Mathematics, Scientific Reasoning and Fuzzy Logic

Abstract

This article tries to show the relationship among general principles of mathematics, human scientific reasoning and Fuzzy Logic (FL). In applied sciences, in engineering and in social sciences Fuzzy Logic can be used in solution of real life problems. Two main types of mathematical reasoning; induction and deduction and also abduction are essential ways of FL. If we take into consideration dedication we can assume it is always a valid process, but it is not an infallible method. Before the concept FL, in Western World, logic was based on the principle of the bivalent Logic. Ideas of multivalued or even infinite valued logic is based on the mathematical theory of Fuzzy Sets (FS). It means one can pass from bivalent logic to infinitely many values lying in the interval [0,1]. Philosophy of Mathematics and Scientific Reasoning gives us the opportunity to discuss the mathematical background of FL. Rather than being strictly on engineering problems, FL provides a number of broader applications; Artificial intelligence, neural networks, genetic algorithms, biological processes are some of these applications. What kind of mathematical tool we use, in application? We have to show that instead of deterministic or probabilistic solution, FL gives better result. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.