# Fuzzy Measures and Integrals: Theory and Applications

@inproceedings{Grabisch2000FuzzyMA, title={Fuzzy Measures and Integrals: Theory and Applications}, author={Michel Grabisch and Michio Sugeno and Toshiaki Murofushi}, year={2000} }

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 Concepts and Their Role for Applications.- M. Grabisch: The Interaction and Mobius Representations of Fuzzy Measures on Finite Spaces, k-Additive Measures: A Survey.- K. Fujimoto, T. Murofushi: Hierarchical Decomposition of the Choquet Integral.- I. Kramosil: Towards Generalized Belief Functions.- G. De…

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## 549 Citations

Ternary Kleenean non-additive measures

- Computer Science
- 2003

The authors attempt to translate the vagueness of fuzzy set theory and fuzzy logic to the ambiguity of fuzzy measure by considering the fact that the Sugeno integral in fuzzy measure theory can be represented using fuzzy switching functions with constants in fuzzy logic.

Monotone Measures-Based Integrals

- MathematicsHandbook of Computational Intelligence
- 2015

This chapter summarizes basic types of monotone measures together with the basic monot one measures-based integrals, and the concept of universal integrals proposed by Klement etal to give a common roof for all mentioned integrals are introduced.

Sugeno fuzzy integral generalizations for Sub-normal Fuzzy set-valued inputs

- Computer Science2012 IEEE International Conference on Fuzzy Systems
- 2012

This article discusses a direct generalization of the Sugeno FI for sub-normal FS integrands and numeric FMs, called the Sub-normal Fuzzy Integral (SuFI).

Generalization of the Fuzzy Integral for discontinuous interval- and non-convex interval fuzzy set-valued inputs

- Computer Science2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)
- 2013

The Fuzzy Integral (FI) is a powerful approach for non-linear data aggregation. It has been used in many settings to combine evidence (typically objective) with the known “worth” (typically…

A Universal Integral as Common Frame for Choquet and Sugeno Integral

- Computer ScienceIEEE Transactions on Fuzzy Systems
- 2010

This work provides a concept of integrals generalizing both the Choquet and the Sugeno case, and introduces and investigates universal integrals, which can be defined on arbitrary measurable spaces and for arbitrary monotone measures.

A Conjoint Measurement Approach to the Discrete Sugeno Integral

- Computer ScienceThe Mathematics of Preference, Choice and Order
- 2009

The connections between the discrete Sugeno integral and a non-numerical model called the noncompensatory model are studied and it is shown that the main condition used in the result of S. Greco, B. Matarazzo and R. Sowi´ nski can be factorized in such a way that the discrete sugarseno integral model can be viewed as a particular case of a general decomposable representation.

Fuzzy Measures and Integrals in MCDA

- Computer Science
- 2005

This chapter aims at a unified presentation of various methods of MCDA based onfuzzy measures (capacity) and fuzzy integrals, essentially the Choquet andSugeno integral. A first section sets the…

Approximating fuzzy measures by hierarchically decomposable ones

- Computer ScienceProceedings of the Fifth International Conference on Information Fusion. FUSION 2002. (IEEE Cat.No.02EX5997)
- 2002

This work proposes a method to approximate a general fuzzy measure by a Hierarchically Decomposable one (one type of fuzzy measure of reduced complexity).

Choquet fuzzy integral based modeling of nonlinear system

- Computer ScienceAppl. Soft Comput.
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New Fuzzy Aggregations . Part II : Associated Probabilities in the Aggregations of the POWA operator

- Computer Science
- 2016

Several variants of the generalizations of the fuzzy-probabilistic OWA operator POWA are presented in the environment of fuzzy uncertainty, where different monotone measures (fuzzy measure) are used as an uncertainty measure.