An approach for predicting and describing patient outcome using multicriteria decision analysis and decision rules

Patient outcome in brain trauma patients is affected by a multiplicity of factors, beginning with ambulatory transportation and routing, to the grade of the receiving facility and treatment therein, and finally the treatment and monitoring in definitive care (the brain trauma intensive care unit). Factors and events in each of these phases can be modeled as a multicriteria problem, where the objective is to optimize patient outcome; moreover, a more comprehensive model can embody the interactions of all three phases. This study focuses on modeling the factors that affect patient outcome in definitive care and on expressing these in machine readable format so that we can better describe or predict patient outcome using data mining tools. We use multicriteria decision analysis and decision rules for knowledge representation. Preliminary results suggest that the incorporation of a priori knowledge does help better predict or describe patient outcome when using decision tree induction.     

An interactive approach for multiobjective decision making

We develop an interactive approach for multiobjective decision-making problems, where the solution space is defined by a set of constraints. We first reduce the solution space by eliminating some undesirable regions. We generate solutions (partition ideals) that dominate portions of the efficient frontier and the decision maker (DM) compares these with feasible solutions. Whenever the decision maker prefers a feasible solution, we eliminate the region dominated by the partition ideal. We then employ an interactive search method on the reduced solution space to help the DM further converge toward a highly preferred solution. We demonstrate our approach and discuss some variations.     

An anisotropic geometrical approach for non-relativistic extended dynamics

In this paper we present the distinguished (d-) Riemannian geometry (in the sense of nonlinear connection, Cartan canonical linear connection, together with its d-torsions and d-curvatures) for a possible Lagrangian inspired by optics in non-uniform media. The corresponding equations of motion are also exposed, and some particular solutions are given. For instance, we obtain as geodesic trajectories some circular helices (depending on an angular velocity $\omega $ ), certain circles situated in some planes (ones are parallel with $xOy $ , and other ones are orthogonal on $xOy$ ), or some straight lines which are parallel with the axis $Oz$ . All these geometrical geodesics are very specific because they are completely determined by the non-constant index of refraction $n(x)$ .     

An efficient DC programming approach for portfolio decision with higher moments

Portfolio selection with higher moments is a NP-hard nonconvex polynomial optimization problem. In this paper, we propose an efficient local optimization approach based on DC (Difference of Convex functions) programming—called DCA (DC Algorithm)—that consists of solving the nonconvex program by a sequence of convex ones. DCA will construct, in each iteration, a suitable convex quadratic subproblem which can be easily solved by explicit method, due to the proposed special DC decomposition. Computational results show that DCA almost always converges to global optimal solutions while comparing with the global optimization methods (Gloptipoly, Branch-and-Bound) and it outperforms several standard local optimization algorithms.     

An extended shortest path problem: A data envelopment analysis approach

A special and important network structured linear programming problem is the shortest path problem. Classical shortest path problems assume that there are unit of shipping cost or profit along an arc. In many real occasions, various attributes (various costs and profits) are usually considered in a shortest path problem. Because of the frequent occurrence of such network structured problems, there is a need to develop an efficient procedure for handling these problems. This paper studies the shortest path problem in the case that multiple attributes are considered along the arcs. The concept of relative efficiency is defined for each path from initial node to final node. Then, an efficient path with the maximum efficiency is determined.     

An extended Galerkin analysis for elliptic problems

A general analysis framework is presented in this paper for many different types of finite element methods(including various discontinuous Galerkin methods). For the second-order elliptic equation-div(α▽u) = f, this framework employs four different discretization variables, uh, p_h, uhand p_h, where uh and phare for approximation of u and p =-α▽u inside each element, and uhand phare for approximation of the residual of u and p·n on the boundary of each element. The resulting 4-field discretization is proved to satisfy two types of inf-sup conditions that are uniform with respect to all discretization and penalization parameters. As a result, many existing finite element and discontinuous Galerkin methods can be analyzed using this general framework by making appropriate choices of discretization spaces and penalization parameters.     

An introduction and survey of the evidential reasoning approach for multiple criteria decision analysis

The Evidential Reasoning (ER) approach is a general approach for analyzing multiple criteria decision problems under various types of uncertainty using a unified framework—belief structure. In this paper, the ER approach is surveyed from two aspects: theoretical development and applications. After a brief outline of its development and extension over a twenty year period, the ER approach is outlined with a focus on the links among its various developments. Future research directions in the area are also explored in the survey.     

An extended slacks-based measure model for data envelopment analysis with negative data

Data envelopment analysis (DEA) is a non-parametric approach based on linear programming that has been widely applied for evaluating the relative efficiency of a set of homogeneous decision-making units (DMUs) with multiple inputs and outputs. The original DEA models use positive input and output variables that are measured on a ratio scale, but these models do not apply to the variables in which negative data can appear. However, with the widespread use of interval scale data and undesirable data, the emphasis has been directed towards the simultaneous consideration of the positive and negative data in DEA models. In this paper, using the slacks-based measure, we propose an extended model to evaluate the efficiency of DMUs, even if some variables are measured on an interval scale and some on a ratio scale. Moreover, the extended model allows for the presence of all interval-scale variables, which are capable of taking both negative and positive values.     

An extended cost estimation model for a multi-material topology optimization approach

The manufacturing costs of hybrid parts comprise several different proportions depending on the manufacturing process and the materials used. A simplified cost model based on the material weights is therefore no longer sufficient. In this paper, an approach for the weight and costs optimization of hybrid parts is presented. An extended costs calculation function regarding additional manufacturing costs and the integration of a new cost objective in the optimization process is investigated. The effects of the consideration of costs on the optimization results will be qualitatively shown on a simple example structure. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An extended transportation problem: a DEA-based approach

The transportation problem is an important network structured linear programming problem that arises in several contexts and that has received a great deal of attention in the literature. The existing transportation problems are limited to consideration unit of shipping cost or profit along an arc. However, in many real applications, various attributes are usually considered in a transportation problem. The current paper, proposes an extension to this problem in the presence of multiple in-commensurate inputs and outputs for each arc. The concept of relative efficiency is defined for each possible transportation plan. Two linear programming models are proposed to determine the transportation plan with the maximum efficiency. A numerical example is used to illustrate the applicability of the approach.     

Completing extended metric spaces: An alternative approach

This paper proves the completion of extended metric spaces using the concept of $\epsilon$-approach nearness spaces, in terms of clusters that are a generalization of Cauchy sequences.     

Quasi-likelihood or extended quasi-likelihood? An information-geometric approach

When the variance is a known function of the mean, as in quasi-likelihood applications, the sample variance also contains information about the mean and extensions of quasi-likelihood functions have been suggested that incorporate this additional information. In order to be sure these extensions are an improvement, further assumptions are made typically on the higher moments of the data so that there is a trade-off between the greater robustness of the quasi-likelihood estimates and the potentially improved estimates based on the extended quasi-likelihood functions. Improvement is often measured by relative efficiency but more insight can be gained by considering optimality of estimating functions, information loss, and sufficiency. All these measures can be described using the dual geometries of the quasi- and extended quasi-likelihood estimators. For a substantial range of models, the extended estimates offer little improvement when the coefficient of variation is small.     

Model and extended Kuhn–Tucker approach for bilevel multi-follower decision making in a referential-uncooperative situation

When multiple followers are involved in a bilevel decision problem, the leader’s decision will be affected, not only by the reactions of these followers, but also by the relationships among these followers. One of the popular situations within this bilevel multi-follower issue is where these followers are uncooperatively making their decisions while having cross reference to decision information of the other followers. This situation is called a referential-uncooperative situation in this paper. The well-known Kuhn–Tucker approach has been previously successfully applied to a one-leader-and-one-follower linear bilevel decision problem. This paper extends this approach to deal with the above-mentioned linear referential-uncooperative bilevel multi-follower decision problem. The paper first presents a decision model for this problem. It then proposes an extended Kuhn–Tucker approach to solve this problem. Finally, a numerical example illustrates the application of the extended Kuhn–Tucker approach.     

A data envelopment approach to decision analysis

A decision aid to assist the development of a linear valuation function for multiple attribute problems is proposed, based on a linear programming formulation using a constraint set structured in a similar manner to data envelopment analysis (DEA). Value functions which favour each decision option are calculated, and efficient, potentially optimal, options identified. These are used to help a decision maker progressively to articulate preferences, indicators of his/her values, in an interactive, structurally flexible manner. As preference indications are provided, candidate value functions and hitherto efficient options inconsistent with his/her declarations are eliminated, thus proceeding towards an explicit value function and, if needed a corresponding complete option order.     

An approach for solving fuzzy multi-criteria decision problem under linguistic information

Fuzzy Optimization and Decision Making - Linguistic information processing exists in multi-criteria decision making, and linguistic truth-valued lattice implication algebra (LTV-LIA) has definite...     

Convex analytic approach to constrained discounted Markov decision processes with non-constant discount factors

In this paper we develop the convex analytic approach to a discounted discrete-time Markov decision process (DTMDP) in Borel state and action spaces with N constraints. Unlike the classic discounted models, we allow a non-constant discount factor. After defining and characterizing the corresponding occupation measures, the original constrained DTMDP is written as a convex program in the space of occupation measures, whose compactness and convexity we show. In particular, we prove that every extreme point of the space of occupation measures can be generated by a deterministic stationary policy for the DTMDP. For the resulting convex program, we prove that it admits a solution that can be expressed as a convex combination of N+1 extreme points of the space of occupation measures. One of its consequences is the existence of a randomized stationary optimal policy for the original constrained DTMDP.     

The evidential reasoning approach for multi-attribute decision analysis under interval uncertainty

The evidential reasoning (ER) approach is a method for multiple attribute decision analysis (MADA) under uncertainties. It improves the insightfulness and rationality of a decision making process by using a belief decision matrix (BDM) for problem modelling and the Dempster–Shafer (D–S) theory of evidence for attribute aggregation. The D–S theory provides scope and flexibility to deal with interval uncertainties or local ignorance in decision analysis, which is not explored in the original ER approach and will be investigated in this paper. Firstly, interval uncertainty will be defined and modelled in the ER framework. Then, an extended ER algorithm, IER, is derived, which enables the ER approach to deal with interval uncertainty in assessing alternatives on an attribute. It is proved that the original ER algorithm is a special case of the IER algorithm. The latter is demonstrated using numerical examples.