Multi ¿criteria decision making problems in fuzzy environment has received wide attention from researches in view of its practical application to real life situations. Based on the type of data used to express the different alternatives, different approaches/methodologies are employed to tackle the fuzzy MCDM problems. The mostly used tools to deal with such problems are aggregation operators and score functions. In this monograph we elaborate the use of score functions in solving fuzzy MCDM problems, introduce a new weighted geometric aggregation operator, discuss the drawbacks and short comings of the existing score functions and emphasize the need for new score functions to overcome the existing deficiencies. Some new score functions based on a new type of fuzzy set are defined and some theoretical properties of these functions are established. These score functions are used in solving the most general fuzzy MCDM problems with the help of new methodology. A comparative analysis is also carried out to establish the supremacy and efficient working of the new methods and the new score functions.