A theorem on nonconvex functions and its application to vector optimization

Article Abstract:

The Fundamental Theorem on Convex Functions is one of the basic results of convex analysis. A counterpart theorem called the Theorem on Nonconvex Functions is presented for the case when the convexity assumption does not apply. It was shown that some necessary requirements for proper efficiency and weak efficiency in nonconvex vector optimization are implicit. The implications of this finding for vector optimization and decision-making support are discussed.

Multiple criteria decision making, Models, Nonlinear programming

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Cognitive maps and fuzzy implications

Article Abstract:

A framework defining a node as a logical proposition and a link as an implication has been presented. The idea behind the given definitions, which were arrived at with the use of the fuzzy implication concept, is to provide a clear set of rules for the study and analysis of cognitive maps. The move to develop a cognitive map model that is consistent with how people define nodes and arcs is expected to lead to the improvement of work done on cognitive maps.

Analysis, Usage, Fuzzy algorithms, Fuzzy logic, Cognition, Mappings (Mathematics), Maps (Mathematics)

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