A note to the sum of fuzzy variables
The paper deals with a model of fuzzy variables which is a possibilistic analogue of probability spaces and random variables. The structure composed of a set, the class of its subsets and a possibility measure, is called a pattern space; a fuzzy variable is a real-valued function on it. The sum of fuzzy variables is defined by means of the extension principle using their membership functions which are analogous to probability distributions. The attention is focused on the property of unrelativeness which is analogous to probabilistic independence. The main results show necessary and sufficient conditions under which a convex combination of unrelated fuzzy variables with identical membership function has also this membership function.
scientific article; zbMATH DE number 1283800