Midpoint-Based Decision-Making Criterion Between Fuzzy Sets: An Application to Medical Diagnosis Domain

Abstract The need to reach an agreement between two fixed positions arises in many practical problems. A typical example of this type of situation is given when two independent and reputed physicians provide two different patient descriptions. Here, healthcare professionals need to identify the most relevant description to support the diagnostic outcome. In 2003, Nieto and Torres provided an appropriated mathematical framework for decision-making when the aforementioned situation is under consideration through the application of the midpoint notion between fuzzy sets. They stated that the decision-maker can adopt the consensus position within a typically unbounded (in general) collection of midpoints. Inspired by the preceding fact, in this paper we focus our efforts on developing an assisted decision-making technique based on the use of midpoints between fuzzy sets and a scoring function. This approach reduces the consensus position between the two fixed ones to a finite number of distinguished midpoints, i.e., those midpoints at which the scoring is minimized and maximized, respectively. Concretely, we provide two possible alternatives. The first one consists of letting the decision-maker choose between the minimizer or maximizer midpoints of the scoring function values. The second alternative consists in providing a working midpoint which is obtained as a weighted average of the minimizer and maximizer criterions. An example of the applicability of the exposed theory is presented in the framework of medical diagnosis when two physicians want to determine whether a patient has a potential risk of suicide.