Abstract:
The problem of multicriteria choice with a fuzzy preference relation is considered, the main objects of which are a set of feasible alternatives, a numerical vector criterion and the fuzzy preference relation of the decision maker (DM). Concepts of a fuzzy vector space, a polyhedral fuzzy set and the distance between convex fuzzy sets and cones are used. To reduce the Pareto set the ultimate possibilities of information about the fuzzy preference relation in the form of quanta of information set are studied. It is proved that in a sufficiently wide class of above problems with a finite set of quanta of fuzzy information, one can arbitrarily accurate approximate an initially unknown fuzzy set of nondominant elements.
Keywords:
multicriteria choice problem, reduction of the Pareto set, quanta of fuzzy information, completeness theorem.
Citation:
V. D. Nogin, “Ultimate possibilities of the Рareto set reduction based on quanta of fuzzy information”, Artificial Intelligence and Decision Making, 2017, no. 4, 69–77; Scientific and Technical Information Processing, 45:6 (2018), 452–457
\Bibitem{Nog17}
\by V.~D.~Nogin
\paper Ultimate possibilities of the Рareto set reduction based on quanta of fuzzy information
\jour Artificial Intelligence and Decision Making
\yr 2017
\issue 4
\pages 69--77
\mathnet{http://mi.mathnet.ru/iipr267}
\elib{https://elibrary.ru/item.asp?id=30771445}
\transl
\jour Scientific and Technical Information Processing
\yr 2018
\vol 45
\issue 6
\pages 452--457
\crossref{https://doi.org/10.3103/S0147688218060084}
Linking options:
https://www.mathnet.ru/eng/iipr267
https://www.mathnet.ru/eng/iipr/y2017/i4/p69
This publication is cited in the following 2 articles:
Yulia V. Kovalenko, Aleksey O. Zakharov, “The Pareto set reduction in bicriteria customer order scheduling on a single machine with setup times”, J. Phys.: Conf. Ser., 1546:1 (2020), 012087
V Sudakov, T Sivakova, “Use of fuzzy areas of preference in tasks of multi – criteria evaluation of freight air transport”, IOP Conf. Ser.: Mater. Sci. Eng., 927:1 (2020), 012060
Citation in format AMSBIB
Contact us: