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Fuzzy mathematics
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<p>Fuzzy mathematics is a branch of <a href="/facts/Mathematics/pxTouaz4">mathematics</a> that extends classical set theory and logic to model reasoning under uncertainty. Initiated by <a href="/facts/Lotfi_Asker_Zadeh/WojTlG4Y">Lotfi Asker Zadeh</a> in 1965 with the introduction of fuzzy sets, the field has since evolved to include <a href="/facts/Fuzzy_set/BGWudHJq">fuzzy set</a> theory, <a href="/facts/Fuzzy_logic/1PvN4Att">fuzzy logic</a>, and various fuzzy analogues of <a href="/facts/Traditional_mathematics/ak01PhpL">traditional mathematic</a> structures. </p><p>Unlike classical mathematics, which usually relies on <a href="/facts/Binary_number/a6JDSRPs">binary</a> membership (an element either belongs to a set or it does not), fuzzy mathematics allows elements to partially belong to a set, with degrees of membership represented by values in the interval [0, 1]. This framework enables more flexible modeling of imprecise or vague concepts. </p><p>Fuzzy mathematics has found applications in numerous domains, including <a href="/facts/Control_theory/aIuERpn6">control theory</a>, <a href="/facts/Artificial_intelligence/lJGauQwX">artificial intelligence</a>, <a href="/facts/Decision_theory/TbXcQX0v">decision theory</a>, <a href="/facts/Pattern_recognition/o1s38opj">pattern recognition</a>, and <a href="/facts/Linguistics/oQuamvf2">linguistics</a>, where the modeling of gradations and uncertainty is essential. </p>