Parameterized approximation of fuzzy number with minimum variance weighting functions

In the parameterized fuzzy number expectation and fuzzy number interval approximation with the weighting function method, we once considered the weighting function form with maximum entropy, which has some interesting properties. In the present paper, we will propose another kind of parameterized weighting function with minimum variance, and apply it to the fuzzy number expectation and fuzzy number interval approximation problems. It shows that the minimum variance weighting function also has some similar interesting properties, and can be used to express the decision maker’s preference information in the fuzzy number defuzzification process.