The Choquet and Sugeno Integrals as Measures of Total Effectiveness of Medicines

Abstract

The concepts of the Choquet and Sugeno integrals, based on a fuzzy measure, can be adopted as useful tools in estimation of the total effectiveness of a drug when appreciating its positive influence on a collection of symptoms typical of a considered diagnosis. The expected effectiveness of the medicine is evaluated by a physician as a verbal expression for each distinct symptom. By converting the words at first to fuzzy sets and then numbers we can regard the effectiveness structures as measures in the Choquet and Sugeno problem formulations. After comparing the quantities of total effectiveness among medicines, expressed as the values of the Choquet or Sugeno integrals, we accomplish the selection of the most efficacious drug.

The Choquet Integral Applied to Ranking Therapies in Radiation Cystitis

“…By interpreting the utilities of treatments as measures we have furnished total utility estimates with such tools as the Choquet integrals to extend the model of the classical fuzzy decision-making. This complement to decision making constitutes an original contribution as it has been impossible to find the similar effects in literature apart from our own [7]. The method of constructing families of membership functions, depending only of the length of a reference set and the number of constraints, reveals another own idea of the authors.…”

“…For ω = 11 and E = 100 (the typical length of the reference set [0, 100] tested in medical investigations of frequencies) we derive membership functions of N q , q = 1,…,11, by employing formulas (5)- (7).…”

“…In general, we are able to perform the computations of total utilities of a i , i = 1,…,n, by [7] ∑ · :…”

Multi-criteria Decision Making on the Best Drug for Rheumatoid Arthritis

“…. Hence, we have the ordered triplet where is a space of symptoms, is a set of alternatives, and is the utility matrix [4].…”

“…Also, there exist some multi-criteria decision making problems in medical applications, especially in medical diagnosis. According to fuzzy decision making models [2] based on utility theory in medical diagnosis, Rakus-Andersson and Jogreus facilitated the choice of the drug, especially in the diagnosis of coronary heart disease [3,4].…”