Coordination of Contrariety and Ambiguity in Comparative Compositional Contexts: Balance of Normalized Definitive Status in Multi-indicator Systems

We address oppositional aspects of comparative compositional contexts for some particular purpose. Compositional components of land cover in localities provide our context, with the exemplifying purpose being cooperative conservation. A subset of cover components is considered definitely propitious (pro) for the purpose, with another subset being definitely contraindicative (con), and the rest as ambiguous “other.” Plotting percent pro on the ordinate and percent con on the abscissa gives a “definitive domain display” for visualization. A “Balance Of Normalized Definitive Status” (BONDS) is used for scalar sequencing. Using concepts of “down-set” and “up-set” from theory of partially ordered sets (posets), this is extended to obtain an intrinsically compositional context of pro and con that applies objectively to any suite of (monotonic) indicators. Indicators are eliminated in a systematic manner to resolve ties in the extended version by lexicographic suborder. Computations are specified in terms of R software.