Quasi-homogeneous associative functions
A triangular norm is a special kind of associative function on the closed unit interval [0,1]. Triangular norms (or t-norms) were introduced in the context of probabilistic metric space theory, and they have found applications also in other areas, such as fuzzy set theory. We determine the explicit...
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| Format: | Article |
| Language: | English |
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Wiley
1998-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171298000489 |
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| _version_ | 1850172270133116928 |
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| author | Bruce R. Ebanks |
| author_facet | Bruce R. Ebanks |
| author_sort | Bruce R. Ebanks |
| collection | DOAJ |
| description | A triangular norm is a special kind of associative function on the closed unit interval [0,1].
Triangular norms (or t-norms) were introduced in the context of probabilistic metric space theory, and they
have found applications also in other areas, such as fuzzy set theory. We determine the explicit forms of all
t-norms which satisfy a generalized homogeneity property called quasi-homogeneity. |
| format | Article |
| id | doaj-art-cff39c3dbdfb47b7b647cac221fc10ed |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1998-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-cff39c3dbdfb47b7b647cac221fc10ed2025-08-20T02:20:07ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251998-01-0121235135710.1155/S0161171298000489Quasi-homogeneous associative functionsBruce R. Ebanks0Department of Mathematics, Marshall University, Huntington 25755, WV, USAA triangular norm is a special kind of associative function on the closed unit interval [0,1]. Triangular norms (or t-norms) were introduced in the context of probabilistic metric space theory, and they have found applications also in other areas, such as fuzzy set theory. We determine the explicit forms of all t-norms which satisfy a generalized homogeneity property called quasi-homogeneity.http://dx.doi.org/10.1155/S0161171298000489Triangular norm (t-norm)homogeneous functionprobabilistic metric space. |
| spellingShingle | Bruce R. Ebanks Quasi-homogeneous associative functions International Journal of Mathematics and Mathematical Sciences Triangular norm (t-norm) homogeneous function probabilistic metric space. |
| title | Quasi-homogeneous associative functions |
| title_full | Quasi-homogeneous associative functions |
| title_fullStr | Quasi-homogeneous associative functions |
| title_full_unstemmed | Quasi-homogeneous associative functions |
| title_short | Quasi-homogeneous associative functions |
| title_sort | quasi homogeneous associative functions |
| topic | Triangular norm (t-norm) homogeneous function probabilistic metric space. |
| url | http://dx.doi.org/10.1155/S0161171298000489 |
| work_keys_str_mv | AT brucerebanks quasihomogeneousassociativefunctions |