Characterizations of Upward and Downward Sets in Semimodules by Using Topical Functions. (1st November 2016) - Barsam, H.; Mohebi, H.
ABSTRACT: In this article, we study topical functions f : X → K defined on a b-complete idempotent semimodule X over a b-complete idempotent semifield K with values in K . We characterize the abstract concavity and support set of this class of functions. Next, we investigate the abstract concavity of extended valued topical functions, where and ⊤: = sup K . Finally, as an application, we present characterizations of upward and downward sets by using extended valued elementary topical functions.