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Communications of the ACM
Fuzzy sets, uncertainty, and information
Fuzzy sets, uncertainty, and information
Constrained interpolants with minimal Wk,p-norm
Journal of Approximation Theory
Am algorithm for constrained interpolation
SIAM Journal on Scientific and Statistical Computing
The concept of grade of membership
Fuzzy Sets and Systems - Interpretations of Grades on Membership
Shape-preserving bivariate interpolation
SIAM Journal on Numerical Analysis
Interpolation and approximation by monotone cubic splines
Journal of Approximation Theory
Curve and surface fitting with splines
Curve and surface fitting with splines
Fuzzy sets and membership functions based on probabilities
Information Sciences: an International Journal
Fuzzy set theory—and its applications (3rd ed.)
Fuzzy set theory—and its applications (3rd ed.)
Fuzzy Sets and Systems
Surface fitting using convex tensor-product splines
Journal of Computational and Applied Mathematics
The ordered weighted averaging operators: theory and applications
The ordered weighted averaging operators: theory and applications
Definition of general aggregation operators through similarity relations
Fuzzy Sets and Systems
Algorithm 587: Two Algorithms for the Linearly Constrained Least Squares Problem
ACM Transactions on Mathematical Software (TOMS)
Learning Weights in the Generalized OWA Operators
Fuzzy Optimization and Decision Making
On the random generation of monotone data sets
Information Processing Letters
Construction of aggregation functions from data using linear programming
Fuzzy Sets and Systems
Construction of k-Lipschitz triangular norms and conorms from empirical data
IEEE Transactions on Fuzzy Systems
Monotone Approximation of Decision Problems
Operations Research
On the median and its extensions
IPMU'10 Proceedings of the Computational intelligence for knowledge-based systems design, and 13th international conference on Information processing and management of uncertainty
Piecewise linear aggregation functions based on triangulation
Information Sciences: an International Journal
Fuzzy Sets and Systems
Information aggregation in intelligent systems: An application oriented approach
Knowledge-Based Systems
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The need for monotone approximation of scattered data often arises in many problems of regression, when the monotonicity is semantically important. One such domain is fuzzy set theory, where membership functions and aggregation operators are order preserving. Least squares polynomial splines provide great flexibility when modeling non-linear functions, but may fail to be monotone. Linear restrictions on spline coefficients provide necessary and sufficient conditions for spline monotonicity. The basis for splines is selected in such a way that these restrictions take an especially simple form. The resulting non-negative least squares problem can be solved by a variety of standard proven techniques. Additional interpolation requirements can also be imposed in the same framework. The method is applied to fuzzy systems, where membership functions and aggregation operators are constructed from empirical data.