Triangular Norms:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
2000
|
| Schriftenreihe: | Trends in Logic, Studia Logica Library
8 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (XIX, 387 p) |
| ISBN: | 9789401595407 9789048155071 |
| ISSN: | 1572-6126 |
| DOI: | 10.1007/978-94-015-9540-7 |
Internformat
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| 500 | |a 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 | ||
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Datensatz im Suchindex
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| author | Klement, Erich Peter |
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| author_sort | Klement, Erich Peter |
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| bvnumber | BV042424149 |
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| dewey-hundreds | 100 - Philosophy & psychology |
| dewey-ones | 160 - Philosophical logic |
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| dewey-tens | 160 - Philosophical logic |
| discipline | Mathematik Philosophie |
| doi_str_mv | 10.1007/978-94-015-9540-7 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:15Z |
| institution | BVB |
| isbn | 9789401595407 9789048155071 |
| issn | 1572-6126 |
| language | English |
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| spelling | Klement, Erich Peter Verfasser aut Triangular Norms by Erich Peter Klement, Radko Mesiar, Endre Pap Dordrecht Springer Netherlands 2000 1 Online-Ressource (XIX, 387 p) txt rdacontent c rdamedia cr rdacarrier Trends in Logic, Studia Logica Library 8 1572-6126 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 Philosophy (General) Logic Algebra Logic, Symbolic and mathematical Philosophy Order, Lattices, Ordered Algebraic Structures Mathematical Logic and Foundations Philosophie Probabilistischer Raum (DE-588)4611732-5 gnd rswk-swf Logik (DE-588)4036202-4 gnd rswk-swf Triangulation (DE-588)4186017-2 gnd rswk-swf Metrischer Raum (DE-588)4169745-5 gnd rswk-swf Metrischer Raum (DE-588)4169745-5 s Probabilistischer Raum (DE-588)4611732-5 s Triangulation (DE-588)4186017-2 s Logik (DE-588)4036202-4 s 1\p DE-604 Mesiar, Radko Sonstige oth Pap, Endre Sonstige oth https://doi.org/10.1007/978-94-015-9540-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Klement, Erich Peter Triangular Norms Philosophy (General) Logic Algebra Logic, Symbolic and mathematical Philosophy Order, Lattices, Ordered Algebraic Structures Mathematical Logic and Foundations Philosophie Probabilistischer Raum (DE-588)4611732-5 gnd Logik (DE-588)4036202-4 gnd Triangulation (DE-588)4186017-2 gnd Metrischer Raum (DE-588)4169745-5 gnd |
| subject_GND | (DE-588)4611732-5 (DE-588)4036202-4 (DE-588)4186017-2 (DE-588)4169745-5 |
| title | Triangular Norms |
| title_auth | Triangular Norms |
| title_exact_search | Triangular Norms |
| title_full | Triangular Norms by Erich Peter Klement, Radko Mesiar, Endre Pap |
| title_fullStr | Triangular Norms by Erich Peter Klement, Radko Mesiar, Endre Pap |
| title_full_unstemmed | Triangular Norms by Erich Peter Klement, Radko Mesiar, Endre Pap |
| title_short | Triangular Norms |
| title_sort | triangular norms |
| topic | Philosophy (General) Logic Algebra Logic, Symbolic and mathematical Philosophy Order, Lattices, Ordered Algebraic Structures Mathematical Logic and Foundations Philosophie Probabilistischer Raum (DE-588)4611732-5 gnd Logik (DE-588)4036202-4 gnd Triangulation (DE-588)4186017-2 gnd Metrischer Raum (DE-588)4169745-5 gnd |
| topic_facet | Philosophy (General) Logic Algebra Logic, Symbolic and mathematical Philosophy Order, Lattices, Ordered Algebraic Structures Mathematical Logic and Foundations Philosophie Probabilistischer Raum Logik Triangulation Metrischer Raum |
| url | https://doi.org/10.1007/978-94-015-9540-7 |
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