Hong, Dug Hun; Kim Hoyong A note to the sum of fuzzy variables. (English) Zbl 0919.04007 Fuzzy Sets Syst. 93, No. 1, 121-124 (1998). 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) Cited in 1 ReviewCited in 10 Documents MSC: 03E72 Theory of fuzzy sets, etc. Keywords:fuzzy variables; possibility measure; pattern space; membership functions; unrelativeness Citations:Zbl 0383.03038; Zbl 0467.03052 PDFBibTeX XMLCite \textit{D. H. Hong} and \textit{Kim Hoyong}, Fuzzy Sets Syst. 93, No. 1, 121--124 (1998; Zbl 0919.04007) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.