Elementary Fuzzy Matrix Theory and Fuzzy Models for Social Scientists

This book gives the basic notions of fuzzy matrix theory and its applications to simple models. The approach is non-traditional in order to attract many students to use this methodology in their research. The traditional approach of mathematicians has conditioned students of sociology in such a manner that they averse to using mathematical tools. Six simple types of fuzzy models that make use of fuzzy matrices are given. These models are distinct because they are time dependent and can even be used for statistical data. The Fuzzy Cognitive Maps model gives the hidden pattern. Fuzzy Relational Maps model not only gives the inter-relations between two sets of disjoint attributes. The Bidirectional Associative Memories model analyzes data depending on the time-period while the Fuzzy Associative memories model can give the gradation of importance of each attribute. Finally, the Fuzzy Relational Equation model is capable of giving a solution closer to the predicted solution. All the methods are illustrated through elaborate examples of particular social problems.