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Non-reversible betting games on fuzzy events: Complexity and algebra

AutorFedel, Martina; Flaminio, Tommaso
Palabras claveNon-reversible bookmakers
Fuzzy events
Computational complexity
Fecha de publicación2011
CitaciónFuzzy Sets and Systems 169: 91- 104 (2011)
ResumenA bad bet is a bet for which we can find an alternative system of bets over the same class of events ensuring to the bettor a strictly better payoff, independently on the truth values of the events involved. In this paper we study the computational complexity for the problem of deciding whether a book arranged on fuzzy events avoids bad bets or not. Call admissible a book that avoids bad bets. Following the approach initiated by Mundici and pursued by Flaminio and Bova for reversible betting situations, we settle the complexity of the admissibility-problem to be NP-complete. We also present a variety of algebras, and an algebraizable modal logic, that allow us to characterize admissible books in terms of 1-satisfiability of suitable defined theories. Studying the computational complexity for the 1-satisfiability problem of a formula in this variety, we provide a second, algebraic-based, NP algorithm to check admissible books. © 2010 Elsevier B.V. All rights reserved.
Identificadoresdoi: 10.1016/j.fss.2010.12.009
issn: 0165-0114
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