This section introduces a multi-attribute decision making (MADM) problem, where alternatives are evaluated based on multiple attributes. The problem involves decision makers selecting the best alternative from a set of possible courses of action, each evaluated on various attributes. Traditional MADM methods assume all performance scores and attribute weights are crisp numbers. However, in reality, performance ratings can be crisp, fuzzy, or linguistic. For example, attributes like creativity or communication skills are often described using linguistic terms rather than numerical values. This leads to a mix of fuzzy and crisp data in real-world MADM problems. Fuzzy MADM methods have been developed to handle such fuzzy data. Bellman and Zadeh were among the first to connect fuzzy set theory with decision making. Baas and Kwakernaak proposed a classic fuzzy MADM method in 1977. Over the past decade, several fuzzy MADM methods have been introduced. Systematic reviews of these methods have been conducted by Kickert and Zimmermann, who described the fuzzy MADM process as a two-phase method: first, determining fuzzy utilities for alternatives, and second, applying fuzzy ranking methods to determine the preference order. This chapter provides a comprehensive review of existing fuzzy MADM methods. There are 18 such methods, classified into eight categories based on four factors: their ability to handle large problems, the type of data they allow, the classical MADM method they relate to, and the technique they use. Each method is explained with theoretical background, algorithms, and numerical examples. The advantages and disadvantages of each method are discussed. Finally, a new approach to solving fuzzy MADM problems is proposed.This section introduces a multi-attribute decision making (MADM) problem, where alternatives are evaluated based on multiple attributes. The problem involves decision makers selecting the best alternative from a set of possible courses of action, each evaluated on various attributes. Traditional MADM methods assume all performance scores and attribute weights are crisp numbers. However, in reality, performance ratings can be crisp, fuzzy, or linguistic. For example, attributes like creativity or communication skills are often described using linguistic terms rather than numerical values. This leads to a mix of fuzzy and crisp data in real-world MADM problems. Fuzzy MADM methods have been developed to handle such fuzzy data. Bellman and Zadeh were among the first to connect fuzzy set theory with decision making. Baas and Kwakernaak proposed a classic fuzzy MADM method in 1977. Over the past decade, several fuzzy MADM methods have been introduced. Systematic reviews of these methods have been conducted by Kickert and Zimmermann, who described the fuzzy MADM process as a two-phase method: first, determining fuzzy utilities for alternatives, and second, applying fuzzy ranking methods to determine the preference order. This chapter provides a comprehensive review of existing fuzzy MADM methods. There are 18 such methods, classified into eight categories based on four factors: their ability to handle large problems, the type of data they allow, the classical MADM method they relate to, and the technique they use. Each method is explained with theoretical background, algorithms, and numerical examples. The advantages and disadvantages of each method are discussed. Finally, a new approach to solving fuzzy MADM problems is proposed.