Entropy Measures Of Fuzzy Information Environment And Their Applications

Fuzzy theory, as an important part of uncertain theory, describe and measure its uncertain information have important theoretical value and real meaning, and have become one of hot topics for domestic and foreign scholars. Foucs on problems that axiomatic principles and methods of constructing fuzzy entropy measures in excisting references cannot reflect fuzzy nature and interval information, and discrimination uncertain information between different fuzzy sets lacks of measurments and so on. This paer introduce systematically concepts, opterations and aggregating operators. Construct and refine axiomatic principles of constructing entropy measurs, explor and discuss some classical constructing methods. Propose a kind of cross-entropy measures to measure distcrimination uncertain information, and discuss relations between entropy measures and cross-entropy measures, analysis decomposition formulas of entropy measures and introduce parameterized methods. Main results are as follows:1. Introduce a fuzzy factor in fuzzy information, refine the axiomatic principles of constructing fuzzy entropy, and propose the constructing methods of fuzzy entropy based on distance and cosine function. Define fuzzy cross-entropy to measure discrimination uncertain information between different fuzzy sets, discuss relationship with fuzzy entropy, and apply fuzzy entropy measures to medical diagnosis and multi-attributes decision making problems.2. Introduce a width factor in interval-valued fuzzy information, construct the axiomatic principles of constructing fuzzy entropy, and give the constructing method of interval-valued fuzzy entropy. Define an interval-valued fuzzy cross-entropy and analysis relationship with interval-valued fuzzy entropy, discuss the decomposition formulas about interval-valued fuzzy entropy, introduce the parameterized mathod into interval-valued entropy measures, and apply them to multi-attributes decison making problems.3. Introduce an intuitionism factor in intuitionistic fuzzy information, refine the axiomatic principles of constructing intuitionistic fuzzy entropy, propose the constructing methods of intuitionistic fuzzy entropy based on isentropic plane and isentropic circle. Define intuitionistic fuzzy cross-entropy and discuss relationship with intuitionistic fuzzy entropy, analysis decomposition formulas about intuitionistic fuzzy entropy, introduce the parameterized mathod into intuitionistic fuzzy entropy measures, and make a comparative examples about intuitionistic fuzzy entropy with existing references, apply the results to pattern recoginition and multi-attributes decison making problems.4. Define the tansformation operator in interval-valued intuitionistic fuzzy information, propose the axiomatic principles of constructing interval-valued intuitionistic fuzzy entropy based on fuzzy factor, intuitionism factor and width factor. Define interval-valued intuitionistic fuzzy cross-entropy and discuss relation with interval-valued intuitionistic fuzzy entropy, analysis decomposition formulas about interval-valued intuitionistic fuzzy entropy, introduce the parameterized mathod into interval-valued intuitionistic fuzzy entropy measures, and apply to multi-experts group decision making problems.