Fuzzy Set and Its Extension

2Playing with Fuzzy/Intuitionistic Fuzzy Numbers

2.1 Introduction

This chapter provides an approach to model unknown data by means of fuzzy set theory. As precise data are out of reach, fuzzy numbers can address the problem of deriving uncertainty on a sum of variables whose values lie within fuzzy intervals. Such data may be modeled by a fuzzy set which acts as “more or less” on non‐fuzzy values of the data. The term “more or less” is used here to emphasize the fact that not only there are two usual degrees: “complete possibility” and “impossibility” but it also contains intermediate values.

Fuzzy numbers are used widely in decision‐making problems, where values of parameters or decision variables are not precisely fixed or assessed. To name a few, applications could be multi‐criteria optimization and decision making under uncertainty, where fuzzy‐expected utilities can be obtained out of incomplete assessed probabilities. Sometimes, it may happen that the data are dependent and in that case, the variables are interactive. To deal with such type of interaction in real‐life problems, fuzzy arithmetic is an important tool in aggregating the values. It is used in sensitivity analysis in systems modeling, computer‐aided design, and operations research.

2.2 Fuzzy Numbers

Uncertainty is frequently encountered in day‐to‐day life. Concrete problems often involve many quantities that are idealizations of inaccurate information involving numerical values. For instance, when we measure ...