Interpolation of fuzzy data: Analytical approach and overview

Authors:
Irina Perfilieva;Didier Dubois;Henri Prade;Francesc Esteva;Lluis Godo;Petra Hoďáková
Affiliations:
University of Ostrava, Institute for Research and Applications of Fuzzy Modeling, 30. dubna 22, 701 03 Ostrava 1, Czech Republic;IRIT, CNRS and Universit de Toulouse, 118 route de Narbonne, 31062 Toulouse, France;IRIT, CNRS and Universit de Toulouse, 118 route de Narbonne, 31062 Toulouse, France;Artificial Intelligence Research Institute (IIIA), Spanish National Research Council (CSIC), 08193 Bellaterra, Spain;Artificial Intelligence Research Institute (IIIA), Spanish National Research Council (CSIC), 08193 Bellaterra, Spain;University of Ostrava, Institute for Research and Applications of Fuzzy Modeling, 30. dubna 22, 701 03 Ostrava 1, Czech Republic
Venue:
Fuzzy Sets and Systems
Year:
2012

Citing 8
Cited 3

Foundations of fuzzy sets

Fuzzy Sets and Systems - Special memorial volume on mathematical aspects of fuzzy set theory
Fuzzy sets and fuzzy logic: the foundations of application—from a mathematical point of view

Fuzzy sets and fuzzy logic: the foundations of application—from a mathematical point of view
Interpolative reasoning with insufficient evidence in sparse fuzzy rule bases

Information Sciences: an International Journal
Reasoning conditions on Ko´czy's interpolative reasoning method in sparse fuzzy rule bases

Fuzzy Sets and Systems
Fuzzy points, fuzzy relations and fuzzy functions

Discovering the world with fuzzy logic
Fundamentals of M-vague algebra and M-vague arithmetic operations

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
System of fuzzy relation equations as a continuous model of IF-THEN rules

Information Sciences: an International Journal
A generalized concept for fuzzy rule interpolation

IEEE Transactions on Fuzzy Systems

Order compatible fuzzy relations and their elicitation from general fuzzy partitions

ECSQARU'11 Proceedings of the 11th European conference on Symbolic and quantitative approaches to reasoning with uncertainty
Fuzzy Equilibrium Logic: Declarative Problem Solving in Continuous Domains

ACM Transactions on Computational Logic (TOCL)
Interpolative reasoning with default rules

IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence

Quantified Score

Hi-index	0.20

Visualization

Abstract

We propose a general framework for the interpolation problem. Our framework stems from the classical elaboration of the problem. We introduce the notion of an interpolating fuzzy function and show how this function can be characterized. We examine and analyze previously published fuzzy interpolation algorithms to choose those algorithms that can be represented analytically. We also propose an analytic solution of the interpolation problem that unifies various algorithmic approaches.