Imprecise Knowledge and Fuzzy Modeling in Materials Domain

1. Introduction

A critical issue in design and development of new materials, for advance and complex systems, is that in most cases we do not have complete understanding of the fundamental basis of co-relationships of compositional and processing space, microstructure space and materials response space. The attributes of these variable spaces are too difficult for direct measurements and too difficult to describe their interaction when a particular physical phenomenon is occurring. They exhibit extreme nonlinear behavior across the different length and time scale. As a consequence imprecision and uncertainties are inherent characteristics of many materials phenomenon. Therefore the plausible methods for solving problems, where knowledge or information is imprecise, approximate and incomplete, are developing as an area of interest of the materials designers. Different modeling techniques are there to model the structure and properties of materials either from first principles or from other physical or chemical theories. But in most of the cases practical materials systems are complex enough to be modeled through such theories. Absence of precise scientific knowledge to describe such multivariate materials systems makes it difficult to develop physical models. In some cases databases developed experimentally or from data warehouses of industries could be used to develop empirical relations among the variables. Such data driven models developed through statistical or computational intelligence based techniques viz. artificial neural network could also be used to extract useful knowledge from the data. In recent time, significant success has been achieved in implementation of informatics and machine learning in the effort to describe the features of different complex materials systems. Employment of computational intelligence or soft computing techniques for solving critical materials development issues lead to highly intelligent and more realistic results. Hybrid intelligent systems deal with the integration of two or more of the techniques. The combined use of techniques has been found to result in effective problem solving in comparison to the stand alone applications of such techniques. Hence stochastic models, though difficult to design and manipulate, can provide insights into real-world processes and offer new computational opportunities.

Thus there exist two distinct approaches, knowledge driven physical models and data driven empirical models. In between these two domains remains the sphere of modeling using imprecise knowledge. In case of materials systems there are many such complex cases where the knowledge can be expressed linguistically, but not through mathematical expressions. Fuzzy inference system based on fuzzy set theory is capable of converting such imprecise linguistic expressions to predictive models (Zadeh, 1965). Generally speaking model predictions are never certain. Understanding uncertainty in a model also is important to infer its solutions. So far many techniques are described for solving certain materials problems. The focus of the current chapter is the implementation of a computational technique to solve materials design problem where knowledge information is imprecise, approximate and incomplete by invoke of the tractable information processing and computational learning approaches. Fuzzy set theory, rough set theory, neural network, neuro-fuzzy hybridization, rough-fuzzy hybridization etc are such techniques to name a few. Here the fuzzy inference system and its hybridized form with neural network will be covered with an emphasis on their current abilities and limitations taking few real application example problems. The most important aspect of these techniques is that in addition to their capability to develop relationship between the variables, they can extract knowledge from data through developing comprehensible linguistic if-then rules. Both the aspects are described separately with case studies on their applications in the materials system.