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A fuzzy concept is a concept of which the boundaries of application can vary considerably according to context or conditions, instead of being fixed once and for all.〔Susan Haack, ''Deviant logic, fuzzy logic: beyond the formalism''. Chicago: University of Chicago Press, 1996.〕 This means the concept is ''vague'' in some way, lacking a fixed, precise meaning, without however being unclear or meaningless altogether.〔Richard Dietz & Sebastiano Moruzzi (eds.), ''Cuts and clouds. Vagueness, Its Nature, and Its Logic.'' Oxford University Press, 2009.〕 It has a definite meaning, which can become more precise only through further elaboration and specification, including a closer definition of the context in which the concept is used. A fuzzy concept is understood by scientists as a concept which is "to an extent applicable" in a situation, and it therefore implies gradations of meaning. The best known example of a fuzzy concept around the world is an amber traffic light, and indeed fuzzy concepts are nowadays widely used in traffic control systems.〔Sandeep Mehan & Vandana Sharma, "Development of traffic light control system based on fuzzy logic". ''ACAI '11 Proceedings of the International Conference on Advances in Computing and Artificial Intelligence 2011'', pp. 162-165.〕 The Nordic myth of Loki's wager suggests that concepts which lack a precise meaning or precise boundaries of application cannot be usefully discussed at all. However, the idea of "fuzzy concepts" proposes that "somewhat vague terms" can be operated with, since we can explicate and define the variability of their application, by assigning numbers to it. ==Origin and etymology== The intellectual origins of the idea of fuzzy concepts have been traced to a diversity of famous and less well known thinkers including Plato, Georg Wilhelm Friedrich Hegel, Karl Marx, Friedrich Engels, Friedrich Nietzsche, Jan Łukasiewicz, Alfred Tarski, Stanisław Jaśkowski〔Susan Haack notes that Stanisław Jaśkowski provided axiomatizations of many-valued logics in: Jaśkowski, "On the rules of supposition in formal logic. ''Studia Logica'' No. 1, 1934.() See Susan Haack, ''Philosophy of Logics''. Cambridge University Press, 1978, p. 205.〕 and Donald Knuth.〔Priyanka Kaushal, Neeraj Mohan and Parvinder S. Sandhu, "Relevancy of Fuzzy Concept in Mathematics". ''International Journal of Innovation, Management and Technology'', Vol. 1, No. 3, August 2010.()〕 However, usually the Iranian born, American computer scientist Lotfi A. Zadeh is credited with inventing the specific idea of a "fuzzy concept" in his seminal 1965 paper on fuzzy sets, because he gave a formal mathematical presentation of the phenomenon which was widely accepted by scholars.〔Lotfi A. Zadeh, "Fuzzy sets". In: ''Information and Control'', Vol. 8, June 1965, pp. 338–353.()〕 In fact, the German scholar Dieter Klaua also published a German-language paper on fuzzy sets in the same year,〔Dieter Klaua. "Über einen Ansatz zur mehrwertigen Mengenlehre". ''Monatsberichte der Deutschen Akademie der Wissenschaften'' (Berlin), Vol. 7: pp. 859-867, 1965.〕 but he used a different terminology (he referred to "many-valued sets").〔Siegfried Gottwald, "Shaping the logic of fuzzy set theory". In: Cintula, Petr et al. (eds.), ''Witnessed years. Essays in honour of Petr Hájek''. London: College Publications, 2009, pp. 193-208. ()〕 An earlier attempt to create a theory of sets where set membership is a matter of degree was made by Abraham Kaplan and Hermann Schott in 1951. They intended to apply the idea to empirical research. Kaplan and Schott measured the degree of membership of empirical classes using real numbers between 0 and 1, and they defined corresponding notions of intersection, union, complementation and subset.〔Abraham Kaplan and Hermann F. Schott, "A calculus for empirical classes", Methodos Vol. 3, 1951, pp. 165–188.〕 However, at the time, their idea "fell on stony ground".〔Timothy Williamson, ''Vagueness''. London: Routledge, 1996, p. 120.〕 Radim Belohlavek explains: Hence, a concept is regarded as "fuzzy" by logicians if: *defining characteristics of the concept apply to it "to a certain degree or extent" (or, more unusually, "with a certain magnitude of likelihood") *or, the fuzzy concept itself consists of a fuzzy set (or a combination of such sets). However, not all philosophers would agree that a concept is equal to, or reducible to, a mathematical set, since qualities may not be reducible to quantities. The fact that a concept is fuzzy does not prevent its use in logical reasoning, it merely affects the type of reasoning which can be applied (see fuzzy logic). Zadeh's seminal 1965 paper is acknowledged to be one of the most-cited scholarly articles in the 20th century. 〔''IFSA Newsletter'' (International Fuzzy Systems Association), Vol. 10, No. 1, March 2013 ()〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Fuzzy concept」の詳細全文を読む スポンサード リンク
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