Ario Ohsato

LINEAR COORDINATION METHOD FOR FUZZY MULTI-OBJECTIVE LINEAR PROGRAMMING PROBLEMS WITH CONVEX POLYHEDRAL MEMBERSHIP FUNCTIONS

A fuzzy multi-objective decision-making with nonlinear membership functions is proposed in this paper by assuming that the decision maker has a fuzzy goal for each objective function. The fuzzy goals can be quantified by convex polyhedral membership functions, which are expressed by linguistic terms. The concept of the convex cone is used to formulate a normalized convex polyhedral penalty function, which can also be considered conversely as a convex polyhedral membership function. The most desirable value of membership functions are selected to be reference membership values of achievement of convex polyhedral membership functions that can be viewed as the extension of the idea of reference point method. The formulated model can be solved by existing linear programming solvers and can find the satisficing solution for the decision maker, which can be derived efficiently from among an M-Pareto optimal solution set together with the trade-off rates between the membership functions. The proposed model uses convex polyhedral membership functions to represent vague aspirations of the decision maker. It enriches the existing satisficing methods for fuzzy multi-objective linear programming in a more practical way with the effective method based on convex cone.

A Comment on the Formulation of an Aggregate Production Planning Problem

Conventionally, a revenue function, a cost function and a profit function are selected to be the objective function for aggregate production planning (APP) problems. The theory of constraints (TOC) alternative consideration argues that instead of measuring by cost, factory should evaluate their performance by throughput. Even though, there are a lot of research works on formulations of APP problems, there has been no investigation, which formulation is the most appropriate for APP problems. In this research, the investigation of the formulation of existing APP problems is done. In order to clarify the difference of each objective function, a simple case study has been used to compare the performances of the APP problem with revenue, cost, and profit objective functions when resource constraints (limited processing time) are not included and included in the model. For the profit objective function, two formulations are also compared: profit objective function by TOC and profit objective function by linear programming. From the results, it can be shown that setting the objective function of an APP problem is very important because it may lead to a wrong decision in production planning

Monotone Increasing Binary Similarity and Its Application to Automatic Document-Acquisition of a Category

A technique that acquires documents in the same category with a given short text is introduced. Regarding the given text as a training document, the system marks up the most similar document, or sufficiently similar documents, from among the document domain (or entire Web). The system then adds the marked documents to the training set to learn the set, and this process is repeated until no more documents are marked. Setting a monotone increasing property to the similarity as it learns enables the system to 1) detect the correct timing so that no more documents remain to be marked and to 2) decide the threshold value that the classifier uses. In addition, under the condition that the normalization process is limited to what term weights are divided by a p-norm of the weights, the linear classifier in which training documents are indexed in a binary manner is the only instance that satisfies the monotone increasing property. The feasibility of the proposed technique was confirmed through an examination of binary similarity and using English and German documents randomly selected from the Web.

Efficient linear combination method for multi-objective problems with convex polyhedral preference functions

At present, the most commonly used method for multiobjective linear programming (MOLP) is goal programming (GP) based methods but these methods do not always generate efficient solutions. Recently, an efficient GP-based method, which is called reference goal programming (RGP), has been proposed. However, it is limited to only a certain target point preference, which is too rigid. The more flexible preferences are preferred in many practical problems. In this research, an effective linear combination method for MOLP problems with convex polyhedral preference functions is proposed. The concept of the convex cone is used to formulate convex polyhedral preference functions and the existing reference point method (RPM) is integrated to ensure the efficiency of the solution of the problem. The formulated model can be solved by existing linear programming solvers and can find the satisfactory efficient solution. The convex polyhedral function enriches the existing preferences for efficient methods and increases the flexibility in designing preferences for decision makers. For some situations, it is difficult for the decision maker to state the certain aspiration level for each objective function. Fuzzy goals, which can be considered as convex polyhedral preference functions, can be used to represent aspiration levels with respect to linguistic terms.

Linear Coordination Method for Multi-Objective Problems

At present, the most commonly used satisficing method for multi-objective linear programming (MOLP) is goal programming (GP) based methods but these methods do not always generate efficient solutions. Recently, an efficient GP-based method, which is called reference goal programming (RGP), has been proposed. However, it is limited to only a triangular preference. The more flexible preferences such a convex polyhedral type is preferred in many practical problems. In this research, a satisfactory effective linear coordination method for MOLP problems with convex polyhedral preference functions is proposed. It can be solved by existing linear programming solvers and can find all of the efficient solutions, which satisfy decision maker’s requirements. The convex polyhedral function enriches the existing preferences for efficient methods and increases the flexibility in designing preferences.