Bulanık sayılar ve bulanık doğrusal denklemler

In this thesis, we will first give detailed information about fuzzy sets and their properties. Then, after introducing fuzzy numbers, we will focus on the triangular fuzzy numbers, trapezoidal fuzzy numbers and Gaussian-type bell shape fuzzy numbers. We also used the alpha-cut method for each fuzzy number type. The alpha-cuts method is a technique used in fuzzy set theory to handle and analyze fuzzy sets. The alpha-cuts method allows for the conversion of a fuzzy set into a series of crisp sets, making it easier to perform various mathematical operations and analyses. Then, we will give the solution of first order fuzzy linear equations on each type of fuzzy number. A fuzzy set is an extension of the classical concept of a set, introduced by Zadeh in 1965 as a way to deal with uncertainty and ambiguity. Unlike classical sets, where an element either belongs to the set or does not (binary membership), fuzzy sets allow for degrees of membership. This means that an element can partially belong to a fuzzy set with a membership value between 0 and 1. A fuzzy number is a special type of fuzzy set that represents a quantity with uncertain boundaries. Unlike crisp numbers, fuzzy numbers allow for a range of possible values, each with a degree of membership. This concept is useful in situations where data is imprecise, uncertain, or ambiguous. Fuzzy linear equations are an extension of classical linear equations that incorporate the concept of fuzziness to deal with uncertainty and imprecision. In a fuzzy linear equation, the coefficients, variables, and constants can all be represented as fuzzy numbers or fuzzy sets. This allows solving linear equations where some or all of the data is not known with certainty but is instead represented by fuzzy values. Keywords: Fuzzy Sets, Fuzzy Numbers, Trapezoidal Fuzzy Numbers, Gaussian-Type Bell Shape Fuzzy Numbers, Alpha-Cuts Method, Fuzzy Linear Equations