D-S evidence theory

The theory of evidence was first proposed by Dempster in 1967, an inexact reasoning theory developed by his students Shafer in 1976, also known as dempster/shafer evidence theory (D-S evidence theory), belongs to the category of artificial intelligence, and was first applied to The/c0> expert system has the ability to process uncertain information. As an uncertain reasoning method, the main characteristic of evidence theory is that it satisfies the weaker condition than Bayesian probability theory, and has the ability to express "uncertainty" and "do not know" directly.

DS theory

After this, many techniques have perfected and developed the DS theory, one of which is the evidence synthesis (evidential reasoning, ER) algorithm. ER algorithm is developed on the basis of confidence evaluation framework and DS theory. The ER algorithm has been successfully applied to vehicle evaluation and analysis, cargo ship design, naval system security analysis and synthesis, software system security performance analysis, transformation of ferry design, and evaluation of administrative vehicle evaluation sets.

In medical diagnosis, target recognition, military command and so on, it is necessary to comprehensively consider the uncertain information from multiple sources, such as the information of multiple sensors, the opinions of many experts, etc., in order to solve the problem, and the combination rule of evidence theory plays an important role in the solution. In DS evidence theory, a complete set of incompatible basic propositions (assumptions) is called the recognition Framework, which represents all possible answers to a question, but only one of them is correct. A subset of the framework is called a proposition. The degree of trust assigned to each proposition is called the basic probability allocation (BPA, also called M function), and M (A) is the basic trust number, reflecting the size of the confidence of a. The Trust function Bel (a) indicates the degree of trust in proposition A, and the likelihood function Pl (a) indicates the degree of trust in proposition A that is not false, that is, a measure of uncertainty that seems likely to be established, in fact, [Bel (a), Pl (a)] indicates an indeterminate interval of a, [0,bel (a)] The representation of Proposition A supports the evidence interval, [0,PL (a)] denotes the proposed range of proposition A, [Pl (a), 1] represents the rejection evidence interval for proposition A. The M1 and M2 are the basic probability distribution functions derived from two independent sources of evidence (sensors), then the Dempster combination rule can calculate the new basic probability allocation function which is produced by these two evidences to reflect the fusion information.Composition Rules

DST also gives the combination rule of multi-source information, namely the Dempster combination rule. It synthesizes the basic reliability assignment from multi-sensors and obtains a new reliability assignment as output. The advantages of the Dempster combination rule are mainly reflected in the case of less evidence conflict. If there is a high level of conflict between the evidence, the following defects will appear when used: ① assigns 100% of trust to small possible propositions, produces results that contradict intuition; ② lacks robustness, evidence has a veto power over propositions, and ③ is sensitive to basic reliability distribution. In the actual data processing, the situation of the conflict of evidence is often encountered, so we should try to avoid the error caused by conflicting evidence combination, otherwise it will produce wrong conclusion. There are two ways to solve this problem: one is to use other combination rules, such as Yager rules, d&p rules, Murphy average rules, etc., and second, preprocessing the original evidence, such as discounting. The latest development and application direction of evidence theory include: the rule-based evidence inference model and the offline and online updating decision model of rule base, the combination of evidence theory and support vector machine, the combination of evidence theory and rough set theory, the combination of evidence theory and fuzzy set theory, the combination of evidence theory and neural network, the data-based The Markovian and Dirichlet hybrid methods are used to assign the qualitative function of evidence theory.

D-S evidence theory