Hitoshi Yano

Multiobjective fuzzy linear regression analysis for fuzzy input-output data

Abstract Fuzzy linear regression models, where both input data and output data are fuzzy numbers, are introduced by using three indices for equalities between fuzzy numbers. By considering the conflict between the fuzzy threshold for the three indices and the fuzziness of the fuzzy linear regression model, three types of multiobjective programming problems for obtaining fuzzy linear regression models are formulated corresponding to the three indices. Then a linear programming based interactive decision making method to derive the satisficing solution of the decision maker for the formulated multiobjective programming problems is developed. A numerical example demonstrates the appropriateness and efficiency of the proposed method.

An Interactive Fuzzy Satisficing Method for Multiobjective Linear-Programming Problems and Its Application

A new interactive fuzzy satisficing method is presented for solving multiobjective linear-programming problems by assuming that the decisionmaker (DM) has fuzzy goals for each of the objective functions. Through the interaction with the DM the fuzzy goals of the DM are quantified by eliciting the corresponding membership functions, including nonlinear functions. After determining the membership functions to generate a candidate for the satisficing solution which is also Pareto optimal, if the DM specifies reference membership values, the minimax problem is solved by combined use of the bisection and linear-programming methods, and the DM is supplied with the corresponding Pareto-optimal solution together with the trade-off rates between the membership functions. Then by considering the current values of the membership functions as well as the trade-off rates, the DM responds by updating his/her reference membership values. In this way the satisficing solution for the DM can be derived efficiently from among a Pareto-optimal solution set by updating his/her reference membership values. On the basis of the proposed method, a time-sharing computer program is written and an application to an optimal operation problem in a package system in automated warehouses is demonstrated along with the computer outputs.

Interactive decision making for multiobjective nonlinear programming problems with fuzzy parameters

This paper presents interactive decision making methods for multiobjective linear, linear fractional and nonlinear programming problems with fuzzy parameters. On the basis of the α-level sets of the fuzzy numbers, the concept of α-multiobjective programming and (local) M-α-Pareto optimality is introduced. Through the interaction with the decision maker (DM), the fuzzy goals of the DM for each of the objective functions in α-multiobjective programming are quantified by eliciting the corresponding membership functions. After determining the membership functions, in order to generate a candidate for the (local) satisficing solution which is also (local) M-α-Pareto optimal, if the DM specifies the degree α of the α-level sets and the reference membership values, the (augmented) minimax problem is solved and the DM is supplied with the corresponding (local) M-α-Pareto optimal solution together with the trade-off rates among the values of the membership functions and the degree α. Then by considering the current values of the membership functions and α as well as the trade-off rates, the DM responds by updating his/her reference membership values and/or the degree α. In this way the (local) satisficing solution for the DM can be derived efficiently from among an M-α-Pareto optimal solution set. Based on the proposed methods for multiobjective linear, linear fractional and nonlinear programming problems with fuzzy parameters, interactive computer programs are developed and an illustrative numerical example for nonlinear case is demonstrated.

An interactive fuzzy satisficing method for generalized multiobjective linear programming problems with fuzzy parameters

Abstract A new interactive fuzzy satisficing method for multiobjective linear programming problems with fuzzy parameters is proposed. In general, two types of fuzziness of human judgements should be incorporated in multiobjective programming problems. One is the experts ambiguous understanding of the nature of the parameters in the problem-formulation process, and the other is the fuzzy goals of the decision maker for each of the objective functions. In order to cope with both types of fuzziness, multiobjective linear programming problems with fuzzy parameters which reflect the experts ambiguous understanding in the problem-formulation are formulated and the concept of generalized α-multiobjective linear programming and M-α-Pareto optimality is introduced. In our interactive fuzzy satisficing method, the satisficing solution of the decision maker is derived efficiently from among M-α-Pareto optimal solutions. On the basis of the proposed method, an interactive computer program is written to implement man-machine interactive procedures. Finally, an illustrative numerical example for multiobjective linear programming problems with fuzzy parameters is demonstrated along with the corresponding computer outputs.

An interactive fuzzy satisficing method using augmented minimax problems and its application to environmental systems

A new interactive fuzzy satisficing method for multiobjective nonlinear programming is presented which considers that the decision-maker (DM) has fuzzy goals for each of the objective functions. Through the interaction with the DM, the fuzzy goals of the DM are quantified by eliciting corresponding membership functions. In order to generate a candidate for the satisficing solution (Pareto optimal) after determining the membership functions, if the DM specifies his/her reference membership values, the augmented minimax problem is solved. The DM is thus supplied with the corresponding Pareto optimal solution together with the tradeoff rates between the membership functions. Then by considering the current values of the membership functions as well as the tradeoff rates, the DM acts on this solution by updating his/her reference membership values. A time-sharing computer program is written to implement man-machine interactive procedures based on this method. An application to an industrial pollution control problem is demonstrated.

An interactive fuzzy satisficing method for multiobjective linear fractional programming problems

Abstract We present a new interactive fuzzy decision making method for solving multiobjective linear fractional programming problems by assuming that the decision maker (DM) has fuzzy goals for each of the objective functions. Through the interaction with the DM, the fuzzy goals of the DM are quantified by eliciting the corresponding membership functions including nonlinear functions. After determining the membership functions, if the DM specifies reference membership values, the minimax problem is solved by combined use of the bisection method and the linear programming method, and the DM is supplied with the corresponding Pareto optimal solution together with the trade-off rates between the membership functions. Then by considering the current values of the membership functions as well as the trade-off rates, the DM responds by updating his/her reference membership values. In this way, the compromise or satisficing solution for the DM can be derived efficiently from among a Pareto optimal solution set by updating his/her reference membership values. On the basis of the proposed method, a time-sharing computer program is written and an illustrative numerical example is demonstrated along with the computer outputs.

Feasibility and Pareto optimality for multiobjective nonlinear programming problems with fuzzy parameters

Abstract In this paper, we focus on multiobjective nonlinear programming problems with fuzzy parameters and extend the ordinary feasibility and Pareto optimality concepts based on the concepts of possibility and necessity for fuzzy numbers. Using the four indices for ranking two fuzzy numbers, four types of feasibility and Pareto optimality are defined and the relationships among them are examined in detail. These concepts can be viewed as quite generalized versions of the well-known feasibility and Pareto optimality concepts, and the generalized Pareto optimal solutions for the multiobjective nonlinear programming problems with fuzzy parameters may be obtained on the basis of the method of nonlinear programming.

Interactive decision making for multiobjective linear fractional programming problems with fuzzy parameters

Abstract In this paper, we focus on multiobjective linear fractional programming problems with fuzzy parameters and present a new interactive decision making method for obtaining the satisficing solution of the decision maker (DM) on the basis of the linear programming method. The fuzzy parameters in the objective functions and the constraints are characterized by fuzzy numbers. The concept of a-Pareto optimality is introduced in which the ordinary Pareto optimality is extended based on the α-level sets of the fuzzy numbers. In our interactive decision making method, in order to generate a candidate for the satisficing solution which is also a-Pareto optimal, if the DM specifies the degree α of the a-level sets and the reference objective values, the minimax problem is solved by combined use of the bisection method and the linear programming method and the DM is supplied with the corresponding α-Pareto optimal solution together with the trade-off rates among the values of the objective functions and the d...

Interactive fuzzy decision making for multiobjective nonlinear programming usingaugmented minimax problems

An interactive fuzzy decision-making method for solving multiobjective nonlinear programming problems is presented in this paper by assuming that the decision maker (DM) has fuzzy goals for each of the objective functions. The fuzzy goals of the DM are quantified by eliciting corresponding membership functions through the interaction with the DM. Having determined the membership functions, if the DM specifies his reference membership values, the augmented minimax problem is solved and the DM is supplied with the corresponding Pareto-optimal solution together with the trade-off rates between the membership functions. Then by considering the current values of the membership functions as well as the trade-off rates, the DM responds by updating his reference membership values. In this way the compromise or satisficing solution for the DM can be derived efficiently from among a Pareto-optimal solution set. On the basis of the proposed method, a time-sharing computer program is written and an illustrative numerical example is demonstrated along with the computer outputs.

A fuzzy dual decomposition method for large-scale multiobjective nonlinear programming problems

Abstract In this paper, we propose a fuzzy dual decomposition method for large-scale multiobjective nonlinear programming problems (LS-MONLPs) with the block angular structure. By considering the vague nature of human judgements, we assume that the decision maker (DM) may have a fuzzy goal for each of the objective functions in the LS-MONLP. After eliciting the corresponding membership function for each of the objective functions through the interaction with the DM, an extended primal problem and the corresponding extended dual problem are formulated. Then a two-level optimization algorithm for the extended dual problem is proposed for deriving the compromise solution for the DM to the LS-MONLP. Based on the proposed algorithm, FORTRAN programs are developed and an illustrative numerical example is demonstrated.