The fuzzy linear regression model with fuzzy input-output data andcrisp coefficients is studied in this paper. A linear programmingmodel based on goal programming is proposed to calculate theregression coefficients. In contrast with most of the previous works, theproposed model takes into account the centers of fuzzy data as animportant feature as well as their spreads in the procedure ofconstr...

‎A full Nesterov-Todd (NT) step infeasible interior-point algorithm‎ ‎is proposed for solving monotone linear complementarity problems‎ ‎over symmetric cones by using Euclidean Jordan algebra‎. ‎Two types of‎ ‎full NT-steps are used‎, ‎feasibility steps and centering steps‎. ‎The‎ ‎algorithm starts from strictly feasible iterates of a perturbed‎ ‎problem‎, ‎and, using the central path and feasi...

This study is an investigation of fuzzy linear regression model for crisp/fuzzy input and fuzzy output data. A least absolutes deviations approach to construct such a model is developed by introducing and applying a new metric on the space of fuzzy numbers. The proposed approach, which can deal with both symmetric and non-symmetric fuzzy observations, is compared with several existing models by...

and Applied Analysis 3 The input and output constraints are satisfied if there exists symmetric matrixX and Y such that [ X ∗ Y T Q ] ≥ 0 with X rr ≤ u 2 r,max, r = 1, 2, . . . , m,

Let G be any of the complex classical groups GL(n) , SO(2n + 1) , Sp(2n) , O(2n) , let g denote the Lie algebra of G , and let Z(g) denote the subalgebra of G -invariants in the universal enveloping algebra U(g) . We derive a Taylortype expansion for finite-dimensional characters of G (the binomial formula) and use it to specify a distinguished linear basis in Z(g) . The eigenvalues of the basi...

We explore the orthogonal decomposition of tensors (also known as multidimensional arrays or n-way arrays) using two different definitions of orthogonality. We present numerous examples to illustrate the difficulties in understanding such decompositions. We conclude with a counterexample to a tensor extension of the Eckart-Young SVD approximation theorem by Leibovici and Sabatier [Linear Algebr...

The distribution for the number of searches needed to find k of n lost objects is expressed in terms of a refinement of the q-Eulerian polynomials, for which formulae are developed involving homogeneous symmetric polynomials. In the case when k � n and the find probability remains constant, relatively simple and efficient formulas are obtained. From our main theorem, we further (1) deduce the i...

classes of‎ ‎abaffy-broyden-spedicato (abs) methods have been introduced for‎ ‎solving linear systems of equations‎. ‎the algorithms are powerful methods for developing matrix‎ ‎factorizations and many fundamental numerical linear algebra processes‎. ‎here‎, ‎we show how to apply the abs algorithms to devise algorithms to compute the wz and zw‎ ‎factorizations of a nonsingular matrix as well as...

classes of‎ ‎abaffy-broyden-spedicato (abs) methods have been introduced for‎ ‎solving linear systems of equations‎. ‎the algorithms are powerful methods for developing matrix‎ ‎factorizations and many fundamental numerical linear algebra processes‎. ‎here‎, ‎we show how to apply the abs algorithms to devise algorithms to compute the wz and zw‎ ‎factorizations of a nonsingular matrix as well as...