzzy setting.
Journal of Mathematical Analysis and ApplicationsA theory of fuzzy measures: Representations, the Choquet integral, and null sets
363 Citations1991Toshiaki Murofushi, Michio Sugeno
It is shown that, if there is a certain relation between two measurable functions, then the Choquet integral is additive for these two functions.
Fuzzy Sets and SystemsConnectives and quantifiers in fuzzy sets
330 Citations1991Ronald R. Yager
The concept of linguistic quantifiers is introduced and some applications of these structures are looked at, particularly concerned with their application to linguistic summarizers, syllogistic reasoning and multi-criteria decision making.
A new algorithm for identifying fuzzy measures and its application to pattern recognition
244 Citations2002Michel Grabisch
A new algorithm for identifying fuzzy measures, which is a kind of gradient algorithm with constraints, is presented, whose performance is superior to the one of previous attempts, and its efficiency to a problem of pattern recognition using Choquet integral is shown.
International Journal of Man-Machine StudiesA model of human evaluation process using fuzzy measure
238 Citations1985K. Ishii, Michio Sugeno
The concept of overlap coefficient is introduced to describe the properties of a given fuzzy measure and to characterize the human evaluation process and a new algorithm is developed to identify the fuzzy measure with full degrees of freedom.
Information SciencesWeighted minimum and maximum operations in fuzzy set theory
216 Citations1986Didier Dubois, Henri Prade
This short note comments on the interpretation of weighted minimum and maximum operations introduced in a previous paper as medians, and corrects a misleading statement about it.
Fuzzy Sets and SystemsFuzzy measure analysis of public attitude towards the use of nuclear energy
90 Citations1986Takehisa Onisawa, Michio Sugeno +3 more
It is shown that the attitude of the responders to the questionnaire in each country is well explained with its hierarchical structure obtained by fuzzy measure analysis.
International Journal of Approximate ReasoningA study on subjective evaluations of printed color images
77 Citations1991Kazuhiko Tanaka, Michio Sugeno
This study adopts Choquet's integral as a form of fuzzy integral because it has good properties compared with other forms of fuzzy integrals and is effective in building an evaluation model of printed color images.
Information SciencesInteractive determination of a utility function represented as a fuzzy integral
31 Citations1993Minoru Yoneda, Satoru Fukami +1 more
This paper adopts an alternative point of view for determining the values of the fuzzy measure from few data by interactively changing equation constraints and will contribute to increasing the applicability and the fuzzy integral in the field of decision support systems.
Journal of Japan Society for Fuzzy Theory and SystemsA Clusterwise Regression-type Model for Subjective Evaluation
29 Citations1995Michio Sugeno, Soonhak Kwon
A new approach to time series modeling with fuzzy measures and the Choquet integral
21 Citations2002Michio Sugeno, Soonhak Kwon
A new approach to modeling of time series using nonmonotonic fuzzy measures and the Choquet integral is proposed, which removes the assumption of linear independency between time series data.
RAIRO - Operations ResearchAnalyse et classification de la littérature traitant de l'importance relative des critères en aide multicritère à la décision
15 Citations1992Vincent Mousseau
Characterization of fuzzy integrals viewed as aggregation operators
12 Citations1994Michel Grabisch
This work shows several results on characterization of different kinds of fuzzy integrals, including the weighted average, medians, and weighted minimum and maximum OWA operators.
Analysis of environmental evaluation structure by the Choquet integral model
9 Citations2002Yoshiteru Nakamori, Naoko IWAMOTO
The structure of residents' subjective evaluation of the urban environment is studied by using the fuzzy measures and it is proved that the weight of each item is very small, but the weights of unions of two or three items are large enough to evaluate the environment.
Intelligent alarm method by fuzzy measure and its application to plant abnormality prediction
9 Citations2002Kenji Goto, Y. Toriyama +1 more
An intelligent alarm method which uses a fuzzy integral model based on fuzzy measure that can provide an accurate model of human subjective evaluation mechanism to demonstrate that abnormality prediction by a simulation method is possible and that even for a plant without abnormalities the method can provide estimate of the potential of abnormality.
Journal of Japan Society for Fuzzy Theory and SystemsA Method of State Synthesis Evaluation for Plant based on Fuzzy Memory-based Reasoning and Fuzzy Measure
6 Citations1995Kenji Goto, Y. Toriyama +1 more