References of "Devillet, Jimmy 50009525"
     in
Bookmark and Share    
Full Text
Peer Reviewed
See detailCharacterizations of idempotent discrete uninorms
Couceiro, Miguel; Devillet, Jimmy UL; Marichal, Jean-Luc UL

in Fuzzy Sets & Systems (in press)

In this paper we provide an axiomatic characterization of the idempotent discrete uninorms by means of three conditions only: conservativeness, symmetry, and nondecreasing monotonicity. We also provide an ... [more ▼]

In this paper we provide an axiomatic characterization of the idempotent discrete uninorms by means of three conditions only: conservativeness, symmetry, and nondecreasing monotonicity. We also provide an alternative characterization involving the bisymmetry property. Finally, we provide a graphical characterization of these operations in terms of their contour plots, and we mention a few open questions for further research. [less ▲]

Detailed reference viewed: 72 (16 UL)
Full Text
See detailAssociative and quasitrivial operations on finite sets (invited lecture)
Marichal, Jean-Luc UL; Couceiro, Miguel; Devillet, Jimmy UL

Scientific Conference (2017, November 10)

Detailed reference viewed: 17 (4 UL)
Full Text
See detailOn quasitrivial and associative operations
Devillet, Jimmy UL; Couceiro, Miguel; Marichal, Jean-Luc UL

Presentation (2017, October 25)

Detailed reference viewed: 11 (6 UL)
Full Text
See detailEnumerating quasitrivial semigroups
Devillet, Jimmy UL; Couceiro, Miguel; Marichal, Jean-Luc UL

Presentation (2017, October 03)

We investigate the class of binary associative and quasitrivial operations on a given finite set. Here quasitriviality (also known as conserva-tiveness) means that the operation always outputs one of its ... [more ▼]

We investigate the class of binary associative and quasitrivial operations on a given finite set. Here quasitriviality (also known as conserva-tiveness) means that the operation always outputs one of its input values. We also examine the special situations where the operations are commutative and nondecreasing. In the latter case, these operations reduce to discrete uninorms, which are discrete fuzzy connectives that play an important role in fuzzy logic. As we will see nondecreasing, associative and quasitrivial operations are chara-cterized in terms of total and weak orderings through the so-called single-peakedness property introduced in social choice theory by Duncan Black. This will enable visual interpretaions of the above mentioned algebraic properties. Motivated by these results, we will also address a number of counting issues: we enumerate all binary associative and quasitrivial operations on a given finite set as well as of those operations that are commutative, are nondecreasing, have neutral and/or annihilator elements. As we will see, these considerations lead to several, previously unknown, integer sequences. [less ▲]

Detailed reference viewed: 27 (10 UL)
Full Text
Peer Reviewed
See detailSur les uninormes discrètes idempotentes
Couceiro, Miguel; Devillet, Jimmy UL; Marichal, Jean-Luc UL

in Couceiro, Miguel; Devillet, Jimmy; Marichal, Jean-Luc (Eds.) LFA 2017 - Rencontres francophones sur la logique floue et ses applications (2017, October)

In this paper we provide two axiomatizations of the class of idempotent discrete uninorms as conservative binary operations, where an operation is conservative if it always outputs one of its input values ... [more ▼]

In this paper we provide two axiomatizations of the class of idempotent discrete uninorms as conservative binary operations, where an operation is conservative if it always outputs one of its input values. More precisely we first show that the idempotent discrete uninorms are exactly those operations that are conservative, symmetric, and nondecreasing. Then we show that, in this characterization, symmetry can be replaced with both bisymmetry and existence of a neutral element. [less ▲]

Detailed reference viewed: 12 (5 UL)
Full Text
Peer Reviewed
See detailRecent results on conservative and symmetric n-ary semigroups
Kiss, Gergely UL; Devillet, Jimmy UL; Marichal, Jean-Luc UL

Scientific Conference (2017, June 16)

See attached file

Detailed reference viewed: 39 (10 UL)
Full Text
Peer Reviewed
See detailOn conservative and associative operations on finite chains
Devillet, Jimmy UL; Couceiro, Miguel; Marichal, Jean-Luc UL

Scientific Conference (2017, June 16)

See attached file

Detailed reference viewed: 42 (10 UL)
Full Text
Peer Reviewed
See detailOn idempotent discrete uninorms
Couceiro, Miguel; Devillet, Jimmy UL; Marichal, Jean-Luc UL

in De Baets, Bernard; Torra, Vicenç; Mesiar, Radko (Eds.) Aggregation Functions in Theory and in Practice (2017, June)

In this paper we provide two axiomatizations of the class of idempotent discrete uninorms as conservative binary operations, where an operation is conservative if it always outputs one of its input values ... [more ▼]

In this paper we provide two axiomatizations of the class of idempotent discrete uninorms as conservative binary operations, where an operation is conservative if it always outputs one of its input values. More precisely we first show that the idempotent discrete uninorms are exactly those operations that are conservative, symmetric, and nondecreasing in each variable. Then we show that, in this characterization, symmetry can be replaced with both bisymmetry and existence of a neutral element. [less ▲]

Detailed reference viewed: 73 (16 UL)