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

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

Siddhartha Bhattacharyya (The University of Burdwan, India) and Paramartha Dutta (Visva-Bharati University, India)
DOI: 10.4018/978-1-4666-0294-6.ch003
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The field of industrial informatics has emerged as one of the key disciplines for the purpose of intelligent management and dissemination of information in today’s world. With the advent of newer technical know-how, the subject of informative intelligence has assumed increasing importance in the industrial arena, thanks to the evolution of data intensive industry. Real world data exhibit varied amount of unquantifiable uncertainty in the information content. Conventional logic is often unable to explain the associated uncertainty and imprecision therein due to the principles of finiteness of observations and quantifying propositions employed. Fuzzy sets and fuzzy logic provide a logical framework for description of the varied amount of ambiguity, uncertainty and imprecision exhibited in real world data under consideration. The resultant fuzzy inference engine and the fuzzy logic control theory supplement the power of the framework in design of robust failsafe real life systems.
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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.

Key Terms in this Chapter

Fuzzy Logic: It is a multivalued logic which incorporates all the possible outcomes in an observation apart from the standard bivalent/bivalued logic commonly dealt with in the conventional computing scenario.

Fuzzy Operators: These act as linguistic hedges on fuzzy sets to modify the behavioral characteristics of fuzzy sets.

Fuzzy Control: A fuzzy rule based nonlinear control system which is more failsafe and susceptible to higher degrees of nonlinear input-out relationships.

Fuzzy Sets: These are capable of describing the vagueness and ambiguity inherent in real world data by assigning degrees of containment to the elements of the constituent sets in the universe of discourses.

Fuzzification: It is a mapping from an input crisp/conventional universe of discourse into the fuzzy interval (0, 1) that describes the membership of the fuzzy input variable.

Fuzzy Membership Function: A fuzzy membership function characterizes a fuzzy set. It describes the behavioral characteristics of the fuzzy set, its support, its height and its properties.

Fuzzy Measures: The fuzzy measures provide a quantitative value of the degree of fuzziness in a fuzzy set.

Defuzzification: The reverse mapping from the fuzzy to the crisp domain is referred to as defuzzification.

Fuzzy Inference System: A fuzzy inference system, abbreviated as FIS, mimic human intelligence for quantifying the ambiguity/imprecision in real world scenario through proper modeling of the fuzziness of real world data by appropriate rule bases.

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