HIERARCHICAL CLUSTERING OF PICTURE FUZZY RELATION

Abstract

The paper aims to find the (𝛼̃,𝛽̃𝛾̃) - cuts of picture fuzzy relation and apply it to find its hierarchical clustering. we studied the previous results of Intuitionistic fuzzy relation and its (𝛼̃,𝛽̃,𝛾̃) - cuts. We propose a technique of finding 𝛼̃ - cuts of picture fuzzy sets using results of intuitionistic fuzzy set. Membership of PFS mainly deals with positive, negative and neutral membership while IFS only deals with positive and negative membership. In this paper, we attempt to study picture fuzzy set more deeply and providing the more results in picture fuzzy relation that contains 𝛼̃ - cuts of picture fuzzy set. Further we studied about the various applications of Intuitionistic fuzzy relation and picture fuzzy relation. Intuitionistic fuzzy relation deals with the application on the comparision of distant measures using normalised hamming distance measure. The two applications of picture fuzzy relation is discussed. First application deals with the determination of higher study area selection on the basis of composition of picture fuzzy relations. We found picture fuzzy relation on topic knowledge, study area and the skills. Then, we applied picture fuzzy transformation to obtain new picture fuzzy relation. After defuzzifying the PFR matrix we found the suitable study areas for students to continue higher studies. Second application picture-fuzzy medical diagnosis deals with the medical diagnosis of an illness and patients suffering from a particular disease is identified with the help of composition of picture fuzzy relation.