Henry L. W. Nuttle

Fuzzy data envelopment analysis (DEA): a possibility approach

Abstract Evaluating the performance of activities or organizations by traditional data envelopment analysis (DEA) models requires crisp input/output data. However, in real-world problems inputs and outputs are often imprecise. This paper develops DEA models using imprecise data represented by fuzzy sets (i.e., “fuzzy DEA” models). It is shown that fuzzy DEA models take the form of fuzzy linear programming which typically are solved with the aid of some methods to rank fuzzy sets. As an alternative, a possibility approach is introduced in which constraints are treated as fuzzy events. The approach transforms fuzzy DEA models into possibility DEA models by using possibility measures of fuzzy events (fuzzy constraints). We show that for the special case, in which fuzzy membership functions of fuzzy data are of trapezoidal types, possibility DEA models become linear programming models. A numerical experiment is used to illustrate the approach and compare the results with those obtained with alternative approaches.

Hoist Scheduling For A PCB Electroplating Facility

Abstract This paper describes a model and associated algorithm for generating maximum throughput cyclic schedules for the movements of a hoist in a PCB electroplating facility. The algorithm is enumerative in nature and involves the solution of linear programming subproblems. Computational experience with schedules for real systems is presented.

Fuzzy BCC Model for Data Envelopment Analysis

Fuzzy Data Envelopment Analysis (FDEA) is a tool for comparing the performance of a set of activities or organizations under uncertainty environment. Imprecise data in FDEA models is represented by fuzzy sets and FDEA models take the form of fuzzy linear programming models. Previous research focused on solving the FDEA model of the CCR (named after Charnes, Cooper, and Rhodes) type (FCCR). In this paper, the FDEA model of the BCC (named after Banker, Charnes, and Cooper) type (FBCC) is studied. Possibility and Credibility approaches are provided and compared with an α-level based approach for solving the FDEA models. Using the possibility approach, the relationship between the primal and dual models of FBCC models is revealed and fuzzy efficiency can be constructed. Using the credibility approach, an efficiency value for each DMU (Decision Making Unit) is obtained as a representative of its possible range. A numerical example is given to illustrate the proposed approaches and results are compared with those obtained with the α-level based approach.

Relaxed conditions for radial-basis function networks to be universal approximators

In this paper, we investigate the universal approximation property of Radial Basis Function (RBF) networks. We show that RBFs are not required to be integrable for the REF networks to be universal approximators. Instead, RBF networks can uniformly approximate any continuous function on a compact set provided that the radial basis activation function is continuous almost everywhere, locally essentially bounded, and not a polynomial. The approximation in L(p)(micro)(1 < or = p < infinity) space is also discussed. Some experimental results are reported to illustrate our findings.

An efficient and flexible mechanism for constructing membership functions

Abstract This paper introduces a Bezier curve-based mechanism for constructing membership functions of convex normal fuzzy sets. The mechanism can fit any given data set with a minimum level of discrepancy. In the absence of data, the mechanism can be intuitively manipulated by the user to construct membership functions with the desired shape. Some numerical experiments are included to compare the performance of the proposed mechanism with conventional methods.

A neural network model with bounded-weights for pattern classification

A new neural network model is proposed based on the concepts of multi-layer perceptrons, radial basis functions, and support vector machines (SVM). This neural network model is trained using the least squared error as the optimization criterion, with the magnitudes of the weights on the links being limited to a certain range. Like the SVM model, the weight specification problem is formulated as a convex quadratic programming problem. However, unlike the SVM model, it does not require that kernel functions satisfy Mercers condition, and it can be readily extended to multi-class classification. Some experimental results are reported.

A Stochastic Model of the Apparel-retailing Process for Seasonal Apparel

A computer model is described that simulates the seasonal apparel-retailing process. The model is stochastic in nature and is designed to allow the investigation of the effects of improved retailing procedures on financial and other performance measures. Its principal value lies in the evaluation or Quick Response (QR) supply methodologies that allow frequent re-estimations of consumer demand and reorders of merchandise based on in-season point-of-sale (POS) data at the stock-keeping-unit (SKU) level.

Soft computing for multicustomer due-date bargaining

The due-date bargainer is a useful tool to support negotiation on due dates between a manufacturer and its customers. To improve the computational performance of an earlier version of the due-date bargainer, we present a new soft computing approach. It uses a genetic algorithm to find the best priority sequence of customer orders for resource allocation, and fuzzy logic operations to allocate the resources and determine the order completion times, following the priority sequence of orders. To extend the due-date bargainer to accommodate bargaining with several customers at the same time, we propose a method to distribute the total penalty using marginal penalties for the individual bargainers. A demonstration software package implementing the improved due-date bargainer has been developed. It is targeted at apparel manufacturing enterprises. Experiments using realistic resource data and randomly generated orders have achieved satisfactory results.

Solution Sets of Interval-Valued Fuzzy Relational Equations

This paper introduces the concepts of tolerable solution set, united solution set, and controllable solution set of interval-valued fuzzy relational equations. Given a continuous t-norm, it is proved that each of the three types of the solution sets of interval-valued fuzzy relational equations with a max-t-norm composition, if nonempty, is composed of one maximum solution and a finite number of minimal solutions. Necessary and sufficient conditions for the existence of solutions are given. Computational procedures based on the constructive proofs are proposed to generate the complete solution sets. Examples are given to illustrate the procedures.

An Apparel-supply System for QR Retailing

A novel apparel-supply system is described that is compatible with Quick Response retailing of apparel with a finite shelf life. The system is driven by a retail point-of-sale procedure, which regularly re-estimates customer demand and generates frequent reorders on the manufacturer and fabric supplier. The system is shown to come close to perfect supply over a range of operating conditions and thus allow greatly improved retail performance when compared with traditional retailing procedures.