Defects Control Charts Using Interval-Valued Penthagorean Fuzzy Sets

Abstract

Defects control charts are one of the attributes control charts which are constructed based on the number of defects on a product or in an inspection unit. Since the term ‘defect’ can be vague due to the subjective decisions of the quality control operator, it cannot be precisely defined. In such cases, fuzzy set theory can be used to add more information and flexibility to attribute based-process control. After the introduction of the ordinary fuzzy sets to the literature, it has been extended to many new types of fuzzy sets. One of the recent extensions, q-rung orthopair fuzzy sets, which is a generalization of intuitionistic fuzzy sets and Pythagorean fuzzy sets, provides a broader space to express ambiguous information, For the q-rung orthopair fuzzy sets the sum of the qth power of the membership degree and the qth power of the non-membership degree is equal to or less than one. In this study, the fifth power of the q-rung orthopair fuzzy sets is used to represent the impreciseness in the construction of the defects control charts and names as penthagorean fuzzy sets. An application in a TV production system is presented as an illustrative example.