# zbMATH — the first resource for mathematics

The expected value of a fuzzy number. (English) Zbl 0755.60004
Summary: The notions of expected interval and expected value of fuzzy number are introduced. The expected interval is defined as the expected value of an interval random set generated by the fuzzy number, and the expected value of this number is defined as the centre of the expected interval. The linearity of the expected interval is studied.

##### MSC:
 60A99 Foundations of probability theory 03E72 Theory of fuzzy sets, etc.
Full Text:
##### References:
 [1] Arstein, Z.; Vitale, R.A., A strong law of large numbers for random compact sets, Ann. probab., 3, 879-882, (1975) · Zbl 0313.60012 [2] Chanas, S.; Nowakowski, M., Single value simulation of fuzzy variable, Fuzzy sets and systems, 25, 43-59, (1988) · Zbl 0633.65144 [3] Dempster, A.P., Upper and lower probabilities induced by a multivalued mapping, Ann. math. statist., 38, 325-339, (1967) · Zbl 0168.17501 [4] Dubois, D.; Prade, H., Fuzzy sets and systems — theory and applications, (1980), Academic Press New York · Zbl 0444.94049 [5] Dubois, D.; Prade, H., The Mean value of fuzzy number, Fuzzy sets and systems, 24, 279-300, (1987) · Zbl 0634.94026 [6] Goodman, I.R., Fuzzy sets as equivalence classes of random sets, (), 327-432 [7] Heilpern, S., Fuzzy mapping and fixed point theory, J. math. anal. appl., 83, 566-569, (1981) · Zbl 0486.54006 [8] Heilpern, S., Fuzzy number and interval random sets, Tamsui Oxford J. management sci., 4-5, 1-14, (1989) [9] Heilpern, S., Interval random sets and entropy, Fuzzy sets and systems, 35, 213-218, (1990) · Zbl 0706.62011 [10] Kaufmann, A.; Gupta, M.M., Fuzzy mathematical models in engineering and management science, (1988), North-Holland New York · Zbl 0683.90024
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.