Entropy variation on the fuzzy numbers with arithmetic operations

Abstract

Entropy is always the measure of the fuzziness degree for a fuzzy set. This paper studies the entropy variation on the fuzzy numbers (or fuzzy sets) under the following several cases: (i) two fuzzy sets on the same type but different support size; (ii) the addition of finite number of fuzzy numbers on the same type; (iii) the subtraction of finite number of fuzzy numbers on the same type; (iv) the multiplication of a constant and a fuzzy number. It is shown that through the above arithmetic operations, the resultant fuzzy number is the same type as the original fuzzy numbers and the entropy of the resultant fuzzy number has the arithmetic relation with the entropy of each original fuzzy number.