Fuzzy Numbers and Their Arithmetic

Fuzzy numbers are a mathematical formulation of vague statements about real numbers. They are a special kind of fuzzy sets that have been introduced by Zadeh. A triangular fuzzy number is a fuzzy set whose graph is a triangle. Trapezoidal fuzzy numbers are, of course, fuzzy sets but since their core contains more than one element, they cannot be classified as fuzzy numbers. Gaussian fuzzy numbers are characterized by membership functions that are some special kind of a Gaussian function. A quadratic fuzzy number and exponential fuzzy numbers are yet another general form of fuzzy numbers. This chapter discusses fuzzy arithmetic of fuzzy numbers as well as a linguistic variable which is a special kind of variable whose values are not numbers but words or sentences in a natural language. This chapter discusses how to construct fuzzy numbers from real-world data and presents a few applications of fuzzy numbers to demonstrate their usefulness.