The Joint Entropy of Random Variable Based on Fuzzy Equivalence Relation

Abstract: By introducing probability distrbution into fuzzy approximation space, a fuzzy probability approximation space is built up. The Shannon’s entropy which measures information quantity is generalized; and the entropy and the conditional entropy of fuzzy probabilistic approximation space are given as well. The two fuzzy equivalence relations are investigated. At last, the joint entropy, together with its property, is also put under examination.