Fuzzy: a many-valued logic


The paths of life to guide us towards the knowledge are many and a straight; well-defined line does not always represent them. Among these, the theory of Fuzzy Logic can help us to better understand some of the methods that maybe for too long we have lost the habit to use, if not even forgotten, because of the residuals of the positivist scientism.

Brief mathematical introduction

blur2All the elements making up the majority of the categories of everyday life (feelings, emotions, opinions, values, quality, etc.) cannot be defined in a unique or exact way. Let’s try to define an event that causes severe pain: a hammer blow on the finger? The loss of a loved one? Tooth extraction? It is evident that the answer can vary in a very consistent way, based on the subjectivity of the individual, the environment, boundary conditions and the general context. This is because the “Strong Pain” is a fuzzy set (which we will call SP), characterized by a function of “degree of membership” which maps the elements of a universe in a real continuous interval between 0 and 1. In practical terms…

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