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K-order Additive Discrete Fuzzy Measures and Their Representation
  • M. Grabisch
  • Mathematics, Computer Science
    Fuzzy Sets Syst.
  • 1 December 1997
TLDR
A related topic of the paper is to introduce an alternative representation of fuzzy measures, called the interaction representation, which sets and extends in a common framework the Shapley value and the interaction index proposed by Murofushi and Soneda.
The application of fuzzy integrals in multicriteria decision making
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
Fuzzy integral in multicriteria decision making
Abstract This paper presents a synthesis on the use of fuzzy integral as an aggregation operator in multicriteria decision making. Definitions, essential properties are given, and compared to those
An axiomatic approach to the concept of interaction among players in cooperative games
TLDR
An axiomatization of the interaction between the players of any coalition is given based on three axioms: linearity, dummy and symmetry, which gives an expression of the Banzhaf and Shapley interaction indices in terms of pseudo-Boolean functions.
Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference
From the Publisher: This decade has witnessed increasing interest in fuzzy technology both from academia and industry. It is often said that fuzzy theory is easy and simple so that engineers can
A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid
The main advances regarding the use of the Choquet and Sugeno integrals in multi-criteria decision aid over the last decade are reviewed. They concern mainly a bipolar extension of both the Choquet
A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package
TLDR
The main approaches to capacity identification proposed in the literature are reviewed and their advantages and inconveniences are discussed and their application is illustrated on a detailed example.
A new algorithm for identifying fuzzy measures and its application to pattern recognition
  • M. Grabisch
  • Mathematics
    Proceedings of IEEE International Conference on…
  • 20 March 1995
We present a new algorithm for identifying fuzzy measures, which is a kind of gradient algorithm with constraints. Its performance is superior to the one of previous attempts, and we show its
Fuzzy Measures and Integrals: Theory and Applications
P. Wakker: Foreword.- M. Grabisch, T. Murofushi, M. Sugeno: Preface.- Theory: T. Murofushi, M. Sugeno: Fuzzy Measures and Fuzzy Integrals.- D. Denneberg: Non-additive Measure and Integral, Basic
Bi-capacities - I: definition, Möbius transform and interaction
TLDR
All familiar notions used for fuzzy measures are available in this more general framework and the Mobius transform of bi-capacities is defined, and the Shapley value and the interaction index are introduced.
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