Fuzzy measure theory

Physics

Data mining

Mathematical optimization

Fuzzy classification

Fuzzy set operations

Artificial intelligence

Fuzzy mathematics

Defuzzification

Type-2 fuzzy sets and systems

Fuzzy number

Volume (thermodynamics)

Mathematics

Computer science

Fuzzy set

Membership function

Fuzzy logic

Quantum mechanics

International Journal of Computers Communications & Control

Fuzzy membership function plays an important role in fuzzy set theory. However, how to measure the information volume of fuzzy membership function is still an open issue. The existing methods to determine the uncertainty of fuzzy membership function only measure the first-order information volume, but do not take higher-order information volume into consideration. To address this issue, a new information volume of fuzzy membership function is presented in this paper, which includes the first-order and the higher-order information volume. By continuously separating the hesitancy degree until convergence, the information volume of the fuzzy membership function can be calculated. In addition, when the hesitancy degree of a fuzzy membership function equals to zero, the information volume of this special fuzzy membership function is identical to Shannon entropy. Two typical fuzzy sets, namely classic fuzzy sets and intuitiontistic fuzzy sets, are studied. Several examples are illustrated to show the efficiency of the proposed information volume of fuzzy membership function.

Information Volume of Fuzzy Membership Function