Byeong Seok Ahn

The integrated methodology of rough set theory and artificial neural network for business failure prediction

Abstract This paper proposes a hybrid intelligent system that predicts the failure of firms based on the past financial performance data, combining rough set approach and neural network. We can get reduced information table, which implies that the number of evaluation criteria such as financial ratios and qualitative variables is reduced with no information loss through rough set approach. And then, this reduced information is used to develop classification rules and train neural network to infer appropriate parameters. The rules developed by rough set analysis show the best prediction accuracy if a case does match any of the rules. The rationale of our hybrid system is using rules developed by rough sets for an object that matches any of the rules and neural network for one that does not match any of them. The effectiveness of our methodology was verified by experiments comparing traditional discriminant analysis and neural network approach with our hybrid approach. For the experiment, the financial data of 2400 Korean firms during the period 1994–1997 were selected, and for the validation, k-fold validation was used.

Comparing methods for multiattribute decision making with ordinal weights

This paper is concerned with procedures for ranking discrete alternatives when their values are evaluated precisely on multiple attributes and the attribute weights are known only to obey ordinal relations. There are a variety of situations where it is reasonable to use ranked weights, and there have been various techniques developed to deal with ranked weights and arrive at a choice or rank alternatives under consideration. The most common approach is to determine a set of approximate weights (e.g., rank-order centroid weights) from the ranked weights. This paper presents a different approach that does not develop approximate weights, but rather uses information about the intensity of dominance that is demonstrated by each alternative. Under this approach, several different, intuitively plausible, procedures are presented, so it may be interesting to investigate their performance. These new procedures are then compared against existing procedures using a simulation study. The simulation result shows that the approximate weighting approach yields more accurate results in terms of identifying the best alternatives and the overall rank of alternatives. Although the quality of the new procedures appears to be less accurate when using ranked weights, they provide a complete capability of dealing with arbitrary linear inequalities that signify possible imprecise information on weights, including mixtures of ordinal and bounded weights.

On the properties of OWA operator weights functions with constant level of orness

The result of aggregation performed by the ordered weighted averaging (OWA) operator heavily depends upon the weighting vector used. A number of methods have been presented for obtaining the associated weights. In this paper, we present analytic forms of OWA operator weighting functions, each of which has properties of rank-based weights and a constant level of orness, irrespective of the number of objectives considered. These analytic forms provide significant advantages for generating the OWA weights over previously reported methods. First, the OWA weights can be efficiently generated by using proposed weighting functions without solving a complicated mathematical program. Moreover, convex combinations of these specific OWA operators can be used to generate the OWA operators with any predefined values of orness once specific values of orness are a priori stated by the decision maker. Those weights have a property of constant level of orness as well. Finally, the OWA weights generated at a predefined value of orness make almost no numerical difference with maximum entropy OWA weights in terms of dispersion

Least-Squared Ordered Weighted Averaging Operator Weights

The ordered weighted averaging (OWA) operator by Yager (IEEE Trans Syst Man Cybern 1988; 18; 183–190) has received much more attention since its appearance. One key point in the OWA operator is to determine its associated weights. Among numerous methods that have appeared in the literature, we notice the maximum entropy OWA (MEOWA) weights that are determined by taking into account two appealing measures characterizing the OWA weights. Instead of maximizing the entropy in the formulation for determining the MEOWA weights, a new method in the paper tries to obtain the OWA weights that are evenly spread out around equal weights as much as possible while strictly satisfying the orness value provided in the program. This consideration leads to the least‐squared OWA (LSOWA) weighting method in which the program is to obtain the weights that minimize the sum of deviations from the equal weights since entropy is maximized when all the weights are equal. Above all, the LSOWA method allocates the positive and negative portions to the equal weights that are identical but opposite in sign from the middle point in the number of criteria. Furthermore, interval LSOWA weights can be constructed when a decision maker specifies his or her orness value in uncertain numerical bounds and we present a method, with those uncertain interval LSOWA weights, for prioritizing alternatives that are evaluated by multiple criteria.

Preference relation approach for obtaining OWA operators weights

Actual result of aggregation performed by an ordered weighted averaging (OWA) operator heavily depends upon the weighting vector used. A number of approaches for obtaining the associated weights have been suggested in the academic literature. In this paper, we present a method for determining the OWA weights when (1) the preferences of some subset of alternatives over other subset of alternatives are specified in a holistic manner across all the criteria, and (2) the consequences (criteria values) are specified in one of three different formats: precise numerical values, intervals and fuzzy numbers. The OWA weights are to be estimated in the direction of minimizing deviations from the OWA weights implied by the preference relations, thus as consistent as possible with a priori preference relations.

Some remarks on the LSOWA approach for obtaining OWA operator weights

One of the key issues in the theory of ordered‐weighted averaging (OWA) operators is the determination of their associated weights. To this end, numerous weighting methods have appeared in the literature, with their main difference occurring in the objective function used to determine the weights. A minimax disparity approach for obtaining OWA operator weights is one particular case, which involves the formulation and solution of a linear programming model subject to a given value of orness and the adjacent weight constraints. It is clearly easier for obtaining the OWA operator weights than from previously reported OWA weighting methods. However, this approach still requires solving linear programs by a conventional linear program package. Here, we revisit the least‐squared OWA method, which intends to produce spread‐out weights as much as possible while strictly satisfying a predefined value of orness, and we show that it is an equivalent of the minimax disparity approach. The proposed solution takes a closed form and thus can be easily used for simple calculations.

Parameterized OWA operator weights: An extreme point approach

Since Yager first presented the ordered weighted averaging (OWA) operator to aggregate multiple input arguments, it has received much attention from the fields of decision science and computer science. A critical issue when selecting an OWA operator is the determination of the associated weights. For this reason, numerous weight generating methods, including rogramming-based approaches, have appeared in the literature. In this paper, we develop a general method for obtaining OWA operator weights via an extreme point approach. The extreme points are represented by the intersection of an attitudinal character constraint and a fundamental ordered weight simplex. The extreme points are completely identified using the proposed formula, and the OWA operator weights can then be expressed by a convex combination of the identified extreme points. With those identified extreme points, some new OWA operator weights can be generated by a centroid or a user-directed method, which reflects the decision-makers incomplete preferences. This line of reasoning is further extended to encompass situations in which the attitudinal character is specified in the form of interval with an aim to relieve the burden of specifying the precise attitudinal character, thus obtaining less-specific expressions that render human judgments readily available. All extreme points corresponding to the uncertain attitudinal character are also obtained by a proposed formula and then used to prioritize the multitude of alternatives. Meanwhile, two dominance rules are effectively used for prioritization of alternatives.

Compatible weighting method with rank order centroid: Maximum entropy ordered weighted averaging approach

In a situation where imprecise attribute weights such as a rank order are captured, various approximate weighting methods have been proposed to aid multiattribute decision analysis. Among others, it is well known that the rank order centroid (ROC) weights result in the highest performance in terms of the identification of the best alternative under the ranked attribute weights. In this paper, we aim to reinterpret the meaning of the ROC weights and to develop a compatible weighting method that is based on other well-established academic disciplines. The ordered weighted averaging (OWA) method is a nonlinear aggregation method in that the weights are associated with the objects reordered according to their magnitudes in the aggregation process. Some interesting semantics can be attached to the approximate weights in view of the measure developed in the OWA method. Furthermore, the weights generated by the maximum entropy method show equally compatible performance with the ROC weights under some condition, which is demonstrated by theoretical and simulation analysis.

Multi-attribute decision aid under incomplete information and hierarchical structure

Abstract This paper presents methods for dealing with incomplete information about both attribute weights and values under a hierarchically structured value tree. Incomplete information in this paper covers arbitrary linear inequalities and is hence to treat a more general situation than a previous restrictive definition of incomplete information that typically includes interval judgment. This may give decision makers chances that is enhanced freedom of choice and comforts of specification. We propose two techniques for prioritizing alternatives by (strict) dominance relationship. One is the extension of a previous method for operating flat-structured value trees to hierarchical ones. The other approach propagates pairwise dominance values from leaf nodes to topmost node consecutively which is also an extension of a previous method. Because the strict dominance rule fails to fully prioritize alternatives, as is usual the case under incomplete information, we suggest a new method, a measure of preference strength, which can provide decision makers with a single optimal alternative or full rank of alternatives without any further interaction with decision makers.

The uncertain OWA aggregation with weighting functions having a constant level of orness

Since the ordered weighted averaging (OWA) operator was introduced by Yager [IEEE Trans Syst Man Cybern 1988;18:183–190], numerous aggregation operators have been presented in academic journals. Apart from a setting where exact numerical assessments on weights and input arguments can be obtained, the issue of generalizing the OWA to take into account uncertainties in weights and/or input arguments has been considered. Recently, Xu and Da [Int J Intell Syst 2002;17:569–575] proposed an uncertain OWA operator in which input arguments are given in the form of interval numbers. The interval numbers within the interval sometimes do not have the same meaning for the decision maker as is implied by the use of interval ranges. Thus, we present a way of prioritizing interval numbers, taking into account the strength of preference based on the probabilistic measure. Further, rank‐based weighting functions having constant values of orness irrespective of the number of objectives aggregated are presented and a final rank ordering of courses of action is performed by the use of those weighing functions.