On some geomtric transformation of t-norms
Given a triangular norm $T$, its $t$-reverse $T^*$, introduced by C. Kimberling ({\it Publ. Math. Debrecen} 20, 21-39, 1973) under the name invert, is studied. The question under which conditions we have $ T^{**} = T$ is completely solved. The $t$-reverses of ordinal sums of $t$-norms are investigat...
| Authors: | , , |
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| Format: | article |
| Publication Date: | 1998 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2099/3504 |
| Online Access: | https://hdl.handle.net/2099/3504 |
| Access Level: | Open access |
| Keyword: | T-norms Conjunts, Teoria de Classificació AMS::03 Mathematical logic and foundations::03E Set theory |
| Summary: | Given a triangular norm $T$, its $t$-reverse $T^*$, introduced by C. Kimberling ({\it Publ. Math. Debrecen} 20, 21-39, 1973) under the name invert, is studied. The question under which conditions we have $ T^{**} = T$ is completely solved. The $t$-reverses of ordinal sums of $t$-norms are investigated and a complete description of continuous, self-reverse $t$-norms is given, leading to a new characterization of the continuous $t$-norms $T$ such that the function $ G(x,y) = x + y - T(x,y)$ is a $t$-conorm, a problem originally studied by M.J. Frank ({\it Aequationes Math.} 19, 194-226, 1979). Finally, some open problems are formulated. |
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