Cardinality and the Borda score

Article Abstract:

An illustration of the Borda rule was undertaken to assess the significance of the variation of the Borda scores. The implementation of the Borda rule to a profile of fuzzy relations showed that the method was able to yield results that place few limitations on a set that either includes the total orders or rational relations. The results obtained by the Borda method were also proven to be highly applicable in other situations.

Research and Development in the Physical, Engineering, and Life Sciences, Mathematics, Multiple criteria decision making

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On the properly efficient points of nonconvex sets

Article Abstract:

K. Belkezis and M. Pirlot's question concerning the derivation of a supported and properly efficient point of set Z, a nonempty subset of an n-dimensional Euclidean space R(sup n), is considered. Specifically, it is shown that the optimal solution to a specific scalar problem cannot be obtained by generating the properly efficient and supported points of Z because of the special characteristics of such points.

Vector analysis

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A general model for deriving preference structures from data

Article Abstract:

An alternative mathematical justification for the integrated model for valued preferences introduced by Fodor, Ovchinnikov and Roubens (FOR) is proposed. The justification, denoted as FORM, provides a functional characterization of the whole family of solutions provided by the FOR model. Among the improvements of FORM are symmetry of indifference and incomparability functions and strict monotonicity.

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