Entropy And Application Under Uncertainty Environment

Exploration of uncertain phenomenon has a long history. There are lots of impreciseinformation in our life. They can’t be described by probability or fuzzy theory. In order to modelthis type of imprecise phenomena，uncertainty theory was founded by Liu and became a branch ofmathematics based on the Normality, monotonicity, self-duality, countable subadditivity andproduct measure axioms. The theory provides a new theoretical basis for us to solve the subjectiveuncertainty.In the phenomenon of random and fuzzy phenomenon, entropy as a function of thedescription information uncertainty degree, it is widely used in areas such as cybernetics,information theory, physics, and management science. In uncertainty theory, uncertain entropy isdefined as a measure of the uncertainty of an uncertain variable degree of function, it reflects thesize of the exact judgment of the uncertain variable values.In order to further improve the entropy of uncertain variables in the theoretical framework,this paper puts forward the uncertain variables in single parameter definition of entropy, theentropy properties of the single parameter are analyzed. Finally introduce the uncertainty variablesof entropy in the risk measurement, puts forward a new model of measurement of risk.In this paper, the main content and work are as follows:1. The single-parameter entropy definition derived single parameter uncertain variablesuncertain variables related nature.2. The similarities and differences of the single-parameter entropy of uncertain variables andentropy of uncertain variables. And the entropy of uncertain variables is a special case when thesingle-parameter entropy parameters of uncertain variables q1.3. Single parameter entropy analysis of uncertain variables based on the subjective judgment ofthe experts to select the appropriate parameters to measure the uncertainty of the uncertainvariables, this is its superiority.4. The risk of uncertain variables entropy metric, meet the consistency of risk metrics entropystandard deviation model and a numerical example illustrates its feasibility.