The concept of interval-valued fuzzy control is introduced.

In this paper,the similarity degree of two interval-valued fuzzy sets in one point is defined on the basis of the similarity degree of two vectors,then a new fuzzy reasoning method is given on the guide of this definition: reasoning method by similarity degree of interval-valued fuzzy sets.

First, the definitions and descriptions of extensions of fuzzy sets, such as Intuitionistic fuzzy Sets, L-fuzzy sets and L-IFS, interval-valued fuzzy sets and IVIFS and Vague sets, etc.

In order to use the reasoning theory,a method of interval-valued fuzzification is presented.

Upper(lower) Approximation of an Interval-valued Fuzzy Set;

Upper and Lower Approximation of an Interval-valued Fuzzy Set Based on Weak Inclusion

Based on the analysis of interval-valued fuzzy set theory and the existing fuzzy classifiers,a new algorithm created with the interval-valued reasoning theory was proposed and applied to the Iris data created by R.

This study develop the interval-valued fuzzy Shapley values with the fuzzy characteristic of trigonometric payoff functions for n-person cooperative games and three axioms of classical Shapley value are extended on the basis of relevant theory of fuzzy mathematics.