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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 412045, 10 pages
http://dx.doi.org/10.1155/2015/412045
Research Article

Probability Estimation in the Framework of Intuitionistic Fuzzy Evidence Theory

Air and Missile Defense College, Air Force Engineering University, Xi’an 710051, China

Received 10 November 2014; Revised 24 March 2015; Accepted 9 April 2015

Academic Editor: Joao B. R. Do Val

Copyright © 2015 Yafei Song and Xiaodan Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Intuitionistic fuzzy (IF) evidence theory, as an extension of Dempster-Shafer theory of evidence to the intuitionistic fuzzy environment, is exploited to process imprecise and vague information. Since its inception, much interest has been concentrated on IF evidence theory. Many works on the belief functions in IF information systems have appeared. Although belief functions on the IF sets can deal with uncertainty and vagueness well, it is not convenient for decision making. This paper addresses the issue of probability estimation in the framework of IF evidence theory with the hope of making rational decision. Background knowledge about evidence theory, fuzzy set, and IF set is firstly reviewed, followed by introduction of IF evidence theory. Axiomatic properties of probability distribution are then proposed to assist our interpretation. Finally, probability estimations based on fuzzy and IF belief functions together with their proofs are presented. It is verified that the probability estimation method based on IF belief functions is also potentially applicable to classical evidence theory and fuzzy evidence theory. Moreover, IF belief functions can be combined in a convenient way once they are transformed to interval-valued possibilities.