This chapter introduces the concept of Fuzzy Multiple Attribute Decision Making (FMADM) methods, which are designed to handle decision-making problems involving fuzzy data. The classical MADM methods assume crisp numbers for performance ratings and attribute weights, but in reality, these values can be crisp, fuzzy, or linguistic. For example, when evaluating candidates for a professor position, attributes like creativity, maturity, communication skills, and number of publications may have linguistic terms such as "good," "average," and "poor" as ratings. FMADM methods were first introduced by Bellman and Zadeh, and later developed by Baas and Kwakernaak. Over the past decade, several FMADM methods have been proposed, and systematic reviews have been conducted by Kickert and Zimmermann. Zimmermann's approach treats FMADM as a two-phase process: finding fuzzy utilities and applying fuzzy ranking methods. This chapter provides a comprehensive review of 18 existing FMADM methods, classifying them into eight categories based on their ability to solve large-size problems, the type of data allowed, their relation to classical MADM methods, and the techniques used. Theoretical backgrounds, algorithms, and numerical examples are provided for each method, along with their advantages and disadvantages. Additionally, a new approach to FMADM problems is proposed.This chapter introduces the concept of Fuzzy Multiple Attribute Decision Making (FMADM) methods, which are designed to handle decision-making problems involving fuzzy data. The classical MADM methods assume crisp numbers for performance ratings and attribute weights, but in reality, these values can be crisp, fuzzy, or linguistic. For example, when evaluating candidates for a professor position, attributes like creativity, maturity, communication skills, and number of publications may have linguistic terms such as "good," "average," and "poor" as ratings. FMADM methods were first introduced by Bellman and Zadeh, and later developed by Baas and Kwakernaak. Over the past decade, several FMADM methods have been proposed, and systematic reviews have been conducted by Kickert and Zimmermann. Zimmermann's approach treats FMADM as a two-phase process: finding fuzzy utilities and applying fuzzy ranking methods. This chapter provides a comprehensive review of 18 existing FMADM methods, classifying them into eight categories based on their ability to solve large-size problems, the type of data allowed, their relation to classical MADM methods, and the techniques used. Theoretical backgrounds, algorithms, and numerical examples are provided for each method, along with their advantages and disadvantages. Additionally, a new approach to FMADM problems is proposed.