Ching-Lai Hwang

Fuzzy Multiple Attribute Decision Making

Decision makers are often faced with several conflicting alternatives [1]. How do they evaluate trade-offs when there are more than three criteria? To help people make optimal decisions, scholars in the discipline of multiple criteria decision making (MCDM) continue to develop new methods for structuring preferences and determining the correct relative weights for criteria. A compilation of modern decision-making techniques, Multiple Attribute Decision Making: Methods and Applications focuses on the fuzzy set approach to multiple attribute decision making (MADM). Drawing on their experience, the authors bring together current methods and real-life applications of MADM techniques for decision analysis. They also propose a novel hybrid MADM model that combines DEMATEL and analytic network process (ANP) with VIKOR procedures.

Group decision making under multiple criteria

Note: Bibliogr. : p. 355-400 Reference Record created on 2004-09-07, modified on 2016-08-08

TOPSIS for MODM

Abstract In this study, we extend TOPSIS to solve a multiple objective decision making problem. The principle of compromise (of TOPSIS) for multiple criteria decision making is that the chosen solution should have the shortest distance from the positive ideal solution as well as the longest distance from the negative ideal solution. Thus, we reduce a k -dimensional objective space to a two-dimensional objective space by a first-order compromise procedure. We then use membership functions of fuzzy set theory to represent the satisfaction level for both criteria. We obtain a single-objective programming problem by using the max-min operator for the second-order compromise operation. To illustrate the procedure, the Bow River Valley water quality management problem is solved by use of TOPSIS.

A new approach to some possibilistic linear programming problems

Abstract In practice, the unit costs/profits of new products or new projects, the lending and borrowing interest rates, and cash flows are always imprecise. We provide an auxiliary multiple objective linear programming model to solve a linear programming problem with imprecise objective and/or constraint coefficients. Our strategy is to maximize the most possible value of the imprecise profit. At the same time, we would like to minimize the risk of obtaining lower profit and maximize the possibility of obtaining higher profit. This strategy is equivalent to the practical considerations of financial problems. In this paper, a numeric investment problem is solved for illustrating the new approach.

A new approach for multiple objective decision making

The proposed TOPSIS for MODM algorithm is developed for solving multiple objective decision-making problems by considering two reference points of the positive ideal solution and the negative ideal solution simultaneously. The basic principle of compromise of TOPSIS for MODM is that the chosen solution should be as close to the positive ideal solution as possible and as far away from the negative ideal solution as possible. Thus, we can reduce a k-objective decision-making problem into an auxiliary bi-objective decision-making problem. That is: instead of k incommensurable and conflicting objective function, we consider two commensurable but conflicting objective functions (distance functions). Then, by using the max-min operator, we can obtain a compromise solution for the auxiliary bi-objective problem and the original k-objective problem. To illustrate the TOPSIS algorithm, a numerical nutrition problem is solved.

Optimization Techniques for System Reliability with RedundancyߞA Review

This paper is a state-of-art review of the literature related to optimal system reliability with redundancy. The literature is classified as follows. Optimal system reliability models with redundancy Series Parallel Series-parallel Parallel-series Standby Complex (nonseries, nonparallel) Optimization techniques for obtaining optimal system configuration Integer programming Dynamic programming Maximum principle Linear programming Geometric programming Sequential unconstrained minimization technique (SUMT) Modified sequential simplex pattern search Lagrange multipliers and Kuhn-Tucker conditions Generalized Lagrangian function Generalized reduced gradient (GRG) Heuristic approaches Parametric approaches Pseudo-Boolean programming Miscellaneous

Mathematical programming with multiple objectives: A tutorial☆

Abstract A system of classifying about two dozen major methods for mathematical programming with multiple objectives, or multiple objective decision making (MODM) is presented. The classification has been based upon four categories of the preference information given to the analyst by a decision maker: (1) a priori , (2) progressive, (3) a posteriori and (4) no articulation of the preference information. A method or two from each category is illustrated by approaching a simple common numerical example in detail for the comparison and tutorial purpose. Consideration in selecting criteria for comparative evaluation of the methods and availability of computer codes for some methods are discussed.

Determining Component Reliability and Redundancy for Optimum System Reliability

The usual constrained reliability optimization problem is extended to include determining the optimal level of component reliability and the number of redundancies in each stage. With cost, weight, and volume constraints, the problem is one in which the component reliability is a variable, and the optimal trade-off between adding components and improving individual component reliability is determined. This is a mixed integer nonlinear programming problem in which the system reliability is to be maximized as a function of component reliability level and the number of components used at each stage. The model is illustrated with three general non linear constraints imposed on the system. The Hooke and Jeeves pattern search technique in combination with the heuristic approach by Aggarwal et al, is used to solve the problem. The Hooke and Jeeves pattern search technique is a sequential search routine for maximizing the system reliability, RS (R, X). The argument in the Hooke and Jeeves pattern search is the component reliability, R, which is varied according to exploratory moves and pattern moves until the maximum of RS (R, X) is obtained. The heuristic approach is applied to each value of the component reliability, R, to obtain the optimal number of redundancies, X, which maximizes RS (R, X) for the stated R.

Multiple Objective Decision Making

Decision making is the process of selecting a possible course of action from all available alternatives. In many cases, multiplicity of criteria for judging the alternatives is pervasive. Often the decision maker wants to attain more than one objective or goal in selecting a course of action, while satisfying constraints dictated by environment, processes, and resources.

Possibilistic linear programming for managing interest rate risk

Abstract In this study, we consider the linear programming problem with the objective of the investment discounted value, where the interest rate is imprecise and has a triangular possibilistic distribution. An (crisp) auxiliary bi-objective linear programming model is proposed to resolve this possibilistic nature. Furthermore, we develop an extended Zimmermann approach, called augmented max-min approach, for solving this auxiliary bi-objective linear programming problem and other multiple objective linear programming problems. Finally, a numerical bank balance sheet problem, where interest rates, price of futures contract, loan demand, deposit supply and ratio of desired loan to deposit are assumed to be fuzzy, is solved for illustrating the new approach.