Chapter 9 - Fuzzy Methods

Abstract

This chapter deals with applications of fuzzy methods, which give the ability to study quantitatively problems characterized by ambiguity, imprecision, uncertainty, linguistic variables, and missing or few or no data. The fuzzy method introduces another way of thinking: a statement, instead of being true or false, may be partially true or false. Thus, instead of taking into account the typically used fixed numerical values (such as, e.g., 2.34), the fuzzy method employs a set of plausible values (e.g., around the value 2.34) within a specific domain. Although this approach may look similar to the error of statistical methods, the fuzzy method can tackle situations (such as missing or vague data), for which classic methods are inefficient. The principles of fuzzy numbers, fuzzy sets, and fuzzy logic are presented. The case of symmetric triangular fuzzy numbers is analyzed in detail. Next, linear regression analysis with the use of fuzzy numbers is explained. A detailed application of fuzzy linear regression for a transport demand problem is surveyed analytically. The chapter includes many applications of fuzzy linear regression for the forecast of a variety of transport demand problems: air transport, rail transport, road transport, transport at urban level, and transport economics. Applications of the fuzzy method to other transport problems are explained: route choice, road safety, accident analysis, logistics and routing of freight vehicles, and the optimization of capacity of airports.