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Open AccessJournal ArticleDOI

Bi-capacities—I: definition, Möbius transform and interaction

Michel Grabisch, +1 more
- 16 Apr 2005 - 
- Vol. 151, Iss: 2, pp 211-236
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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.
About: 
This article is published in Fuzzy Sets and Systems.The article was published on 2005-04-16 and is currently open access. It has received 167 citations till now. The article focuses on the topics: Decision theory & Shapley value.

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The measurement of meaning

John M. Kittross
Dissertation

Theory of fuzzy integrals and its applications

道夫 菅野
Posted Content

A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid

Michel Grabisch, +1 more
- 01 Mar 2008 - 
TL;DR: The main advances regarding the use of the Choquet and Sugeno integrals in multi-criteria decision aid over the last decade are reviewed in this paper, mainly a bipolar extension of both Choquet integral and the Sugeno integral.
Journal ArticleDOI

A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid

Michel Grabisch, +1 more
- 01 Mar 2010 - 
TL;DR: The main advances regarding the use of the Choquet and Sugeno integrals in multi-criteria decision aid over the last decade are reviewed, which concern mainly a bipolar extension of both theChoquet integral and the Sugeno integral.
Journal ArticleDOI

Corrections to “TOPSIS-Based Nonlinear-Programming Methodology for Multi-attribute Decision Making With Interval-Valued Intuitionistic Fuzzy Sets”

Jia-Cai Liu, +1 more
- 01 Apr 2010 - 
TL;DR: A nonlinear-programming methodology based on the technique for order preference by similarity to ideal solution to solve multiattribute decision-making (MADM) problems with both ratings of alternatives on attributes and weights of attributes expressed with IVIF sets is developed.
References
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Journal ArticleDOI

Advances in prospect theory: cumulative representation of uncertainty

Amos Tversky, +1 more
- 01 Oct 1992 - 
TL;DR: Cumulative prospect theory as discussed by the authors applies to uncertain as well as to risky prospects with any number of outcomes, and it allows different weighting functions for gains and for losses, and two principles, diminishing sensitivity and loss aversion, are invoked to explain the characteristic curvature of the value function and the weighting function.
Book

The Measurement of Meaning

Charles E. Osgood, +2 more
TL;DR: In this article, the authors deal with the nature and theory of meaning and present a new, objective method for its measurement which they call the semantic differential, which can be adapted to a wide variety of problems in such areas as clinical psychology, social psychology, linguistics, mass communications, esthetics, and political science.
Book ChapterDOI

A Value for n-person Games

Lloyd S. Shapley
TL;DR: In this paper, an examination of elementary properties of a value for the essential case is presented, which is deduced from a set of three axioms, having simple intuitive interpretations.
Book

Introduction to lattices and order

Brian A. Davey, +1 more
TL;DR: The Stone Representation Theorem for Boolean algebras and its application to lattices in algebra can be found in this article, where the structure of finite distributive lattices and finite Boolean algebraic structures are discussed.
Journal ArticleDOI

Theory of capacities

Gustave Choquet
- 01 Jan 1954 - 
TL;DR: In this article, the conditions générales d'utilisation (http://www.numdam.org/legal.php) of a fichier do not necessarily imply a mention of copyright.
Frequently Asked Questions (1)
Q1. What are the contributions mentioned in the paper "Bi-capacities – part i: definition, möbius transform and interaction" ?

The aim of this paper in two parts is to present the machinery behind bicapacities, and thus remains on a rather theoretical level, although some parts are firmly rooted in decision theory, notably cooperative game theory. Then, the authors introduce derivatives of bi-capacities, by analogy with what was done for pseudoBoolean functions ( another view of capacities and set functions ), and this is the key point to introduce the Shapley value and the interaction index for bi-capacities. In summary, all familiar notions used for fuzzy measures are available in this more general framework.