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Four different approaches to the normalized Banzhaf values of games with a priori unions

Honorata Sosnowska (2006)

Banach Center Publications

Applying the Owen construction of value of games with a priori unions to the normalized Banzhaf value gives a new type of the normalized Banzhaf value for games with a priori unions. Using a simple example of a four-person voting game with a priori unions, it is shown that this value is different from those known in the literature: the normalized Owen-Banzhaf value, the Banzhaf share function defined by van der Laan and van den Brink and the Banzhaf index for simple games with a priori unions introduced...

Fuzzy coalitional structures (alternatives).

Milan Mares, Milan Vlach (2006)

Mathware and Soft Computing

The uncertainty of expectations and vagueness of the interests belong to natural components of cooperative situations, in general. Therefore, some kind of formalization of uncertainty and vagueness should be included in realistic models of cooperative behaviour. This paper attempts to contribute to the endeavour of designing a universal model of vagueness in cooperative situations. Namely, some initial auxiliary steps toward the development of such a model are described. We use the concept of fuzzy...

Fuzzy Mathematical Programming approach for Solving Fuzzy Linear Fractional Programming Problem

Chinnadurai Veeramani, Muthukumar Sumathi (2014)

RAIRO - Operations Research - Recherche Opérationnelle

In this paper, a solution procedure is proposed to solve fuzzy linear fractional programming (FLFP) problem where cost of the objective function, the resources and the technological coefficients are triangular fuzzy numbers. Here, the FLFP problem is transformed into an equivalent deterministic multi-objective linear fractional programming (MOLFP) problem. By using Fuzzy Mathematical programming approach transformed MOLFP problem is reduced single objective linear programming (LP) problem. The proposed...

Game saturation of intersecting families

Balázs Patkós, Máté Vizer (2014)

Open Mathematics

We consider the following combinatorial game: two players, Fast and Slow, claim k-element subsets of [n] = 1, 2, …, n alternately, one at each turn, so that both players are allowed to pick sets that intersect all previously claimed subsets. The game ends when there does not exist any unclaimed k-subset that meets all already claimed sets. The score of the game is the number of sets claimed by the two players, the aim of Fast is to keep the score as low as possible, while the aim of Slow is to postpone...

Generalized Choquet spaces

Samuel Coskey, Philipp Schlicht (2016)

Fundamenta Mathematicae

We introduce an analog to the notion of Polish space for spaces of weight ≤ κ, where κ is an uncountable regular cardinal such that κ < κ = κ . Specifically, we consider spaces in which player II has a winning strategy in a variant of the strong Choquet game which runs for κ many rounds. After discussing the basic theory of these games and spaces, we prove that there is a surjectively universal such space and that there are exactly 2 κ many such spaces up to homeomorphism. We also establish a Kuratowski-like...

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