The dominance concept of Dempster-Shafer (D-S) belief structure in the modeling decisions

  • Authors:

  • Zakaria Karsaulidze;Gia Sirbiladze;Bezhan Ghvaberidze

  • Affiliations:

  • Department of Computer Sciences, Faculty of Exact and Natural Sciences, I.Javakhishvili Tbilisi State University, Tbilisi, Georgia;Department of Computer Sciences, Faculty of Exact and Natural Sciences, I.Javakhishvili Tbilisi State University, Tbilisi, Georgia;Department of Computer Sciences, Faculty of Exact and Natural Sciences, I.Javakhishvili Tbilisi State University, Tbilisi, Georgia

  • Venue:
  • ECC'09 Proceedings of the 3rd international conference on European computing conference
  • Year:
  • 2009

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Abstract

A General model for decision problems is presented in the structure of a body of evidence in the framework of utility theory. Decision maker's preferences valuations on the states of decision systems and possible alternatives (decisions) are presented by utility function. In this case the concept of stochastic dominance is changed by the dominance concept of D-S belief structure, when the utility function is unknown, but there exists some analytical information about it. First, second and higher dominance relations are established. We present theorems about their connections. The maximum principle of Shapley expected utility is explained instead of the maximum principle of Bernoulli expected utility. Because of this, conditional optimization problem is created as nonspecificity measure maximum principle, for which unknown parameters are focal probabilities of a body of evidence.