Young-Jou Lai

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.

Fuzzy approach for multi-level programming problems

Abstract Multi-level programming techniques are developed to solve decentralized planning problems with multiple decision makers in a hierarchical organization. These become more important for contemporary decentralized organizations where each unit or department seeks its own interests. Traditional approaches include vertex enumeration and transformation approaches. The former is in search of a compromise vertex based on adjusting the control variable(s) of the higher level and thus is rather inefficient. The latter transfers the lower-level programming problem to be the constraints of the higher level by its Kuhn-Tucker conditions or penalty function; the corresponding auxiliary problem becomes non-linear and the decision information is also implicit. In this study, we use the concepts of tolerance membership functions and multiple objective optimization to develop a fuzzy approach for solving the above problems. The upper-level decision maker defines his or her objective and decisions with possible tolerances which are described by membership functions of fuzzy set theory. This information then constrains the lower-level decision makers feasible space. A solution search relies on the change of membership functions instead of vertex enumeration and no higher order constraints are generated. Thus, the proposed approach will not increase the complexities of original problems and will usually solve a multilevel programming problem in a single iteration. To demonstrate our concept, we have solved numerical examples and compared their solutions with classical solutions.

Hierarchical optimization: a satisfactory solution

Abstract Hierarchical optimization or multi-level programming techniques are extensions of Stackelberg games for solving decentralized planning problems with multiple decision makers in a hierarchical organization. They become more important for contemporary decentralized organizations where each unit or department seeks its own interests. Traditional approaches include vertex enumeration algorithms and approaches based on Kuhn-Tucker conditions or penalty functions. These are not only technically inefficient, but also lead to a paradox that the followers decision power dominates the leaders. In this study, concepts of memberships of optimalities and degrees of decision powers are proposed to solve the above problems efficiently. In the proposed hierarchy decision process, the leader first sets memberships of optimalities of his/her possible objective values and decisions, as well as his/her decision power; and then asks the follower for his/her optima calculated in isolation under given constraints. The followers decision with the corresponding levels of optimalities and decision powers are submitted to and modified by the leader with considerations of overall benefit for the organization and distribution of decision power until a best preferred solution is reached.

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.

A fuzzy approach for multiresponse optimization: an off-line quality engineering problem

Abstract Multiresponse optimization techniques are used to identify settings of process parameters that make the products performance close to target values in the presence of multiple quality characteristics. In this study, a fuzzy multiresponse optimization procedure is proposed to search an appropriate combination of process parameter settings based on multiple quality characteristics or responses. Fuzzy regression models are first used to model the relations between process parameters and responses. The possibility distributions of the prediction responses are then obtained. The problem is reduced to a multiobjective optimization problem with fuzzy objectives. A strategy of optimizing the most possible response values and minimizing the deviations from the most possible values is proposed. We consider not only the most possible value, but also the imprecision of the prediction responses. Through a die casting example, we show how to use our approach to reach an appropriate machine setting which simultaneously optimize both casting quality and die life.

Interactive fuzzy linear programming

Abstract In this study, an interactive fuzzy linear programming approach is investigated to improve the flexibility and robustness of linear programming (LP) technique. This paper provides a practical modelling method which is a symmetric integration of Zimmermanns, Wernerss, Vergegays and Chanass fuzzy LP approaches and additionally provides a decision support system for solving a specific domain of practical LP problems. The interactive concept provides a learning process about the system, whereby the decision maker can learn to recognize good solutions, relative importance of factors in the system and then, design a high-productivity system, instead of optimizing a given system. This interactive fuzzy LP system provides integration-oriented, adaptation and learning features by considering all the possibilities of a specific domain of LP problems which are integrated in logical order using an if-then rule.

A stochastic possibilistic programming model for bank hedging decision problems

Abstract For a practical bank hedging decision optimization problem, interest rates and price of futures contract may involve both fuzziness and randomness. For subjective nature of satisfaction, maximum desired values of loan demand, deposit supply and ratio of desired loan to deposit are often fuzzy. In this study, we consider and solve a stochastic possibilistic programming model of bank hedging decision problems with the above characters. We first use the expected value to obtain an auxiliary possibilistic linear programming problem which is further resolved by use of β-level cut. An (crisp) auxiliary bi-objective linear programming model is then proposed and solved by our augmented maximum approach. For illustration purpose, a numerical bank hedging decision problem is solved.