Application of fuzzy Z-Hesitant data information in fuzzy C-means clustering analysis.

This paper aims to offer a new fuzzy Z-Hesitant methodology as a novel approach to analyzing fuzzy data information. In a nutshell, Z-Hesitant is the combination of Z-numbers with Hesitant Fuzzy Sets in which Z-numbers represent an ordered pair of fuzzy numbers having a structure of restriction (A) and reliability (B). The restriction (A) represents the uncertainty of the evaluation, while the reliability (B) represents a measure of certainty towards the restriction (A). On the other hand, Hesitant Fuzzy Sets hold the definition that the membership degree with respect of an element is a set of a variety of possible values in the range of [0,1]. Here, the importance of both extensions is evident. Z-numbers have a more remarkable ability to describe human knowledge because it considers the level of certainty in their calculation. On top of that, Hesitant Fuzzy Sets are beneficial because each of the opinions is considered, resulting in a more reasonable decision. Moreover, when the data information is converted using fuzzy Z-Hesitant methodology, it can significantly hold a substantial amount of what Z-numbers and Hesitant Fuzzy Sets offer. In this approach, the Z-Hesitant is described as an ordered pair of fuzzy numbers whose restriction (A) as well as reliability (B) are hesitant fuzzy numbers, resulting in more than one possible membership degree. Furthermore, applying Z-Hesitant data information in fuzzy clustering analysis using the fuzzy c-means algorithm is used to better comprehend this information. The results indicate that the fuzzy c-means algorithm successfully clusters the fuzzy Z-Hesitant data information. The comparison with other types of fuzzy data information shows that fuzzy Z-Hesitant data information clustering is more compact in internal cluster validation analysis. [ABSTRACT FROM AUTHOR]