Fuzzy Linear Programming with Interactive Uncertain Parameters

In this paper, we treat fuzzy linear programming problems with uncertain parameters whose ranges are specified as fuzzy polytopes. The problem is formulated based on fractile optimization model using a necessity measure. It is shown that the problem can be reduced to a semi-infinite linear programming problem and that a solution algorithm based on a relaxation procedure can be applied. A simple numerical example is given to illustrate the solution procedure. This revised version was published online in June 2006 with corrections to the Cover Date.     

A unified approach to reducts in dominance-based rough set approach

The Dominance-based Rough Set Approach (DRSA), which is an extension of the Rough Set Approach (RSA), analyzes a sorting problem for a given data set. Attribute reduction is one of major topics in RSA as well as DRSA. By attribute reduction, we can find an important attribute set, which is called a reduct. In this paper, we propose a new approach to reducts in DRSA. A few kinds of reducts have been already proposed in DRSA, therefore, we clarify relations among the proposed and previous ones. We prove that they are consolidated into four kinds. Moreover, we show that all kinds of reducts can be enumerated based on two discernibility matrices.     

Decomposition of Petri nets and Lagrangian relaxation for solving routing problems for AGVs

In this paper, we propose a Lagrangian relaxation method for solving routing problems for multiple AGVs by decomposition of timed Petri nets. The AGV routing problem is represented by an optimal transition firing sequence problem for timed Petri nets. The timed Petri net is decomposed into several subnets in which the subproblem for each subnet can be easily solved by Dijkstra's algorithm. We show that each subproblem generated by each subnet is polynomially solvable. The optimality of the solution can be evaluated by the duality gap derived by the Lagrangian relaxation method. The performance of the proposed method is compared with a conventional optimisation algorithm with the penalty function method. The effectiveness of the proposed method is demonstrated.     

Self-organizing fuzzy aggregation models to rank the objects withmultiple attributes

In this paper, a kind of ranking system, called agent-clients evaluation system, is proposed and investigated where there is no such authority with the right to predetermine weights of attributes of the entities evaluated by multiple evaluators for obtaining an aggregated evaluation result from the given fuzzy multiattribute values of these entities. Three models are proposed to evaluate the entities in such a system based on fuzzy inequality relation, possibility, and necessity measures, respectively. In these models, firstly the weights of attributes are automatically sought by fuzzy linear programming (FLP) problems based on the concept of data envelopment analysis (DEA) to make a summing-up assessment from each evaluator. Secondly, the weights for representing each evaluator's credibility are obtained by FLP to make an integrated evaluation of entities from the viewpoints of all evaluators. Lastly, a partially ordered set on a one-dimensional space is obtained so that all entities can be ranked easily. Because the weights of attributes and evaluators are obtained by DEA-based FLP problems, the proposed ranking models can be regarded as fair-competition and self-organizing ones so that the inherent feature of evaluation data can be reflected objectively     

Lagrangian relaxation with cut generation for hybrid flowshop scheduling problems to minimize the total weighted tardiness

In this paper, we address a new Lagrangian relaxation (LR) method for solving the hybrid flowshop scheduling problem to minimize the total weighted tardiness. For the conventional LR, the problem relaxing machine capacity constraints can be decomposed into individual job-level subproblems which can be solved by dynamic programming. The Lagrangian dual problem is solved by the subgradient method. In this paper, a Lagrangian relaxation with cut generation is proposed to improve the Lagrangian bounds for the conventional LR. The lower bound is strengthened by imposing additional constraints for the relaxed problem. The state space reductions for dynamic programming for subproblems are also incorporated. Computational results demonstrate that the proposed method outperforms the conventional LR method without significantly increasing the total computing time.