Triangular Norms(1st Edition)

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Book Price $153.99 : 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 & 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 & 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. See more