Complex fuzzy sets and their applications

Fuzzy logic suggested by Zadeh (1965) is an infinite valued logic with fuzzy sets whose range is all real numbers in closed interval [0,1]. Many new studies and applications have been done with fuzzy logic. Complex fuzzy sets defined firstly by Moses et al. (1999a) and then by Ramot et al. (2002) are some of these studies. In applications using fuzzy logic have appeared a lot of sector such as electric-electronic, transportation, automotive, health, economy, cleaning and building. In this thesis study, firstly, general information about fuzzy logic was given. Thereafter crisp sets, properties of crisp sets, fuzzy sets and properties of fuzzy sets were studied. Then, interval numbers, interval operation features, fuzzy numbers and different types of fuzzy numbers were investigated. Complex numbers, arithmetic operations of complex numbers and their polar notation were expressed. Complex fuzzy sets by Moses et al. (1999a) and Ramot et al. (2002) and their set operations were presented and as an original study regional complex fuzzy sets and their set operations were defined. Finally, an application of regional complex fuzzy sets was obtained.