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An Axiomatic Foundation for Yager's Decision Theory
Author(s) -
Xiong Wei,
Liu Hailin
Publication year - 2014
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.21642
Subject(s) - decision theory , axiom , interpretation (philosophy) , axiomatic system , foundation (evidence) , dempster–shafer theory , causal decision theory , mathematical economics , argument (complex analysis) , evidential decision theory , set (abstract data type) , function (biology) , set theory , mathematics , computer science , observable , artificial intelligence , decision analysis , evidential reasoning approach , history , business decision mapping , chemistry , archaeology , biology , biochemistry , geometry , quantum mechanics , evolutionary biology , programming language , statistics , physics
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.