Intelligent Decision System via Evidential Reasoning

Transcription

1 Intelligent Decision System via Evidential Reasoning Dr Dong-Ling XU RELI LTD, Armstrong House Brancaster Road Manchester M1 7ED Dr Jian-Bo Yang Manchester School of Management UMIST PO Box 88, Manchester M60 1QD I. Introduction Intelligent Decision System (IDS) is a software package designed to assist multiattribute decision analysis (MADA) or multi-criteria decision-making (MCDM). This paper will demonstrate how to use IDS to solve MADA problems using several examples: assessment and selection of cars, houses and contract bidders, and organisation self-assessment. The main features of the MADA problems are illustrated by the car selection example in the following section. The currently available tools for solving the MADA problems can not cope with all these features. For example, they can only handle simple deterministic numbers; not the information presented in the format of random numbers, subjective judgement or even incomplete data elements. IDS has been under constant development for several years in order to overcome the shortcomings of the available tools. The applications of IDS have shown that it not only has achieved its original goal, but also is capable of dealing with large-scale MADA problems with thousands of attributes easily on a PC. The other packages do not have such a capacity. II. Features of Large Scale MADA: Car Selection Example Let s use an example to demonstrate the features of a MADA problem. Suppose you want to buy a car. After some initial research, you get a short list of 6 cars: Acura 3.2 TL Premium, BMW 3251, Infinity I30t, Lexus ES300, Mazda Mellenia and Mercedes Benz. You have got the following information for these cars (Table 1) from various resources. The problem is how you make your proper choice based on the information in hand? From Table 1, for the car selection problem, we can see the following features. They are also the main features of other MADA problems. 1. A hierarchy of performance attributes (Figure 1) 2. Both quantitative and qualitative information 3. Possible absence of data 4. Subjective judgements with uncertainty 5. Precise data and uncertain (random) numbers The paper was presented at the ACE Software Group Meeting on 11/12/99, Manchester, UK. The copyright is reserved by the authors. 1

2 III. IDS: The Solution to the Car Selection Problem The currently available packages for solving MADA problems can only cope with deterministic numbers, like AHP and Multi-Attribute Utility function approach ([Saaty 1988] [Hwang and Yoon 1981]). IDS utilises the latest research results, the Evidential Reasoning (ER) approach [Yang etc 1994], [Yang 2000]. It is flexible and versatile. It can deal with various types of information, such as deterministic numbers, random numbers and subjective judgements of various formats. It has an incomparable capacity in dealing with large scale MADA problems with thousands of attributes. For the car selection example above, the final result generated using the IDS package is summarised in Table 2. The final results are expressed in distributed assessments with degrees of belief over all grades (Table 2). For example, for BMW 3251, the assessment results are interpreted as in Table 3. The results can also be graphically displayed in different combinations so that the comparison between candidates is made easy. For example, Figure 8 displays the distributed assessments of car 4 and car 5. Car 4 is assessed to be good and average to a large degree whilst car 5 has more excellent features. Figure 7 displays the assessment results for three of the assessed cars. It displays the overall ranking of the 3 cars as well as their rankings on each of the three selected attributes: Price, Performance and Chassis. You can add or delete cars and attributes to draw different graphs as you wish. To rank the candidates, the distributed assessments are converted to utilities. The car with the highest utility value is the best (Figure 9). Infinity I30t is ranked as number one, based on the weights given by the car purchaser (Table 2 or Figure 9). A few bitmap snap shots are taken during the process of solving the car selection problem using IDS and are shown in Figure 2, Figure 3, Figure 4 and Figure 5. 2

3 Table 1 Original Car Evaluation Data Acura 3.2 TL Premium BMW 3251 Infinity I30t Lexus ES300 Mazda Mellenia Mercedes Benz Price ($) Cargo capacity Fuel cap Weight/ power Dimensions Performance Chassis General Dimension Acceleration Braking Handling B A B B- B+ A Horsepower Ride quality A- B- B B+ B+ A- Powertrain B B+ A B A- A Speed through Slalom Fuel economy Steering B No No C+ B A- data data Safety A A A No A A+ features data Turning Styling B- No No B A- B+ data data Trunk utility A- B- A B B B+ Ergonomics No data B- B+ B+ B+ B+ Noise B+ C+ B+ B+ No data A- isolation Interior A B- A- B+ No data No data comfort 3

4 Level 1 Level 2 Level 3 Price (0.15) General dimension (0.1) Cargo capacity (0.3) Fuel capacity (0.2) Weight / Power (0.4) Dimension (0.1) Car ranking Performance (0.5) Chassis (0.15) Acceleration (0.1) Braking (0.2) Handling (0.15) Horsepower (0.1) Ride quality (0.15) Powertrain (0.2) Speed through Slalom (0.1) Fuel economy (0.15) Steering (0.25) Safety feature (0.6) Turning (0.15) General (0.1) Styling (0.3) Trunk utility (0.1) Ergonomics (0.1) Noise isolation (0.25) Interior comfort (0.25) Figure1. A Hierarchy of Performance Attributes for Car Evaluation Table 2 Final Evaluations and Ranking of the Cars Overall assessment Acura 3.2 TL remium BMW 3251 Infinity I30t Lexus ES300 Distributed assessment Maximum utility Minimum utility Average utility {(P, )*, (A, ), (G, ), (E, ), (T, )} {(W, ), (P, ), (A, ), (G, ), (E, ), (T, )} {(P, ), (A, ), (G, ), (E, ), (T, )} {(P, ), (A, 0.227), (G, ), (E, 0.054), (T, )} Mazda Mellenia S {(W, ), (P, ), (A, 0.125), (G, ), (E, ), (T, 0.043)} Mercedes Benz C280 {(W, 0.035), (P, ), (A, ), (G, ), (E, ), (T, )} Ranking 3 5 (4, 6) 1 6 (5) 4 (5) 2 *W: Worst, P: Poor; A: Average, G: Good, E: Excellent, T: Top 4

5 Table 3 Car Assessment Results for BMW 3251 Results Interpretation (W, ) Worst, degree of belief is (P, ) Poor, degree of belief is (A, ) Average, degree of belief is (G, ) Good, degree of belief is (E, ) Excellent, degree of belief is (T, ) Top, degree of belief is Figure 2. Overview Window of the Car Assessment Problem. In Figure 2, the yellow boxes hold the information for candidates (or alternatives), including the candidate name, the ranking and the utility value. The blue boxes are used for inputting and displaying information for attributes: the attribute name, the weight of the attribute and the value of the attribute (in case of a quantitative attribute) or average utility value of the attribute (in case of an qualitative one). Double click on any of the three parts of the blue box you are interested in, and then a window similar to Figure 3, Figure 4 or Figure 5 will pop up. 5

6 Figure 3 Attribute Definition Dialogue Figure 3 is an example of the dialogue window for defining an attribute. It is activated by double clicking on the attribute name (upper space) of any blue boxes (Figure 2). The attribute defined here is Fuel Economy, which is a quantitative attribute, with the best and worst values of 22 and 17 miles/gallon for all the cars to be assessed. Figure 4 Dialogue Window for assigning weight to an attribute Figure 4 is activated when double clicking on the lower left corner of the blue box. It provides a dialogue window for assigning weight for each attribute. The weight is determined by the decision makers or the assessors according to their preferences. 6

7 Figure 5 Quantitative Attribute Value Input Dialogue To input a value for an attribute, double click on the lower right space of the blue boxes. If the attribute is quantitative, a dialogue window similar to Figure 5 will pop up. If the attribute is qualitative, the dialogue window will be similar to Figure 6. Figure 6 Qualitative Attribute Value Input Dialogue 7

8 Figure 7 Graphics Display of Assessment Results for 3 of the Assessed Cars Figure 8 Graphical Comparison of Distributed Assessment Results 8

9 Figure 9 Graphics Display of Car Ranking IV. More Examples To illustrate the potential application areas of IDS, a few more real life examples are presented below. They are house selection, bidder selection and organisation selfassessment. These are very simple examples and only used to illustrate what IDS can do and how IDS is used House Selection The attributes for assessing houses in the example are (Figure 10) Location Distance to Office Price Size (Number of Bedrooms) Attractiveness (Structure or style) Location and Attractiveness are qualitative attributes (Figure 11 and Figure 12). Four candidates are assessed. The ranking is shown in Figure 10, at the lower left corner of each candidate s box (yellow box). 9

10 Figure 10 Overview Window of the House Selection Problem Figure 11 Values of Attractiveness Attribute in House Selection Problem 10

11 Figure 12 Values of Location Attribute in House Selection Problem Figure 13 Overview Window of the Bidder Selection Problem 4.2. Bidder Selection Bidders are assessed by the following 6 top-level attributes (Figure 13): 11

12 Bid amount Finical soundness Technical ability Management capability Health and safety record Reputation Each of the 6 top level attributes has 4 sub-attributes. Therefore there are 24 second level attributes. The final ranking is again displayed at the lower left corner of the yellow boxes with its utility function value on its right side (Figure 13) Organisation self-assessment Organisation self-assessment uses the EFQM model: European Foundation for Quality Management model. This model has more than 300 assessment attributes. Thousands of organisations in Europe have conducted self-assessment using this model. The example below shows only part of the model, which is part 3, People s Management. Part 3 of EFQM model: People s Management 3a) How people resources are planned and improved. 3a1) How organisation aligns the human resources with policy and strategy. 3a2) How the organisation uses and develops people surveys 3a3) How organisation ensures fairness in terms of employment 3a4) How organisation aligns remuneration, redeployment, redundancy and other terms of employment with policy and strategy. The example data shown in Figure 14 are from two North West utility companies. The overview window of this example uses a different format from that of the other examples. This tree view style of overview window is especially suitable for MADA problem with a large number of attributes or alternatives, or attributes and alternatives with long names, or for people who are used to Microsoft Window Explorer and list windows. V Conclusion The above application examples of IDS demonstrated its capability in handling MADA problems. It is flexible, user friendly and practical. Its application areas could be endless, for example, supplier assessment for superstores and large companies, investment strategy assessment for investment institutes, engineering safety analysis and environment risk assessment. It has already generated a lot of interests among some of the blue chip companies in the UK. 12

13 Figure 14 Overview Window of the Organisation Self-Assessment (EFQM Model) Example References [1] Hwang, C. L. and Yoon, K. Multiple Attribute Decision Making Methods and Applications, A State-of-Art Survey. Springer-Verlag, Berlin, [2] Saaty, T. L. The Analytic Hierarchy Process. University of Pittsburgh, [3] Yang, J. B. and Singh, M. G., An evidential reasoning approach for multiple attribute decision making with uncertainty, IEEE Transactions on Systems, Man, and Cybernetics 24/1 (1994) [4] Yang, J. B. and Sen, P., A general multi-level evaluation process for hybrid MADM with uncertainty, IEEE Transactions on Systems, Man, and Cybernetics 24/10 (1994) [5] Yang, J B, Rule and utility based evidential reasoning approach for multiattribute decision analysis under uncertainties, European Journal of Operational Research, 2000, pp.1-31 (in press and long proof checked, EJOR Paper #98287). 13