scholarly journals Coincidences of the Concave Integral and the Pan-Integral

Symmetry ◽  
2017 ◽  
Vol 9 (6) ◽  
pp. 90 ◽  
Author(s):  
Yao Ouyang ◽  
Jun Li ◽  
Radko Mesiar
Keyword(s):  
Concave Integral

Partially Specified Probabilities: Decisions and Games

2012 ◽  
Vol 4 (1) ◽  
pp. 70-100 ◽  
Author(s):  
Ehud Lehrer
Keyword(s):  
Decision Making ◽  
Nash Equilibrium ◽  
Axiomatic Approach ◽  
Concave Integral ◽  
Interactive Models

The paper develops a theory of decision making based on partially specified probabilities. It takes an axiomatic approach using Anscombe and Aumann's (1963) setting, and is based on the concave integral for capacities. This theory is then expanded to interactive models in order to extend Nash equilibrium by introducing the concept of partially specified equilibrium. (JEL C70, D81, D83)

scholarly journals The Shapley Values on Fuzzy Coalition Games with Concave Integral Form

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Jinhui Pang ◽  
Xiang Chen ◽  
Shujin Li
Keyword(s):  
Cooperative Game ◽  
Integral Form ◽  
Simple Calculation ◽  
Calculation Formula ◽  
Concave Integral ◽  
Shapley Values ◽  
Linear Aggregation ◽  
Fuzzy Game ◽  
Expected Values

A generalized form of a cooperative game with fuzzy coalition variables is proposed. The character function of the new game is described by the Concave integral, which allows players to assign their preferred expected values only to some coalitions. It is shown that the new game will degenerate into the Tsurumi fuzzy game when it is convex. The Shapley values of the proposed game have been investigated in detail and their simple calculation formula is given by a linear aggregation of the Shapley values on subdecompositions crisp coalitions.

scholarly journals The concave integral over large spaces

2008 ◽  
Vol 159 (16) ◽  
pp. 2130-2144 ◽  
Author(s):  
Ehud Lehrer ◽  
Roee Teper
Keyword(s):  
Concave Integral

scholarly journals General Concave Integral Control

2013 ◽  
Vol 04 (04) ◽  
pp. 356-361 ◽  
Author(s):  
Baishun Liu ◽  
Xiangqian Luo ◽  
Jianhui Li
Keyword(s):  
Integral Control ◽  
Concave Integral

The concave integral with respect to Riesz space-valued capacities

2009 ◽  
Vol 59 (6) ◽  
Author(s):  
Antonio Boccuto ◽  
Beloslav Riečan
Keyword(s):  
Riesz Space ◽  
Convergence Theorems ◽  
Comparison Results ◽  
Concave Integral ◽  
Definition Of

AbstractA definition of concave integral is given for real-valued maps and with respect to Dedekind complete Riesz space-valued “capacities”. Some comparison results with other integrals are given and some convergence theorems are proved.

On the continuity of the concave integral

2009 ◽  
Vol 160 (9) ◽  
pp. 1318-1326 ◽  
Author(s):  
Roee Teper
Keyword(s):  
Concave Integral

Some convergence theorems of fuzzy concave integral on fuzzy σ-algebra

2021 ◽  
Author(s):  
Sun Rong
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Convergence Theorems ◽  
Concave Integral

Abstract In this paper, we consider the extension of concave integral from classic σ -algebra to fuzzy σ -algebra of fuzzy sets. We introduce the concept of the fuzzy concave integral on a fuzzy set. Then we give some properties of this integral. Finally, various kinds of convergence theorems of a sequence of fuzzy concave integrals are proved.

scholarly journals Integral Representations of Cooperative Game with Fuzzy Coalitions

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Jinhui Pang ◽  
Xiang Chen
Keyword(s):  
Characteristic Function ◽  
Explicit Formula ◽  
Cooperative Game ◽  
Integral Representations ◽  
New Class ◽  
Concave Integral ◽  
Fuzzy Game ◽  
Fuzzy Coalitions ◽  
Expected Values ◽  
Special Case

Classical extensions of fuzzy game models are based on various integrals, such as Butnariu game and Tsurumi game. A new class of symmetric extension of fuzzy game with fuzzy coalition variables is put forward with Concave integral, where players’ expected values are on a partial set of coalitions. Some representations and properties of some limited models are compared in this paper. The explicit formula of characteristic function determined by coalition variables is given. Moreover, a calculation approach of imputations is discussed in detail. The new game could be regarded as a general form of cooperative game. Furthermore, the fuzzy game introduced by Tsurumi is a special case of the proposed game when game is convex.

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