Książka = Book ; KS/3/2012/T1P[3]
Instytut Badań Systemowych. Polska Akademia Nauk ; Systems Research Institute. Polish Academy of Sciences
[6], 41-59 pages ; 21 cm ; Bibliography p. 58-59
This paper concerns applications of Duality Principle in fuzzy algebra, fuzzy logics and approximate reasoning. Usually dual definitions, theorems, proofs and examples are neglected, omitted or left as a simple exercise. They are treated as an image in mirror. However, such opinion can be quite false, because duality is an equivalence relation. Thus both dual objects are equally important or non important. It can be easy seen in the case of linear programming: one handbook describesmainly maximization of linear functionals, while another concentrates on minimization. We tray to fill up this gap in treating of dual objects by presentation of examples of important dual notions and properties from lattice theory to relation theory and from fuzzy logic to fuzzy relational equations. In particular we describe properties of dual connectives of multivalued logic and summarize properties of dual relation compositions. Finally, a similarity between fuzzy coimplication and poset difference is analyzed.
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Systems Research Institute of the Polish Academy of Sciences
Library of Systems Research Institute PAS
15 paź 2021
19 lip 2021
36
https://rcin.org.pl./publication/235013
Torzecki, Ryszard (1925–2003) Jonca, Karol (1930–2008) Stawecki, Piotr (1930– ) Kędzierski, Jerzy Zdzisław (1920–1985) Chmielewski, Paweł (1946– ) Dunin-Wąsowicz, Krzysztof (1923–2013) Sobczak, Janusz (1927–1983) Wojtas, Andrzej (1942– ) Drewniak, Bogusław (1927– ) Jakubowski, Józef
Drewniak, Józef
Drewniak, Józef
Drewniak, Józef
Drewniak, Józef
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Krawczak, Maciej Szmidt, Eulalia Kacprzyk, Janusz (1947– ) Zadrożny, Sławomir Baczyński, Michał Krzysztof Drewniak, Józef Wygralak, Maciej Atanassov, Krassimir Todorov (1954– )