Hierarchical cooperation of neighbors in defuzzification

Defuzzification has been viewed as a problem of optimal selection of an element from a fuzzy set. In this paper we enlarge the concept of defuzzification as selection procedure by associating a belief value to the selected element. Based on analogies in nature, recently an attempt has been made to understand how cooperative elements in a fuzzy set can make a better selection of its representative element. Such a selection of an element from a set is done through a process of selective transformations. In this study an extended scheme of a hierarchical process of defuzzification involving cooperative neighbors defuzzification at each layer is proposed. A fuzzy set is divided into sub-fuzzy sets. Each cooperative module extracts, from a sub-fuzzy set, its representative along with a sub-fuzzy set belief value. At the next higher layer, representatives again form a fuzzy set. At that level the elements poll and elect their most ideal representative of their original fuzzy set. We refer to this structured defuzzification as hierarchical cooperative neighbors in defuzzification