Fuzzy Logic: Concepts, System Design, and Applications to Industrial Informatics

Introduction

Industrial informatics (Acciani, 2011; Gomperts, 2011) has assumed importance of late thanks to intelligent management and dissemination of information. With the rapid advancement of technology, there has been a stupendous increase in the exchange of data based information leading to data explosion. As a result, for keeping pace with this ever-increasing data and knowledge base, new subjects like informative intelligence and intelligent informatics have come to the fore.

Information is manifested in several different forms. It may be either in the form of raw data, images, video content, speech signals or in any other electronic form. Any form of consumed real world data contains a varied amount of ambiguity and imprecision, which cannot always be measured in practice. As such, classical computing systems seldom account for the associated uncertainty and imprecision in the principles of finiteness of observations and quantifying propositions employed.

Fuzzy sets (Zadeh, 1965; Cox, 1994; Dubois 1980; Kosko, 1997; Ross, 2003; Ross, 2004; Berkan, 2000) evolved by Professor Lotfi Zadeh of the University of California at Berkley are capable of describing the vagueness and ambiguity inherent in real world data. Professor Zadeh reasoned on the intelligence in human reasoning to pave the way for foundation of fuzzy sets and fuzzy logic. He was motivated by the fact that human beings more often communicate via natural language terms or linguistic expressions, which cannot be always quantified by numeric values (Zadeh65, Zadeh73, Cox94, Dubois80, Zadeh78, Zadeh94). Typical human expressions include either one or several linguistic phrases, viz., very, very tall boy, very fast car, quite a few people, etc. These phrases, though aptly describe human feelings, cannot be numerically quantified in the strict sense of the term. Thus, even in the absence of any precise, numerical input information, human beings are capable of highly adaptive control. Moreover, as the complexity of a system increases, it becomes more difficult and eventually impossible to make a precise statement about its behavior, culminating in a point of complexity, which cannot be adjudged by means of a value. Zadeh coined the term “fuzzy” (standing for something which is vague, obscure and imprecise) to replicate the notion of non-measurable human understanding and logic. Thus, fuzzy sets form the backbone of more efficient and robust systems, which are immune to all sorts of uncertainties and imprecisions prevalent in the real world. Hence, fuzzy systems operate in a linguistic framework and their strength lies in their capability to handle linguistic information and perform approximate reasoning (Ross2003, Ross2004) through the assignment of non-measurable logical qualities.