SIAM Review
Fuzzy Sets and Systems
Fuzzy regression methods—a comparative assessment
Fuzzy Sets and Systems
Hybrid fuzzy least-squares regression analysis and its relibabilty measures
Fuzzy Sets and Systems
Primal-Dual Interior-Point Methods for Self-Scaled Cones
SIAM Journal on Optimization
Linear regression analysis for fuzzy/crisp input and fuzzy/crisp output data
Computational Statistics & Data Analysis
Support vector interval regression networks for interval regression analysis
Fuzzy Sets and Systems - Theme: Learning and modeling
Convex Optimization
Non-convex quadratic minimization problems with quadratic constraints: global optimality conditions
Mathematical Programming: Series A and B
Centre and Range method for fitting a linear regression model to symbolic interval data
Computational Statistics & Data Analysis
Forecasting models for interval-valued time series
Neurocomputing
Least squares estimation of a linear regression model with LR fuzzy response
Computational Statistics & Data Analysis
SIAM Review
Support vector interval regression machine for crisp input and output data
Fuzzy Sets and Systems
Interval regression analysis by quadratic programming approach
IEEE Transactions on Fuzzy Systems
Interval regression analysis using quadratic loss support vector machine
IEEE Transactions on Fuzzy Systems
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Building a linear fitting model for a given interval-valued data set is challenging since the minimization of the residue function leads to a huge combinatorial problem. To overcome such a difficulty, this article proposes a new semidefinite programming-based method for implementing linear fitting to interval-valued data. First, the fitting model is cast to a problem of quadratically constrained quadratic programming QCQP, and then two formulae are derived to develop the lower bound on the optimal value of the nonconvex QCQP by semidefinite relaxation and Lagrangian relaxation. In many cases, this method can solve the fitting problem by giving the exact optimal solution. Even though the lower bound is not the optimal value, it is still a good approximation of the global optimal solution. Experimental studies on different fitting problems of different scales demonstrate the good performance and stability of our method. Furthermore, the proposed method performs very well in solving relatively large-scale interval-fitting problems.