Efficient points in a sum of sets of alternatives
Anas Mifrani
TL;DR
This paper investigates the conditions under which the efficient points in a sum of sets of alternatives match those in individual sets, providing criteria applicable to both finite and infinite cases.
Contribution
It establishes necessary and sufficient conditions for the equivalence of efficient points in a sum of sets and individual sets, extending to infinite sets.
Findings
Conditions for efficiency equivalence in finite sets.
Conditions for efficiency equivalence in infinite sets.
Illustrative examples demonstrating the theoretical results.
Abstract
The concept of efficiency plays a prominent role in the formal solution of decision problems that involve incomparable alternatives. This paper develops necessary and sufficient conditions for the efficient points in a sum of sets of alternatives to be identical to the efficient points in one of the summands. Some of the conditions cover both finite and infinite sets; others are shown to hold only for finite sets. Examples are provided that illustrate these results.
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Taxonomy
TopicsOptimization and Packing Problems · Optimization and Variational Analysis · Advanced Theoretical and Applied Studies in Material Sciences and Geometry