# zbMATH — the first resource for mathematics

Aggregation of fuzzy opinions - an axiomatic approach. (English) Zbl 0597.90005
Summary: The importance of fuzzy valuations in diagnostics is mentioned. The problem of aggregation of fuzzy opinions obtained from a group of experts in answer to the question: ”Has an object the property labeled A and no property labeled $$\neg A?''$$ is formulated. The set of aggregation axioms of L. W. Fung and K. S. Fu [Fuzzy sets Appl. cogn. Decis. Processes, U.S.-Japan Semin., Berkeley 1974, 227-256 (1975; Zbl 0366.90003)] is shortly described. The idea of weighting expert’s opinions is formalized. Then a new set of aggregation axioms is presented and an aggregating operator is introduced. ’A posteriori’ weighting of opinions in aggregation is examined.

##### MSC:
 91B10 Group preferences 03E72 Theory of fuzzy sets, etc.
Full Text:
##### References:
 [1] Albert, P., The algebra of fuzzy logic, Fuzzy sets and systems, 1, 203-230, (1978) · Zbl 0407.03031 [2] Arrow, K.J., Social choice and individual values, (1963), Wiley New York · Zbl 0984.91513 [3] Baas, S.M.; Kwakernaak, H., Rating and ranking of multi-aspect alternatives using fuzzy sets, Automatica, 13, 47-58, (1977) · Zbl 0363.90010 [4] Bezdek, J.C.; Spillman, B.; Spillman, R., Fuzzy measures of preference and consensus in group decision-making, (), 1303-1314 [5] De Luca, A.; Termini, S., A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory, Information and control, 20, 301-312, (1972) · Zbl 0239.94028 [6] De Luca, A.; Termini, S., Entropy and energy measures of fuzzy sets, (), 321-338 [7] Dubois, D.; Prade, H., Fuzzy sets and systems, (1980), Academic Press New York [8] Farris, D.R.; Sage, A.P., Introduction and survey of group decision making with applications to worth assessment, IEEE trans. systems man cybernet., 5, 346-358, (1975) · Zbl 0302.90075 [9] Freeling, A.N.S., Fuzzy sets and decision analysis, IEEE trans. systems man cybernet., 10, 341-354, (1980) [10] Fung, L.W.; Fu, K.S., An axiomatic approach to rational decision making in a fuzzy environment, (), 227-256 · Zbl 0366.90003 [11] Jain, R., Procedure for multi-aspect decision making using fuzzy sets, Internat. J. systems sci., 8, 1-7, (1977) · Zbl 0347.90001 [12] Kacprcyk, J., Multistage decision-making under fuzziness. theory and applications, (1983), Verlag TOV Rheinland Köln [13] Kickert, W.J.M., Fuzzy theories on decision-making, (1978), Nijhoff Leiden · Zbl 0364.93022 [14] Kuzmin, V.B.; Ovchinnikov, S.V., Group decisions I- in arbitrary spaces of fuzzy binary relations, Fuzzy sets and systems, 4, 53-62, (1980) · Zbl 0435.90018 [15] Kuzmin, V.B.; Ovchinnikov, S.V., Design of group decisions II-in spaces of partial ordered fuzzy relations, Fuzzy sets and systems, 4, 153-165, (1980) · Zbl 0444.90007 [16] Nahmias, S., Fuzzy variables, Fuzzy sets and systems, 1, 97-110, (1978) · Zbl 0383.03038 [17] Nojiri, H., On the fuzzy team in a changing environment, Fuzzy sets and systems, 3, 137-150, (1980) · Zbl 0433.90003 [18] Orlovsky, S.A., On formulization of a general fuzzy mathematical problem, Fuzzy sets and systems, 3, 311-321, (1980) · Zbl 0435.90008 [19] Paun, G., An impossibility theorem for indicators aggregation, Fuzzy sets and systems, 9, 205-210, (1983) · Zbl 0503.90029 [20] Suzumura, K., Rational choice, collective decisions and social welfare, (1983), Cambridge University Press Cambridge [21] Tanino, T., Fuzzy preference orderings in group decision making, Fuzzy sets and systems, 12, 117-131, (1984) · Zbl 0567.90002 [22] Yager, R.R., Fuzzy decision making including unequal objectives, Fuzzy sets and systems, 1, 87-95, (1978) · Zbl 0378.90011 [23] Zadeh, L.A., Fuzzy sets, Information and control, 8, 338-353, (1965) · Zbl 0139.24606 [24] Zimmermann, H.-J.; Zysno, P., Decisions and evalutions by hierarchical aggregation of information, Fuzzy sets and systems, 10, 243-260, (1983) · Zbl 0519.90049
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.