{"product_id":"triangular-norms-erich-peter-klement-9780792364160","title":"Triangular Norms","description":"The history of triangular norms started with the paper \"Statistical metrics\" [Menger 1942]. The main idea of Karl Menger was to construct metric spaces where probability distributions rather than numbers are used in order to de- scribe the distance between two elements of the space in question. Triangular norms (t-norms for short) naturally came into the picture in the course of the generalization of the classical triangle inequality to this more general set- ting. The original set of axioms for t-norms was considerably weaker, including among others also the functions which are known today as triangular conorms. Consequently, the first field where t-norms played a major role was the theory of probabilistic metric spaces ( as statistical metric spaces were called after 1964). Berthold Schweizer and Abe Sklar in [Schweizer \u0026amp; Sklar 1958, 1960, 1961] provided the axioms oft-norms, as they are used today, and a redefinition of statistical metric spaces given in [Serstnev 1962]led to a rapid development of the field. Many results concerning t-norms were obtained in the course of this development, most of which are summarized in the monograph [Schweizer \u0026amp; Sklar 1983]. Mathematically speaking, the theory of (continuous) t-norms has two rather independent roots, namely, the field of (specific) functional equations and the theory of (special topological) semigroups.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Erich Peter Klement,R. Mesiar,E. Pap\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 0792364163\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9780792364160\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 07\/31\/2000\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 387\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.66lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.94d","brand":"Erich Peter Klement","offers":[{"title":"Hardcover","offer_id":48483700965631,"sku":"9780792364160","price":219.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_2075bbcd-7a6d-4910-987e-bdff148c5027.jpg?v=1778040094","url":"https:\/\/www.whiterainbookhouse.com\/products\/triangular-norms-erich-peter-klement-9780792364160","provider":"WR Book House","version":"1.0","type":"link"}