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Decision-making is a process of choosing among alternative courses of action for solving complicated problems where multi-criteria objectives are involved. The past few years have witnessed a growing recognition of soft computing (SC) (Zadeh, 1998) technologies that underlie the conception, design, and utilization of intelligent systems. In this chapter, we present different SC paradigms involving an artificial neural network (Zurada, 1992) trained by using the scaled conjugate gradient algorithm (Moller, 1993), two different fuzzy inference methods (Abraham, 2001) optimised by using neural network learning/evolutionary algorithms (Fogel, 1999), and regression trees (Breiman, Friedman, Olshen, & Stone, 1984) for developing intelligent decision support systems (Tran, Abraham, & Jain, 2004). We demonstrate the efficiency of the different algorithms by developing a decision support system for a tactical air combat environment (TACE) (Tran & Zahid, 2000). Some empirical comparisons between the different algorithms are also provided. 2 Tran, Abraham & Jain Copyright © 2006, Idea Group Inc. Copying or distributing in print or electronic forms without written permission of Idea Group Inc. is prohibited. INTRODUCTION Several decision support systems have been developed in various fields including medical diagnosis (Adibi, Ghoreishi, Fahimi, & Maleki, 1993), business management, control system (Takagi & Sugeno, 1983), command and control of defence and air traffic control (Chappel, 1992), and so on. Usually previous experience or expert knowledge is often used to design decision support systems. The task becomes interesting when no prior knowledge is available. The need for an intelligent mechanism for decision support comes from the well-known limits of human knowledge processing. It has been noticed that the need for support for human decision-makers is due to four kinds of limits: cognitive, economic, time, and competitive demands (Holsapple & Whinston, 1996). Several artificial intelligence techniques have been explored to construct adaptive decision support systems. A framework that could capture imprecision, uncertainty, learn from the data/information, and continuously optimise the solution by providing interpretable decision rules, would be the ideal technique. Several adaptive learning frameworks for constructing intelligent decision support systems have been proposed (Cattral, Oppacher, & Deogo, 1999; Hung, 1993; Jagielska, 1998; Tran, Jain, & Abraham, 2002b). Figure 1 summarizes the basic functional aspects of a decision support system. A database is created from the available data and human knowledge. The learning process then builds up the decision rules. The developed rules are further fine-tuned, depending upon the quality of the solution, using a supervised learning process. To develop an intelligent decision support system, we need a holistic view on the various tasks to be carried out including data management and knowledge management (reasoning techniques). The focus of this chapter is knowledge management (Tran & Zahid, 2000), which consists of facts and inference rules used for reasoning (Abraham, 2000). Fuzzy logic (Zadeh, 1973), when applied to decision support systems, provides formal methodology to capture valid patterns of reasoning about uncertainty. Artificial neural networks (ANNs) are popularly known as black-box function approximators. Recent research work shows the capabilities of rule extraction from a trained network positions neuro-computing as a good decision support tool (Setiono, 2000; Setiono, Leow, & Zurada, 2002). Recently evolutionary computation (EC) (Fogel, 1999) has been successful as a powerful global optimisation tool due to the success in several problem domains (Abraham, 2002; Cortes, Larrañeta, Onieva, García, & Caraballo, 2001; Ponnuswamy, Amin, Jha, & Castañon, 1997; Tan & Li, 2001; Tan, Yu, Heng, & Lee, 2003). EC works by simulating evolution on a computer by iterative generation and alteration processes, operating on a set of candidate solutions that form a population. Due to the complementarity of neural networks, fuzzy inference systems, and evolutionary computation, the recent trend is to fuse various systems to form a more powerful integrated system, to overcome their individual weakness. Decision trees (Breiman et al., 1984) have emerged as a powerful machine-learning technique due to a simple, apparent, and fast reasoning process. Decision trees can be related to artificial neural networks by mapping them into a class of ANNs or entropy nets with far fewer connections. In the next section, we present the complexity of the tactical air combat decision support system (TACDSS) (Tran, Abraham, & Jain, 2002c), followed by some theoretical foundation on neural networks, fuzzy inference systems, and decision trees in the Soft Computing Paradigms and Regression Trees 3 Copyright © 2006, Idea Group Inc. Copying or distributing in print or electronic forms without written permission of Idea Group Inc. is prohibited. following section. We then present different adaptation procedures for optimising fuzzy inference systems. A Takagi-Sugeno (Takagi & Sugeno, 1983; Sugeno, 1985) and Mamdani-Assilian (Mamdani & Assilian, 1975) fuzzy inference system learned by using neural network learning techniques and evolutionary computation is discussed. Experimental results using the different connectionist paradigms follow. Detailed discussions of these results are presented in the last section, and conclusions are drawn. TACTICAL AIR COMBAT DECISION SUPPORT SYSTEM Implementation of a reliable decision support system involves two important factors: collection and analysis of prior information, and the evaluation of the solution. The data could be an image or a pattern, real number, binary code, or natural language text data, depending on the objects of the problem environment. An object of the decision problem is also known as the decision factor. These objects can be expressed mathematically in the decision problem domain as a universal set, where the decision factor is a set and the decision data is an element of this set. The decision factor is a sub-set of the decision problem. If we call the decision problem (DP) as X and the decision factor (DF) as “A”, then the decision data (DD) could be labelled as “a”. Suppose the set A has members a 1 , a 2 , ... , a n then it can be denoted by A = {a 1 ,a 2 ,..,a n } or can be written as: A = {a i | i∈R n } (1) where i is called the set index, the symbol “|” is read as “such that” and R n is the set of n real numbers. A sub-set “A” of X, denoted A⊆ X, is a set of elements that is contained within the universal set X. For optimal decision-making, the system should be able to Figure 1. Database learning framework for decision support system

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@inproceedings{Fulcher2005PrintedA, title={Printed at:}, author={John Fulcher and Michelle Potter and Kristin M. Roth and Jennifer Neidig and Susanna Svidunovich and Sharon S. Berger and David Zhang and Xiaoyuan Jing and Jian Yang and Chung-Ching Tai and M. Palaniswami and Goran Trajkovski and Cong Chi Tran and Ajith Abraham}, year={2005} }