concave integral
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2021 ◽  
Author(s):  
Sun Rong

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.



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


2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Jinhui Pang ◽  
Xiang Chen ◽  
Shujin Li

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.



2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Jinhui Pang ◽  
Xiang Chen

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.



2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Jinhui Pang ◽  
Shujin Li

We propose a new fuzzy game model by the concave integral by assigning subjective expected values to random variables in the interval[0,1]. The explicit formulas of characteristic functions which are determined by coalition variables are discussed in detail. After illustrating some properties of the new game, its fuzzy core is defined; this is a generalization of crisp core. Moreover, we give a further discussion on the core for the new games. Some notions and results from classical games are extended to the model. The nonempty fuzzy core is given in terms of the fuzzy convexity. Our results develop some known fuzzy cooperative games.



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




2012 ◽  
Vol 4 (1) ◽  
pp. 70-100 ◽  
Author(s):  
Ehud Lehrer

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)



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


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