Abstract
Scientific study of decision making problems are practised on a large scale. It comprises traditional psyco-physiological research, such new areas as modern theory of decision making,development of man machine procedures of decision making, decision support systems, expert systems. In this paper we are interested in formal presentation of decision making problems. It so happened that binary relations and functions of utility turned out to describe problems of decision making with most adequate manner. There is certain relationship between them. Moreover, it was the theory of decision making that began to study some classes of nonconventional binary relations. We shall consider some of them in this paper. Traditionally the problem of decision making is presented by the pare <X,R>, where X is some finite set of comperetive alternatives (decisions) and R ⊆ E is a binary relation,where E=X×X. In the theory of decision making there used a special class of binary relations making it possible to compare a pare of alternatives over some oriterium, e.g. bigger, better,more preferable, heavier, taller etc. Fishburn (11) called these binary relations preference relations.
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References
L.A. Zaden, Fuzzy Sets, Ini’orm. and Control, vol.8,1965, 338–353.
S.Karlin, Mathematical methods and theory in games, programming and economics, Fergamon Press, London-Paris 1959.
V.E. Zhukovin, The multicriberia decision making with vector ruzgy preference relation, Cybernetics and systems research 2,R.Trappl (ed), Elsevier Science Publishers B.V. (North-Holland),1984,179–181.
V.E. Zhukovin, Multicriteria decision making models with uncertainty, Publ. Metsniereba, Tbilisi, 1983, 104.
V.E. Zhukovin, F.V.Burstein, The dialodue procedure of the choice of the best decision with respect to multiple objectives and non-complete information, Proceedings of Tbilisi University, 224, 3, 1981, 19–32.
T.L. Saaty, Exploring the interface between hierarchies, multiple objectives and fuzzy sets, Fuzzy sets and systems, 1 1978,57–68.
L.A.Zadeh, Linguistic Cybernetics, Proc. of the Internat. Sympos. on Syst. Sciences and Cybernetics,Oxford, University, 1972
A.P. Weirzbicki, A Mathematical Basis for Satisticing Decision Making IIASA, Luxemburg, Austria, 1980 80–90.
L.A.Zadeh, Optimality and Non-Scalar-Valued Performance Criteria, IEEE Transactions on Autimatic Control, AC-8, 59 1963.
Z. Pawlak, On conflicts, Int.J.Man Machine Studies, 21, 1984,127–134.
P.C.Fishburn, Decision and Value Theory, Wiley, New York,1964.
Kacprzyk J., Yager K.K, Linguistic quantifiers and belief qualification in fuzzy multicriceria and multistage decision making,Control and Cybernetics Vol. 13, No 3, 1984.
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© 1988 Springer-Verlag Berlin Heidelberg
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Zhukovin, V.E. (1988). Effective Convolutions of Vector Preference Relations in Decision Making Problems. In: Kacprzyk, J., Roubens, M. (eds) Non-Conventional Preference Relations in Decision Making. Lecture Notes in Economics and Mathematical Systems, vol 301. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51711-2_7
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DOI: https://doi.org/10.1007/978-3-642-51711-2_7
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