Data mining

Mathematics

Computer science

Mathematical optimization

Quantum mechanics

Type-2 fuzzy sets and systems

Fuzzy number

Fuzzy mathematics

Volume (thermodynamics)

Membership function

Fuzzy classification

Artificial intelligence

Fuzzy set

Fuzzy logic

Fuzzy measure theory

Physics

Fuzzy set operations

Defuzzification

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 ...

Information Volume of Fuzzy Membership Function