# Fuzzy Logic

## Mathematical Tools for Approximate Reasoning

• Giangiacomo Gerla
Book

Part of the Trends in Logic book series (TREN, volume 11)

1. Front Matter
Pages I-XII
2. Giangiacomo Gerla
Pages 1-18
3. Giangiacomo Gerla
Pages 19-44
4. Giangiacomo Gerla
Pages 45-67
5. Giangiacomo Gerla
Pages 69-87
6. Giangiacomo Gerla
Pages 89-107
7. Giangiacomo Gerla
Pages 109-128
8. Giangiacomo Gerla
Pages 129-150
9. Giangiacomo Gerla
Pages 151-169
10. Giangiacomo Gerla
Pages 171-198
11. Giangiacomo Gerla
Pages 199-220
12. Giangiacomo Gerla
Pages 221-250
13. Back Matter
Pages 251-271

### Introduction

Fuzzy logic in narrow sense is a promising new chapter of formal logic whose basic ideas were formulated by Lotfi Zadeh (see Zadeh [1975]a). The aim of this theory is to formalize the "approximate reasoning" we use in everyday life, the object of investigation being the human aptitude to manage vague properties (as, for example, "beautiful", "small", "plausible", "believable", etc. ) that by their own nature can be satisfied to a degree different from 0 (false) and I (true). It is worth noting that the traditional deductive framework in many-valued logic is different from the one adopted in this book for fuzzy logic: in the former logics one always uses a "crisp" deduction apparatus, producing crisp sets of formulas, the formulas that are considered logically valid. By contrast, fuzzy logical deductive machinery is devised to produce a fuzzy set of formulas (the theorems) from a fuzzy set of formulas (the hypotheses). Approximate reasoning has generated a very interesting literature in recent years. However, in spite of several basic results, in our opinion, we are still far from a satisfactory setting of this very hard and mysterious subject. The aim of this book is to furnish some theoretical devices and to sketch a general framework for fuzzy logic. This is also in accordance with the non­ Fregean attitude of the book.

### Keywords

Extension abstract logic artificial intelligence control formal logic fuzzy fuzzy control fuzzy logic intelligence logic philosophy

#### Authors and affiliations

• Giangiacomo Gerla
• 1
1. 1.Department of Mathematics and Computer SciencesUniversity of SalernoItaly

### Bibliographic information

• DOI https://doi.org/10.1007/978-94-015-9660-2