Motivated by the application problem of sensor fusion the author introduced the concept of graded set. It is reasoned that in classification problem arising in an information system (represented by information table), a novel set called Granular set
naturally arises. It is realized that in any hierarchical classification problem, Granular set naturally arises. Also when the target set of objects forms a graded set the lower and upper approximations of target sets form a graded set. This generalizes the concept of rough set. It is hoped that a detailed theory of granular/ graded sets finds several applications.
In this research paper, the problem of optimization of a quadratic form over the convex hull generated by the corners of hypercube is attempted and solved. It is reasoned that under some conditions, the optimum occurs at the corners of hypercube. Res
ults related to the computation of global optimum stable state (an NP hard problem) are discussed. An algorithm is proposed. It is hoped that the results shed light on resolving the P not equal to NP problem.
