Abstract
Fuzzy logic can deal with information arising from perception and cognition that is uncertain, imprecise, vague, partially true, or without sharp boundaries. Fuzzy logic can be used for assigning linguistic grades and for decision making and data mining with those linguistic grades by teachers, instructors, and professors. Many aspects of fuzzy logic including fuzzy sets, linguistic variables, fuzzy rules, fuzzy math, fuzzy database queries, computational theory of perceptions, and computing with words are useful in uncertainty management of linguistic evaluations for students. This chapter provides many examples of this after describing the theory of fuzzy logic.
TopIntroduction
The attribute of certainty or precision does not exist in human perception and cognition. Albert Einstein wrote, “So far as the laws of mathematics refer to reality, they are not certain. And so far as they are certain, they do not refer to reality.”
There are various types of uncertainty. However, Madan M. Gupta, an author of this research chapter, found that they can be classified under two broad categories (Gupta, 1988a; Gupta, 1988b; Gupta, 1991; Gupta, 1992; Solo and Gupta, 2000; Solo and Gupta, 2007; Gupta and Solo, 2010; Gupta and Solo, 2015): uncertainty type one and uncertainty type two.
Uncertainty Type One
Uncertainty type one deals with information that arises from the random behavior of physical systems. The pervasiveness of this type of uncertainty can be witnessed in random vibrations of a machine, random fluctuations of electrons in a magnetic field, diffusion of gases in a thermal field, random electrical activities of cardiac muscles, uncertain fluctuations in the weather pattern, and turbulent blood flow through a damaged cardiac valve. Uncertainty type one has been studied for centuries. Complex statistical mathematics has evolved for the characterization and analysis of such random phenomena.
Uncertainty Type Two
Uncertainty type two deals with information or phenomena that arise from human perception and cognitive processes or from cognitive information in general. This subject has received relatively little attention. Perception and cognition through biological sensors (eyes, ears, nose, etc.), perception of pain, and other similar biological events throughout our nervous system and neural networks deserve special attention. The perception and cognition phenomena associated with these processes are characterized by many great uncertainties and cannot be described by conventional statistical theory. A person can linguistically express perceptions experienced through the senses, but these perceptions cannot be described using conventional statistical theory.
Uncertainty type two and the associated cognitive information involve the activities of neural networks. It may seem strange that such familiar notions have recently become the focus of intense research. However, it is the relative unfamiliarity of these notions and their technological applications in intelligent systems that have led engineers and scientists to conduct research in the field of uncertainty type two and its associated cognitive information.
Key Terms in this Chapter
Computational Theory of Perceptions and Computing With Words: The methodology of computing with words is focused on the manipulation of words and propositions taken from natural language. Computational theory of perceptions is based on the methodology of computing with words. Computing with words and the computational theory of perceptions are subsets of fuzzy logic. Words act as the labels for perceptions, and perceptions are expressed in natural language propositions.
Qualitative Definition: Qualitative definition is a term coined by Ashu M. G. Solo to refer to a linguistic definition of an imprecise word without numerical parameters, such as is found in dictionaries, instead of a definition of an imprecise word using a crisp set or fuzzy set (quantitative definition). All of these terms were coined by Solo.
Crisp Quantitative Definition: Crisp quantitative definition is a term coined by Ashu M. G. Solo to refer to a quantitative definition of an imprecise word using a crisp set instead of a quantitative definition of an imprecise word using a fuzzy set (fuzzy quantitative definition) or linguistic definition without numerical parameters (qualitative definition). All of these terms were coined by Solo.
Uncertainty Type One: Uncertainty type one is a term coined by Madan M. Gupta for information that arises from the random behavior of physical systems. The pervasiveness of this type of uncertainty can be witnessed in random vibrations of a machine, random fluctuations of electrons in a magnetic field, diffusion of gases in a thermal field, random electrical activities of cardiac muscles, uncertain fluctuations in the weather pattern, and turbulent blood flow through a damaged cardiac valve. Uncertainty type one has been studied for centuries. Complex statistical mathematics has evolved for the characterization and analysis of such random phenomena. Stochastic theory is effective in dealing with uncertainty type one.
Fuzzy Quantitative Definition: Fuzzy quantitative definition is a term coined by Ashu M. G. Solo to refer to a quantitative definition of an imprecise word using a fuzzy set instead of a quantitative definition of an imprecise word using a crisp set (crisp quantitative definition) or linguistic definition without numerical parameters (qualitative definition). All of these terms were coined by Solo.
Fuzzy Sets: In a fuzzy set, elements can have degrees of membership. The concept of a fuzzy set was developed by Lotfi A. Zadeh.
Uncertainty Type Two: Uncertainty type two is a term coined by Madan M. Gupta for information or phenomena that arise from human perception and cognitive processes or from cognitive information in general. This subject has received relatively little attention. Perception and cognition through biological sensors (eyes, ears, nose, etc.), perception of pain, and other similar biological events throughout our nervous system and neural networks deserve special attention. The perception and cognition phenomena associated with these processes are characterized by many great uncertainties and cannot be described by conventional statistical theory. A person can linguistically express perceptions experienced through the senses, but these perceptions cannot be described using conventional statistical theory. Fuzzy logic has proven to be a very promising tool for dealing with uncertainty type two.
Quantitative Definition: Quantitative definition is a term coined by Ashu M. G. Solo to refer to a definition of an imprecise word using a crisp set or fuzzy set instead of a linguistic definition of an imprecise word without numerical parameters (qualitative definition). All of these terms were coined by Solo.
Fuzzy Logic: Fuzzy logic is a field created by Lotfi A. Zadeh for information arising from computational perception and cognition that is uncertain, imprecise, vague, partially true, or without sharp boundaries.