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Fuzzy concept

A fuzzy concept is an idea 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. It lacks a fixed, precise meaning. Yet it is not unclear or meaningless.[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).

For engineers, "Fuzziness is imprecision or vagueness of definition."[4] For scientists, a fuzzy concept is an idea which is "to an extent applicable" in a situation. It means that the concept can have 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. For mathematicians, a "fuzzy concept" is usually a fuzzy set or a combination of such sets (see fuzzy mathematics). In cognitive linguistics, the things that belong to a "fuzzy category" exhibit gradations of family resemblance, and the borders of the category are not clearly defined.[5] In a more general, popular sense – contrasting with its technical meanings – a "fuzzy concept" refers to an imprecise idea which is "somewhat vague" for any kind of reason.

In the past, the very idea of reasoning with fuzzy concepts faced considerable resistance from academic elites.[6] They did not want to endorse the use of imprecise concepts in research or argumentation, and regarded fuzzy logic with suspicion. 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.[7] 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.[8] The Perseverance Mars rover, a driverless NASA vehicle used to explore the Jezero crater on the planet Mars, features fuzzy logic programming that steers it through rough terrain.[9] Similarly, to the North, the Chinese Mars rover Zhurong used fuzzy logic algorithms to calculate its travel route in Utopia Planitia from sensor data.[10]

New neuro-fuzzy computational methods[11] make it possible to identify, measure and respond to fine gradations of significance with great precision.[12] 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.[13] Fuzzy logic can play a significant role in artificial intelligence programming, for example because it can model human cognitive processes more easily.[14]

  1. ^ Radim Behlohlavek & George J. Klir (eds.), Concepts and fuzzy logic. Cambridge, Mass.: MIT Press, 2011; 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. ^ D. Blockley, "Earthquake risk management of civil infrastructure: integrating soft and hard risks", in: Handbook of Seismic Risk Analysis and Management of Civil Infrastructure Systems. Sawston, Cambridge: Woodhead Publishing, 2013, chapter 9, pp. 229-254, at p. 238.
  5. ^ Vyvyan Evans, A glossary of cognitive linguistics. Salt Lake City: University of Utah Press, 2007, p. 88.
  6. ^ Lotfi A. Zadeh, "Is there a need for fuzzy logic?", Information Sciences, No. 178, 2008.
  7. ^ Bart Kosko, "Fuzzy logic". In: Scientific American, July 1993, pp. 76-81[1]; 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.[2]; Didier Dubois et al., "Fuzzy-set based logics - an history-oriented presentation of their main developments", in: Handbook of the history of logic. Volume 8, The many valued and non-monotonic turn in logic. Amsterdam: Elsevier- North Holland, 2007, pp. 3-125.[3] Didier Dubois, Henri Prade, Articles written on the occasion of the 50th anniversary of fuzzy set theory. Institut de Recherche Informatique de Toulouse. 2015.[4]
  8. ^ Radim Bělohlávek, Joseph W. Dauben & George J. Klir, Fuzzy Logic and Mathematics: A Historical Perspective. Oxford University Press, 2017; Didier Dubois et al., "Fuzzy-set based logics - an history-oriented presentation of their main developments", in: Handbook of the history of logic. Volume 8, The many valued and non-monotonic turn in logic. Amsterdam: Elsevier- North Holland, 2007, pp. 3-125.[5] Didier Dubois, Henri Prade, Articles written on the occasion of the 50th anniversary of fuzzy set theory . Institut de Recherche Informatique de Toulouse, 2015.https://hal.science/hal-03198270v1/file/Fuzzy-sets-50.pdf]
  9. ^ Katyanna Quach, "Fuzzy logic makes a comeback – in picking where Earth sticks its probes into alien worlds". The Register, 27 Sep 2018.[6]
  10. ^ Liwei Yang et al., "Path Planning Technique for Mobile Robots: A Review". Machines, Vol. 11, 2023, pp. 980-1026.[7]
  11. ^ Lotfi A. Zadeh, "Fuzzy logic, neural networks, and soft computing". In: Communications of the ACM, Volume 37, Issue 3, March 1994, pp. 77-84; "Artificial neural networks: an overview", in: George J. Klir & Bo Yuan, Fuzzy sets and fuzzy logic. Theory and applications. Upper Saddle River (NJ.): Prentice Hall, 1995, pp. 467-475.
  12. ^ A useful technical overview is provided in: Enrique Ruspini et al. Handbook of fuzzy computation. Bristol & Philadelphia: Institute of Physics Publishing, 1998.
  13. ^ Radim Behlohlavek & George J. Klir (eds.), Concepts and fuzzy logic. Cambridge, Mass.: MIT Press, 2011.
  14. ^ Edy Portmann, Fuzzy humanist. Wiesbaden: Springer, 2019; Mahdi Eftekhari et al., How fuzzy concepts contribute to machine learning. Cham (Switzerland): Springer, 2022.

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