Extension of Functions Defined on Bounded Posets via Retractions and its Properties
Extension of functions; retractions; properties; conditional monotonicity; abstract homogeneity; quasi-overlap; quasi-grouping; bounded (sub/super) posets.
|It is proposed extensions via retractions of functions defined on bounded posets (partially ordered sets) and their properties. As an intermediate step, it is presented what has been done up to this point: (i) the introduction of the concept of conditional monotonicity and other relaxed monotonicities within the scope of intervals equipped with admissible orders; (ii) the introduction of the concept of abstract homogeneity in relation to posets; (iii) the extension of fuzzy negations, quasi-overlap functions, and quasi-grouping functions defined on bounded posets from subposets to superposets. Finilally, it is presented the proposal itself and a schedule.