Neo Arithmetic and Ranking Techniques for Trapezoidal Generalized Interval Valued Fuzzy Numbers: Their Applications in Decision Making for Medical Investigation

摘要

The uncertainty caused mainly by the deficiency of precision and data, artificial/human-made errors, information accessed from expert opinions or very miniature size of samples, etc., is the reason behind the ill-defined nature of most of the real-world problems. Type-I fuzzy set theory (FST) handles these kinds of uncertainties with a better perspective. However, type-I FST cannot always characterize uncertainty in all real-world problems. Examples may be had in the diagnosis of patients that has to be primarily dependent on the medical investigator’s (MI) buoyancy level, where owing to limited knowledge of the MI, results with a higher grade of accuracy cannot be expected. However, on the same note, interval-valued fuzzy set (IVFS) can prove to be a suitable apparatus while embodying vague linguistic expressions of the patients. Moreover, interval-valued fuzzy numbers (IVFNs) have the unique ability to incorporate the confidence degree of the opinions put forward by the MI to fit into a closed region (interval). Various researchers developed a few arithmetic methods for IVFNs with situation-based drawbacks. Furthermore, the ranking of IVFNs plays a crucial role in ordering IVFNs in decision making. Numerous ranking approaches can be encountered in literature with shortcomings. In this regard, this article attempts to devise a neo arithmetic technique along with an appropriate ranking method for trapezoidal generalized interval-valued fuzzy numbers (TrGIVFNs) and furnishes a maiden attempt to swot up decision making for MIs. The advantages of the present proposed methods have been showcased by comparing them with existing methods. It is praiseworthy of TrGIVFNs that their parameter heights can facilitate the buoyancy degree of the decision-maker's judgments in very specific comportment. Finally, a case study using live data has been performed so that the proposed technique could be tested to the core. It is observed that the proposed approach provides a way to perform MI in an explicit demeanor, and the followed consequences are acceptable in comparison to classical techniques. Furthermore, it provides more precision and efficiency to the decision of the medical investigators.