Chia-Cheng Liu

Linear optimization of bipolar fuzzy relational equations with max-Łukasiewicz composition

According to the literature, a linear optimization problem subjected to a system of bipolar fuzzy relational equations with max-Łukasiewicz composition can be translated into a 0-1 integer linear programming problem and solved using integer optimization techniques. However, the technique of integer optimization may involve hight computation complexity. To improve computational efficiency for solving such an optimization problem, this paper proves that each component of an optimal solution obtained from such an optimization problem can either be the corresponding components lower bound or upper bound value. Because of this characteristic, a simple value matrix with some simplified rules can be proposed to reduce the problem size first. A simple solution procedure is then presented for determining optimal solutions without translating such an optimization problem into a 0-1 integer linear programming problem. Two examples are provided to illustrate the simplicity and efficiency of the proposed algorithm.

Pareto-optimal solution for multiple objective linear programming problems with fuzzy goals

Several methods have been addressed to attain fuzzy-efficient solution for the multiple objective linear programming problems with fuzzy goals (FMOLP) in the literature. Recently, Jimenez and Bilbao showed that a fuzzy-efficient solution may not guarantee to be a Pareto-optimal solution in the case that one of fuzzy goals is fully achieved. To show this point they employ Guu and Wu’s two-phase approach to obtain a fuzzy-efficient solution first, then a model like a conventional goal programming problem is proposed to find a Pareto-optimal solution. In this study, a new simplified two-phase approach is proposed to find a Pareto-optimal solution for FMOLP without relying on the results of Guu and Wu’s two-phase approach. This new simplified two-phase approach not only obtains the Pareto-optimal solution but also provides more potential information for decision makers. Precisely, decision makers can find out whether the fuzzy goals of objective function are overestimated or not and the amount of overestimation can easily be computed if it exists.

One Simple Procedure to Finding the Best Approximate Solution for a Particular Fuzzy Relational Equation with Max-min Composition

Fuzzy relational equations have played an important role in fuzzy modeling and applied to many practical problems. Most theories of fuzzy relational equations based on a premise that the solution set is not empty. However, this is often not the case in practical applications. Recently, Chakraborty et al. presented an efficient algorithm to solve the best approximate solution for the fuzzy relational equations, XoA=I, with max-min composition, where I denotes the identity matrix. In this paper, new theoretical results are proposed for solving this particular problem. Hence, one simple procedure can be presented to find the best approximate solution quickly. A numerical example is provided to illustrate the procedure.

Nesting in the Clothing Industry Using Semi-discrete Representations

Marking is a typical 2D nesting operation, but also considers the texture direction. This differs from common metal nesting. In practice, the texture direction of clothes does not totally immobilize. A small quantity of rotational angle is permitted, and this can reduce the waste material. This study proposes a 2D geometric representation, known as a Semi-Discrete Representation. Two dimensional representation of a work piece or panel is completely different from previous continuous and discrete representations, but shares the advantages of both previously studied representations. A rectangle with constant width is used to represent both the work piece and the panel that are to be arranged. As for the rotational angle of the work piece, this study uses the isometric angle to arrange each work piece. The searching range can be set to reduce unnecessary searching time. This study employs semi-discrete information to represent the cloth, and employs genetic algorithms (GAs) to calculate marking sequence and angle, in order to complete marking.

On the power sequence of a fuzzy interval matrix with max-min operation

An

On the max-nilpotent t-norm powers of a fuzzy matrix

n \times n

On Simultaneously Nilpotent Fuzzy Matrices over Max-nilpotent Operations

n×n interval matrix