Implicators based on binary aggregation operators in interval-valued fuzzy set theory

Authors:
Glad Deschrijver;Etienne E. Kerre
Affiliations:
Department of Mathematics and Computer Science, Ghent University, Krijgslaan 281 (S9), B-9000 Gent, Belgium;Department of Mathematics and Computer Science, Ghent University, Krijgslaan 281 (S9), B-9000 Gent, Belgium
Venue:
Fuzzy Sets and Systems
Year:
2005

Citing 7
Cited 13

Contrapositive symmetry of fuzzy implications

Fuzzy Sets and Systems
Triangular norm-based iterative compensatory operators

Fuzzy Sets and Systems - Special issue on triangular norms
On the relationship between some extensions of fuzzy set theory

Fuzzy Sets and Systems - Theme: Basic notions
Aggregation operators for selection problems

Fuzzy Sets and Systems - Special issue: Soft decision analysis
Aggregation operators: properties, classes and construction methods

Aggregation operators
Intuitionistic fuzzy sets

Fuzzy Sets and Systems
On the representation of intuitionistic fuzzy t-norms and t-conorms

IEEE Transactions on Fuzzy Systems

A note on implicators based on binary aggregation operators in interval-valued fuzzy set theory

Fuzzy Sets and Systems
Arithmetic operators in interval-valued fuzzy set theory

Information Sciences: an International Journal
Clustering algorithm for intuitionistic fuzzy sets

Information Sciences: an International Journal
Interval Additive Generators of Interval T-Norms

WoLLIC '08 Proceedings of the 15th international workshop on Logic, Language, Information and Computation
Generalized arithmetic operators and their relationship to t-norms in interval-valued fuzzy set theory

Fuzzy Sets and Systems
Choquet integrals of weighted intuitionistic fuzzy information

Information Sciences: an International Journal
On averaging operators for Atanassov's intuitionistic fuzzy sets

Information Sciences: an International Journal
Triangular norms which are meet-morphisms in interval-valued fuzzy set theory

Fuzzy Sets and Systems
Multiargument relationships in fuzzy databases with attributes represented by interval-valued possibility distributions

RSFDGrC'11 Proceedings of the 13th international conference on Rough sets, fuzzy sets, data mining and granular computing
Interval-Valued and Intuitionistic Fuzzy Mathematical Morphologies as Special Cases of $\mathbb{L}$-Fuzzy Mathematical Morphology

Journal of Mathematical Imaging and Vision
An approach for multiple attribute group decision making problems with interval-valued intuitionistic trapezoidal fuzzy numbers

Computers and Industrial Engineering
Aggregating fuzzy implications

Information Sciences: an International Journal
Mathematical programming methodology for multiattribute decision making using interval-valued intuitionistic fuzzy sets

Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology

Quantified Score

Hi-index	0.20

Visualization

Abstract

In this paper we introduce aggregation operators on the lattice L^*, which is the underlying lattice of both interval-valued fuzzy sets and intuitionistic fuzzy sets in the sense of Atanassov. We consider some particular classes of binary aggregation operators based on t-norms on the unit interval. We investigate the properties of the implicators generated by these classes. In particular, representations in terms of implicators on [0,1] are obtained, and the Smets-Magrez axioms are studied. We compare the results with those obtained for implicators generated by already known classes of t-norms on L^*.