Error Estimation and Controllability Analysis of Contemporary Fuzzy Logic Control Models

Abstract

This research work is outgrowth of many contemporary intelligent control techniques and their implementation. But logically intelligent actions cannot control the conventional models without certain techniques of control, control algorithms, knowledge base models, mathematical models and also the predominant contemporary fuzzy techniques which give us best results under all the factors like complexity, non linearity, parameters varying with time as well as dynamics interactions among all the parameters. This thesis work highlights the need for managing intensive computations through modern upcoming technologies of artificial intelligence in the industry oriented problems. This work presents their association with new contemporary models. The purpose is to understand and explicate the interaction between advance fuzzy logic technologies and their impact on different uncertainties existing in industrial control systems/models. The concept of Fuzzy Logic (FL) was conceived by Lofti Zadeh, is a problem solving industrial control system methodology that lends itself to implementation. Fuzzy set theory provides a mathematical setting for the integration of subjective categories represented by membership functions of all the parameters concerning that control activity. Fuzzy set theory and its contemporary theories are an extension of classical set theory where elements of a set have grades of membership ranging from zero for non-membership to one for full membership. Exactly as for classical sets, there exist operators, relations, and mappings appropriate for these fuzzy sets. Fuzzy set theory is established as a theoretical basis for ordination. The notion central to fuzzy systems is that truth-values in fuzzy logic type -1 or membership values in fuzzy sets are indicated by a value on the range [0.0, 1.0] with 0.0 representing absolute falseness and 1.0 representing absolute truth. Type-2 fuzzy sets let us model and minimize the effects of uncertainties in rule-base fuzzy logic systems. However, they are difficult to understand for a variety of reasons, which we enunciate. Unfortunately, type-2 fuzzy sets are more difficult to use and understand than type-1 fuzzy sets; hence, their use is not yet widespread. In this thesis work we make type-2 fuzzy sets easy to use and understand in the hope that they will be widely used. There are (at least) four sources of uncertainties in type-1 FLCs: (1) The meanings of the words that are used in the antecedents and consequents of rules can be uncertain. (2) Consequents may have a histogram of values associated with them, especially when knowledge is extracted from a group of experts who do not all agree. (3) Measurements that activate a type-1 FLCs may be noisy therefore uncertain. (4) The data that are used to tune the parameters of a type-1 FLCs may also be noisy. All of these uncertainties translate into uncertainties about fuzzy set membership functions. Type-1 fuzzy sets are not able to directly model such uncertainties because their membership functions are totally crisp. On the other hand, type-2 fuzzy sets are able to model such uncertainties because their membership functions are themselves fuzzy. Membership functions of type-1 fuzzy sets are two-dimensional, whereas membership functions of type-2 fuzzy sets are three-dimensional. It is the new third-dimension of type-2 fuzzy sets that provides additional degrees of freedom that make it possible to directly model uncertainties. The derivations of the formulas of type-2 fuzzy sets all rely on using Zadeh’s extension principle, which in itself is a difficult concept and is somewhat adhoc, so that deriving things using it may be considered problematic; using type-2 fuzzy sets is computationally more complicated than using type-1 fuzzy sets. In this work, we focus on overcoming difficulties as stated above, because doing so makes type-2 fuzzy sets easy to use and understand. The price one must pay for achieving better performance in the face of uncertainties and is analogous to using probability rather than determinism.