Search

Your search keyword '"Ordinal sum"' showing total 23 results
Start Over Descriptor "Ordinal sum" Publisher springer international publishing

Refine your results

more »

more »

23 results on '"Ordinal sum"'

4. PBZ–Lattices: Ordinal and Horizontal Sums

Author

Giuntini, Roberto, Mureşan, Claudia, Paoli, Francesco, Wansing, Heinrich, Editor-in-Chief, Avron, Arnon, Editorial Board Member, Bimbó, Katalin, Editorial Board Member, Corsi, Giovanna, Editorial Board Member, Czelakowski, Janusz, Editorial Board Member, Giuntini, Roberto, Editorial Board Member, Goré, Rajeev, Editorial Board Member, Herzig, Andreas, Editorial Board Member, Holliday, Wesley, Editorial Board Member, Indrzejczak, Andrzej, Editorial Board Member, Mundici, Daniele, Editorial Board Member, Odintsov, Sergei, Editorial Board Member, Orlowska, Ewa, Editorial Board Member, Schroeder-Heister, Peter, Editorial Board Member, Venema, Yde, Editorial Board Member, Weiermann, Andreas, Editorial Board Member, Wolter, Frank, Editorial Board Member, Xu, Ming, Editorial Board Member, Malinowski, Jacek, Editorial Board Member, Skurt, Daniel, Assistant Editor, Wojcicki, Ryszard, Founding Editor, Fazio, Davide, editor, Ledda, Antonio, editor, and Paoli, Francesco, editor

Published
2021
Full Text
View/download PDF

5. Ordinal Sums of t-norms and t-conorms on Bounded Lattices

Author

Dvořák, Antonín, Holčapek, Michal, Kacprzyk, Janusz, Series Editor, Pal, Nikhil R., Advisory Editor, Bello Perez, Rafael, Advisory Editor, Corchado, Emilio S., Advisory Editor, Hagras, Hani, Advisory Editor, Kóczy, László T., Advisory Editor, Kreinovich, Vladik, Advisory Editor, Lin, Chin-Teng, Advisory Editor, Lu, Jie, Advisory Editor, Melin, Patricia, Advisory Editor, Nedjah, Nadia, Advisory Editor, Nguyen, Ngoc Thanh, Advisory Editor, Wang, Jun, Advisory Editor, Halaš, Radomír, editor, Gagolewski, Marek, editor, and Mesiar, Radko, editor

Published
2019
Full Text
View/download PDF

6. Ordinal Sum of Fuzzy Implications Fulfilling Left Ordering Property

Author

Drygaś, Paweł, Król, Anna, Kacprzyk, Janusz, Series editor, Pal, Nikhil R., Advisory editor, Bello Perez, Rafael, Advisory editor, Corchado, Emilio S., Advisory editor, Hagras, Hani, Advisory editor, Kóczy, László T., Advisory editor, Kreinovich, Vladik, Advisory editor, Lin, Chin-Teng, Advisory editor, Lu, Jie, Advisory editor, Melin, Patricia, Advisory editor, Nedjah, Nadia, Advisory editor, Nguyen, Ngoc Thanh, Advisory editor, Wang, Jun, Advisory editor, Szmidt, Eulalia, editor, Zadrożny, Sławomir, editor, Atanassov, Krassimir T., editor, and Krawczak, Maciej, editor

Published
2018
Full Text
View/download PDF

7. Two Constructions of Ordinal Sums of Fuzzy Implications

Author

Drygaś, Paweł, Król, Anna, Kacprzyk, Janusz, Series editor, Pal, Nikhil R., Advisory editor, Bello Perez, Rafael, Advisory editor, Corchado, Emilio S., Advisory editor, Hagras, Hani, Advisory editor, Kóczy, László T., Advisory editor, Kreinovich, Vladik, Advisory editor, Lin, Chin-Teng, Advisory editor, Lu, Jie, Advisory editor, Melin, Patricia, Advisory editor, Nedjah, Nadia, Advisory editor, Nguyen, Ngoc Thanh, Advisory editor, Wang, Jun, Advisory editor, Atanassov, Krassimir T., editor, Kałuszko, Andrzej, editor, Krawczak, Maciej, editor, Owsiński, Jan, editor, Sotirov, Sotir, editor, Sotirova, Evdokia, editor, Szmidt, Eulalia, editor, and Zadrożny, Sławomir, editor

Published
2018
Full Text
View/download PDF

8. A New Look on the Ordinal Sum of Fuzzy Implication Functions

Author

Massanet, Sebastia, Riera, Juan Vicente, Torrens, Joan, Diniz Junqueira Barbosa, Simone, Series editor, Chen, Phoebe, Series editor, Du, Xiaoyong, Series editor, Filipe, Joaquim, Series editor, Kara, Orhun, Series editor, Liu, Ting, Series editor, Kotenko, Igor, Series editor, Sivalingam, Krishna M., Series editor, Washio, Takashi, Series editor, Carvalho, Joao Paulo, editor, Lesot, Marie-Jeanne, editor, Kaymak, Uzay, editor, Vieira, Susana, editor, Bouchon-Meunier, Bernadette, editor, and Yager, Ronald R., editor

Published
2016
Full Text
View/download PDF

11. Various Kinds of Ordinal Sums of Fuzzy Implications

Author

Drygaś, Paweł, Król, Anna, Kacprzyk, Janusz, Series editor, Atanassov, Krassimir T., editor, Castillo, Oscar, editor, Krawczak, Maciej, editor, Melin, Patricia, editor, Sotirov, Sotir, editor, Sotirova, Evdokia, editor, Szmidt, Eulalia, editor, De Tré, Guy, editor, and Zadrożny, Sławomir, editor

Published
2016
Full Text
View/download PDF

12. Construction of Associative Functions for Several Fuzzy Logics via the Ordinal Sum Theorem

Author

Kawaguchi, Mayuka F., Kondo, Michiro, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Huynh, Van-Nam, editor, Inuiguchi, Masahiro, editor, and Demoeux, Thierry, editor

Published
2015
Full Text
View/download PDF

14. PBZ$$^{*}$$–Lattices: Ordinal and Horizontal Sums

Author

Roberto Giuntini, Francesco Paoli, and Claudia Muresan

Subjects
Mathematics::Logic, Pure mathematics, Unary operation, High Energy Physics::Lattice, Computer Science::Logic in Computer Science, Lattice (order), Context (language use), Ordinal sum, Variety (universal algebra), Quantum, Quantum logic, Mathematics
Abstract

PBZ\(^{*}\)–lattices are lattices with additional operations that arise in the context of the unsharp approach to quantum logic. They include orthomodular lattices and Kleene algebras with an extra unary operation. We study in the framework of PBZ\(^{*}\)–lattices two constructions—the ordinal sum construction and the horizontal sum construction—that have been widely used in the investigation of both quantum structures and residuated structures. We provide axiomatisations of the varieties generated by certain sums of PBZ\(^{*}\)–lattices, in particular of the variety generated by all horizontal sums of an orthomodular lattice and an antiortholattice.

Published
2020

15. Generalized Ordinal Sum Constructions of t-norms on Bounded Lattices

Author

Antonín Dvořák and Michal Holčapek

Subjects
Pure mathematics, High Energy Physics::Lattice, Bounded function, Lattice (order), Bounded lattice, Ordinal sum, Mathematics
Abstract

In this contribution, we propose an ordinal sum construction of t-norms on bounded lattices from a system of lattices (endowed by t-norms) whose index set forms a bounded lattice. The ordinal sum construction is determined by a lattice-based sum of bounded lattices and interior operators.

Published
2020

16. Ordinal Sums of t-norms and t-conorms on Bounded Lattices

Author

Antonín Dvořák and Michal Holčapek

Subjects
Pure mathematics, Infinite set, Bounded function, Closure (topology), Extension (predicate logic), Ordinal sum, Mathematics
Abstract

This contribution extends a recently proposed novel approach to ordinal sum constructions of t-norms and t-conorms on bounded lattices that are determined by interior and closure operators. The extension lies in a possibility to consider also infinite sets of indices.

Published
2019

17. Two Constructions of Ordinal Sums of Fuzzy Implications

Author

Paweł Drygaś and Anna Król

Subjects
Algebra, Fuzzy implication, Ordinal sum, Type (model theory), Fuzzy logic, Mathematics
Abstract

This contribution deals with ordinal sums of fuzzy implications. New methods of construction as generalizations of the once previously examined are proposed. The generalizations allow consider summands on intervals of different type: open, closed, or half-open. Sufficient properties of fuzzy implications as summands for obtaining a fuzzy implication as a result are presented.

Published
2017

18. Characterizing Ordinal Sum for t-norms and t-conorms on Bounded Lattices

Author

Gül Deniz Çaylı

Subjects
Discrete mathematics, 0209 industrial biotechnology, Limit ordinal, 02 engineering and technology, 020901 industrial engineering & automation, Bounded function, Ordinal arithmetic, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Bounded lattice, Ordinal sum, Mathematics::Symplectic Geometry, Mathematics, Unit interval
Abstract

The ordinal sum of triangular norms on the unit interval has been proposed to construct new triangular norms. However, considering general bounded lattices, the ordinal sum of triangular norms and conorms may not generate triangular norms and conorms. In this paper, we study and propose some new construction methods yielding triangular norms and conorms on general bounded lattices. Moreover, we generalize these construction methods by induction to a ordinal sum construction for triangular norms and conorms, applicable on any bounded lattice. And some illustrative examples are added for clarity.

Published
2017

19. Ordinal Sum of Fuzzy Implications Fulfilling Left Ordering Property

Author

Anna Król and Paweł Drygaś

Subjects
Property (philosophy), Distributed computing, 010102 general mathematics, Fuzzy implication, 02 engineering and technology, 01 natural sciences, Fuzzy logic, Algebra, Residual implication, Mathematics::Logic, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Ordinal sum, 0101 mathematics, Mathematics
Abstract

In the article new methods of constructing of ordinal sum of fuzzy implications are proposed. The concepts are based both on a construction of ordinal sums of overlap functions and residual implication of ordinal sum of triangular norms. Moreover, preservation of some properties of the ordinal sums of fuzzy implications are examined.

Published
2017

20. Extended Threshold Generation of a New Class of Fuzzy Implications

Author

Zhi-Hong Yi and Feng Qin

Subjects
New class, Generalization, Applied mathematics, Ordinal sum, Scaling, Fuzzy logic, Variable (mathematics), Mathematics
Abstract

The threshold generation of a new implication from two given ones is introduced by Massanet and Torrens. Along the lines of the ordinal sum method in the construction of fuzzy connectives, the paper deals with generalization of the e-threshold generation method by applying the scaling method in the second variable, which can generate some implications different from usual implications, such as f-, g-implications, R-implications, S-implications and the ones derived from the ordinal sum method. And generated implications are characterized.

Published
2016

21. Various Kinds of Ordinal Sums of Fuzzy Implications

Author

Paweł Drygaś and Anna Król

Subjects
Algebra, Property (philosophy), Identity (object-oriented programming), Fuzzy implication, Ordinal sum, Fuzzy logic, Mathematics
Abstract

In this contribution new ways of constructing of ordininal sum of fuzzy implications are presented. Moreover, some of their properties are examined, in particular neutral property, identity property, and ordering property.

Published
2015

22. Extremal Completions of Triangular Norms Known on a Subregion of the Unit Interval

Author

Andrea Mesiarová-Zemánková

Subjects
Physics::Fluid Dynamics, Computer Science::Robotics, Discrete mathematics, Sequence, T-norm, Limit (mathematics), Ordinal sum, Computer Science::Numerical Analysis, Mathematics, Unit interval
Abstract

The strongest and the weakest t-norms that coincide with the given t-norm on a subregion of the unit interval are discussed. The question whether such a t-norm can be obtained as a limit of the sequence of continuous t-norms that coincide with the original t-norm on the given subregion is investigated.

Published
2015

23. Tableau Calculus for Basic Fuzzy Logic BL

Author

Agnieszka Kułlacka

Subjects
Mathematics::Logic, Computer Science::Logic in Computer Science, Metamathematics, Calculus, medicine, Ordinal sum, Situation calculus, medicine.disease, Fuzzy logic, Calculus (medicine), Decomposition theorem, Mathematics
Abstract

In this paper we present a tableau calculus for BL, basic fuzzy logic introduced by Petr Hajek in his monograph Metamathematics of Fuzzy Logic. We show that it is sound and complete with respect to continuous t-norms, and demonstrate the refutational procedure and the search for models procedure on a selected example. The idea of the calculus is based on the decomposition theorem for a continuous t-norm, by which this operation is shown to be equivalent to the ordinal sum of a family of t-norms defined on countably many intervals.

Published
2014

Catalog

Books, media, physical & digital resources
See catalog results