Fuzzy concept

A fuzzy concept is a kind of concept of which the boundaries of application can vary considerably according to context or conditions, instead of being fixed once and for all.^[1] This means the concept is vague in some way, lacking a fixed, precise meaning, without however being unclear or meaningless altogether.^[2] It has a definite meaning, which can be made more precise only through further elaboration and specification - including a closer definition of the context in which the concept is used. The study of the characteristics of fuzzy concepts and fuzzy language is called fuzzy semantics.^[3] The inverse of a "fuzzy concept" is a "crisp concept" (i.e. a precise concept).

A fuzzy concept is understood by scientists as a concept which is "to an extent applicable" in a situation. That means the concept has gradations of significance or unsharp (variable) boundaries of application. A fuzzy statement is a statement which is true "to some extent", and that extent can often be represented by a scaled value. The term is also used these days in a more general, popular sense – in contrast to its technical meaning – to refer to a concept which is "rather vague" for any kind of reason.

In the past, the very idea of reasoning with fuzzy concepts faced considerable resistance from academic elites. They did not want to endorse the use of imprecise concepts in research or argumentation. Yet although people might not be aware of it, the use of fuzzy concepts has risen gigantically in all walks of life from the 1970s onward. That is mainly due to advances in electronic engineering, fuzzy mathematics and digital computer programming. The new technology allows very complex inferences about "variations on a theme" to be anticipated and fixed in a program.^[4]

New neuro-fuzzy computational methods make it possible to identify, measure and respond to fine gradations of significance with great precision.^[5] It means that practically useful concepts can be coded and applied to all kinds of tasks, even if ordinarily these concepts are never precisely defined. Nowadays engineers, statisticians and programmers often represent fuzzy concepts mathematically, using fuzzy logic, fuzzy values, fuzzy variables and fuzzy sets.^[6]

^ Susan Haack, Deviant logic, fuzzy logic: beyond the formalism. Chicago: University of Chicago Press, 1996.
^ Richard Dietz & Sebastiano Moruzzi (eds.), Cuts and clouds. Vagueness, Its Nature, and Its Logic. Oxford University Press, 2009; Delia Graff & Timothy Williamson (eds.), Vagueness. London: Routledge, 2002.
^ Timothy Williamson, Vagueness. London: Routledge, 1994, p. 124f; Lotfi A. Zadeh, "Quantitative fuzzy semantics". Information Sciences, Vol. 3, No. 2, April 1971, pp. 159-176.
^ Bart Kosko, Fuzzy Thinking: The New Science of Fuzzy Logic. New York: Hyperion, 1993; Bart Kosko, Heaven in a chip: fuzzy visions of society and science in the digital age. New York: Three Rivers Press, 1999; Daniel McNeill & Paul Freiberger, Fuzzy Logic: The Revolutionary Computer Technology that Is Changing Our World. New York: Simon & Schuster, 1994. Charles Elkan, "The paradoxical success of fuzzy logic." IEEE Expert, August 1994.[1] A useful overview of the field is provided in: Radim Bělohlávek, Joseph W. Dauben & George J. Klir, Fuzzy Logic and Mathematics: A Historical Perspective. Oxford University Press, 2017.
^ A useful overview is provided in: Enrique Ruspini et al. Handbook of fuzzy computation. Bristol & Philadelphia: Institute of Physics Publishing, 1998.
^ Radim Behlohlavek & George J. Klir (eds.), Concepts and fuzzy logic. Cambridge, Mass.: MIT Press, 2011.

[1] Susan Haack, Deviant logic, fuzzy logic: beyond the formalism. Chicago: University of Chicago Press, 1996.

[2] Richard Dietz & Sebastiano Moruzzi (eds.), Cuts and clouds. Vagueness, Its Nature, and Its Logic. Oxford University Press, 2009; Delia Graff & Timothy Williamson (eds.), Vagueness. London: Routledge, 2002.

[3] Timothy Williamson, Vagueness. London: Routledge, 1994, p. 124f; Lotfi A. Zadeh, "Quantitative fuzzy semantics". Information Sciences, Vol. 3, No. 2, April 1971, pp. 159-176.

[4] Bart Kosko, Fuzzy Thinking: The New Science of Fuzzy Logic. New York: Hyperion, 1993; Bart Kosko, Heaven in a chip: fuzzy visions of society and science in the digital age. New York: Three Rivers Press, 1999; Daniel McNeill & Paul Freiberger, Fuzzy Logic: The Revolutionary Computer Technology that Is Changing Our World. New York: Simon & Schuster, 1994. Charles Elkan, "The paradoxical success of fuzzy logic." IEEE Expert, August 1994.[1] A useful overview of the field is provided in: Radim Bělohlávek, Joseph W. Dauben & George J. Klir, Fuzzy Logic and Mathematics: A Historical Perspective. Oxford University Press, 2017.

[5] A useful overview is provided in: Enrique Ruspini et al. Handbook of fuzzy computation. Bristol & Philadelphia: Institute of Physics Publishing, 1998.

[6] Radim Behlohlavek & George J. Klir (eds.), Concepts and fuzzy logic. Cambridge, Mass.: MIT Press, 2011.

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