Design and analysis of acceptance sampling plans based on intuitionistic fuzzy linguistic terms

Acceptance sampling plans (ASPs) offer inspection of a small set of items from a lot within a predefined plan to procure a certain output quality level with minimum cost in terms of time, effort, and damage to the inspected items. Although traditional ASPs use crisp plan parameters, quality characteristics of the incoming items or human evaluations about inspection process may contain uncertainties and may not always be defined as crisp values in real life problems. The fuzzy set theory (FST) is one of the most popular techniques to model these uncertainties by defining plan parameters as fuzzy numbers. Despite the advantages, traditional fuzzy sets are not flexible enough to model all kinds of uncertainties. For example, it has some disadvantages because of defining the status of any item based on defectiveness or non-defectiveness conditions and presuming the parts as non-defective whose defectiveness is not indeed determined. New extensions of FST can improve the quality of uncertainty modeling of ASPs. Intuitionistic Fuzzy Sets (IFSs) allow slackness for non-determination about the membership and give more sensitive modeling opportunity in human-related evaluations by the help of this ability. Since the inspection procedure of the ASPs depends on human-related judgements, IFSs have been used to define the defectiveness degree of the items in this study. ASPs based on interval-valued IFSs (IVIFSs) have also been designed and some characteristic functions of ASPs, such as acceptance probability ($P_a$), average sample number ($ASN$) and average total inspection ($ATI$) have been reformulated. Intuitionistic binomial and Poisson distributions have been defined to be able to formulate the ASPs. Additionally, the defectiveness of the items has been represented by using linguistic terms to overcome the difficulty of quantifying the verbal evaluation results as numerical measures. The $alpha$-cut technique has been combined with the linguistic approach to allow defining with multiple $alpha$ values for different product segments. Finally, some numerical examples have been presented to analyze the effectiveness of proposed ASPs and discuss the obtained results.