Formalizing the Informal, Precisiating the Imprecise: How Fuzzy Logic Can Help Mathematicians and Physicists by Formalizing Their Intuitive Ideas

Abstract. Fuzzy methodology transforms expert ideas { formulated in terms of words from natural language { into precise rules and formu-las. In this paper, we show that by applying this methodology to in-tuitive physical and mathematical ideas, we can get known fundamen-tal physical equations and known mathematical techniques for solving these equations. This fact makes us condent that in the future, fuzzy techniques will help physicists and mathematicians to transform their imprecise ideas into into new physical equations and new techniques for solving these equations. 1 Fuzzy and Physics: Past and Present Fuzzy methodology: main objective. Fuzzy methodology has been invented to transform expert ideas – formulated in terms of words from natural language – into precise rules and formulas, rules and formulas understandable by a computer (and implementable on a computer); see, e.g., [6, 10, 12]. Fuzzy methodology: numerous successes. Fuzzy methodology has led t