Probability, Fuzziness and Information: Defining Missions in Medicine

Abstract

Aristotelian logic has played, and is still nowadays playing, an essential role in health sciences, resulting in sharp classifications where symptoms, diseases and treatments seem to be clearly defined. However, this schema suffers from uncertainty since every human being is an extremely complex biological individual and, for example, some symptoms associated to a given disease can show only mildly or even be absent in a sick person, health conditions usually express themselves with variations into a given set of patients and treatments almost always need to have some sort of personalization. Even in some cases, drugs must be administrated by trial and error attempts. In a traditional way, both probability theories and statistics are a major toolbox of mathematical assistance in health sciences, since they help to describe observed cases into a context of population. In particular, probability is useful as a tool for forecasting and we can say: ”prognosis of patient A is X with probability p”, but it is not useful for describing intrinsic phenomena in states that are vague in nature, as, for example, in the following sentence: ”Patient B, located in room 212, is rather ill”, where ”rather ill” is an imprecise linguistic slab of information. Fuzzy sets theory, introduced by Lofti Zadeh back in 1965, sheds new lights in the very paradigm of classifications, logic and thus medicine. In this work we shall introduce the concepts of Life Illness Curves (LIC) and Life Quality Curves (LQC) that will help us to redefine missions in medicine where human perceptions must be also taken into account for a better representation of the information handled by physicians.