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A note to the sum of fuzzy variables. (English) Zbl 0919.04007

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.
Reviewer: M.Mareš (Praha)

MSC:

03E72 Theory of fuzzy sets, etc.
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References:

[1] Badard, R., The law of large numbers for fuzzy processes and the estimation problem, Inform. Sci., 28, 161-178 (1982) · Zbl 0588.60004
[2] Dubois, D.; Prade, H., Fuzzy Sets and Systems: Theory and Applications (1980), Academic Press: Academic Press New York · Zbl 0444.94049
[3] Nahmias, S., Fuzzy variables, Fuzzy Sets and Systems, 1, 97-110 (1978) · Zbl 0383.03038
[4] Rao, M. B.; Rashed, A., Some comments on fuzzy variables, Fuzzy Sets and Systems, 6, 285-292 (1981) · Zbl 0467.03052
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