Convex Fuzzy Games and Participation Monotonic Allocation Schemes

AMS classifications: 90D12; 03E72Convex games;Core;Decisionmaking;Fuzzy coalitions;Fuzzy games;Monotonic allocation schemes;Weber set

Convex fuzzy games and participation monotonic allocation schemes

90D12;03E72cooperative games

Fuzzy Clan Games and Bi-monotonic Allocation Rules

Clan game;Big boss game;Core;Decision making;Fuzzy coalition;Fuzzy game;Monotonic allocation rule

Hypercubes and compromise values for cooperative fuzzy games

90D12;03E72cooperative games

Hypercubes and Compromise Values for Cooperative Fuzzy Games

AMS classification: 90D12; 03E72;cooperative games;Compromise values;Core;Fuzzy coalitions;Fuzzy games;Hypercubes;Path solutions;Weber set

Capacities and Games on Lattices: A Survey of Result

We provide a survey of recent developments about capacities (or fuzzy measures) and ccoperative games in characteristic form, when they are defined on more general structures than the usual power set of the universal set, namely lattices. In a first part, we give various possible interpretations and applications of these general concepts, and then we elaborate about the possible definitions of usual tools in these theories, such as the Choquet integral, the Möbius transform, and the Shapley value.capacity, fuzzy measure, game, lattice, Choquet integral,Shapley value

A new integral for capacities

A new integral for capacities, different from the Choquet integral, is introduced and characterized. The main feature of the new integral is concavity, which might be interpreted as uncertainty aversion. The integral is then extended to fuzzy capacities, which assign subjective expected values to random variables (e.g., portfolios) and may assign subjective probability only to a partial set of events. An equivalence between minimum over sets of additive capacities (not necessarily probability distributions) and the integral w.r.t. fuzzy capacities is demonstrated. The extension to fuzzy capacities enables one to calculate the integral also when there is information only about a few events and not about all of them.new integral, capacity, choquet integral, fuzzy capacity, concavity

Egalitarianism in convex fuzzy games

cooperative games;algorithm

Egalitarianism in Convex Fuzzy Games

In this paper the egalitarian solution for convex cooperative fuzzy games is introduced.The classical Dutta-Ray algorithm for finding the constrained egalitarian solution for convex crisp games is adjusted to provide the egalitarian solution of a convex fuzzy game.This adjusted algorithm is also a finite algorithm, because the convexity of a fuzzy game implies in each step the existence of a maximal element which corresponds to a crisp coalition.For arbitrary fuzzy games the equal division core is introduced.It turns out that both the equal division core and the egalitariansolution of a convex fuzzy game coincide with the corresponding equal division core and the constrained egalitarian solution, respectively, of the related crisp game.game theory

On Cores and Stable Sets for Fuzzy Games

AMS classifications: 90D12; 03E72;cooperative games;decision making;fuzzy games