ABSTRACT
Some of the tools, both statistics and computational intelligence (CI) based, for data-driven modelling and knowledge discovery from data with their applications in the materials design domain, were discussed in Chapters 3 and 4. But the mappings of the inputs to the output space, using those tools, are either linear or pseudo-linear in nature, or too complex to be perceivable, or require a black box to be inserted between the input and output spaces. Fuzzy logic can provide a superior approach, as the fuzzy system is faster, less expensive and conceptually easier to understand. It is capable of modelling nonlinear arbitrary relationships, highly tolerant of imprecise data, and the most important advantage of analysing data using fuzzy logic is that it could be used for developing linguistic if-then rules to describe the correlation between the predictor variables or the inputs and the response variables or the outputs, making the knowledge inherent in the system easy to understand. In this chapter, methods of extraction of fuzzy if-then rules from data are described after a brief portrayal of the principle of fuzzy logic. Some examples of applications of such rule extraction practice and consequent development of fuzzy models in the materials field are studied also. In the case of data processing, feature selection or finding the important variables in a system is an important task. Rough set theory has the capacity to find the important attributes or variables of a system from the data. Here the data are first analysed to assess relative importance of the parameters, and then the rules are derived using a minimum number of attributes. In both approaches – fuzzy set and rough set theories – finally a set of rules could be extracted from the given data set, which makes the information and knowledge expressed in the rule easy to interpret. These rules then can be utilised to form a fuzzy inference system (FIS), which is simply a modelling concept having an input-output correlation. Even existing imprecise knowledge, if expressed in the form of if-then rules, can also be used for generating an FIS, which is discussed in Chapter 6.
