Elementary fuzzy matrix theory and fuzzy models for social scientists

TL;DR

This book introduces basic fuzzy matrix theory and six simple fuzzy models tailored for social scientists, emphasizing non-traditional, accessible approaches to analyze social data and uncover hidden patterns.

Contribution

It presents a non-traditional, accessible methodology for applying fuzzy matrix models to social science research, including six distinct models with practical examples.

Findings

Models reveal hidden patterns in social data

Time-dependent fuzzy models analyze statistical data

Fuzzy relational models identify attribute inter-relations

Abstract

This book gives the basic notions of fuzzy matrix theory and its applications to simple fuzzy 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 are 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 models gives the hidden pattern. Fuzzy Relational Maps model not only gives the hidden pattern but also 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 models are illustrated through elaborate examples of particular social problems.