An Axiomatic Foundation for Yager's Decision Theory

Abstract

Yager's decision theory, based on the ordered weighted averaging operators and Dempster-Shafer theory, is a very important theory for modeling decision making under uncertainty. This paper attempts to provide an axiomatic foundation for this theory, and thus offers a reasonable interpretation of its basic concept. The properties, presented in terms of observable preferences, enable us to elicit the subjective degree of optimism and the mass function over the set of states. Moreover, some important properties of this decision theory have been established, which in turn show that no Dutch Book argument can be made against agents in this theory. This paper also illustrates the idea of the central result by an example with a particular kind of operators. C 2014 Wiley Periodicals, Inc. = 1 3 , ω M 1 (12) 1 = 2 3 , ω M 2 (5) 2 = 0, and ω M 2 (7) 3 = 1 5 .≤ 2(1 − β), then by formula 2 we have,

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