Perception-based heuristic granular search: Exploiting uncertainty for analysis of certain functions

Conventional approaches to optimization generally utilize a point-based search to scan domains of complex functions. These optimization algorithms, as a result, face a perpetual search that is never concluded with certainty, since the search space can never be completely scanned. In contrast, the proposed approach benefits from a granular view to scan the whole of the domain space. Such perspective can yield an efficient tool for analysis of complex functions, especially when proof is required. In contrast to conventional granular techniques that usually compute with certain granules, this scheme exploits uncertain granules, in addition to certain ones, to improve computational efficiency. To efficiently navigate the search space, Zadeh’s extension principle, along with several heuristics, is introduced to estimate and reduce the likeliness of inaccuracy. Function analysis is then converted to a question–answering process. This method is general and can be applied to all types of functions whether linear or nonlinear, analytical or non-analytical and continuous or discrete. Several examples and a MATLAB toolbox are provided to illustrate the real-world applicability and computational efficiency of the approach.