Xuyang Er in Ace

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The paper was presented at the ACE Software Group Meeting on 11/12/99, Manchester, UK. Thecopyright is reserved by the authors. 1

Intelligent Decision System via

Evidential Reasoning

Dr Dong-Ling XU

RELI LTD, Armstrong HouseBrancaster Road

Manchester M1 7EDEmail: [email protected]

Dr Jian-Bo Yang

Manchester School of ManagementUMIST PO Box 88,

Manchester M60 1QDEmail: [email protected]

I. Introduction

Intelligent Decision System (IDS) is a software package designed to assist multi-

attribute decision analysis (MADA) or multi-criteria decision-making (MCDM). Thispaper will demonstrate how to use IDS to solve MADA problems using severalexamples: assessment and selection of cars, houses and contract bidders, andorganisation self-assessment.

The main features of the MADA problems are illustrated by the car selection example inthe following section. The currently available tools for solving the MADA problems cannot cope with all these features. For example, they can only handle simple deterministicnumbers; 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 theshortcomings of the available tools. The applications of IDS have shown that it not onlyhas achieved its original goal, but also is capable of dealing with large-scale MADAproblems with thousands of attributes easily on a PC. The other packages do not havesuch a capacity.

II. Features of Large Scale MADA: Car Selection ExampleLet’s use an example to demonstrate the features of a MADA problem. Suppose youwant to buy a car. After some initial research, you get a short list of 6 cars: Acura 3.2TL Premium, BMW 3251, Infinity I30t, Lexus ES300, Mazda Mellenia and Mercedes

Benz. You have got the following information for these cars (Table 1) from variousresources. The problem is how you make your proper choice based on the informationin hand?

From Table 1, for the car selection problem, we can see the following features. They arealso 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 uncertainty5. Precise data and uncertain (random) numbers



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III. IDS: The Solution to the Car Selection Problem

The currently available packages for solving MADA problems can only cope withdeterministic numbers, like AHP and Multi-Attribute Utility function approach ([Saaty

1988] [Hwang and Yoon 1981]). IDS utilises the latest research results, the EvidentialReasoning (ER) approach [Yang etc 1994], [Yang 2000]. It is flexible and versatile. Itcan deal with various types of information, such as deterministic numbers, randomnumbers and subjective judgements of various formats. It has an incomparable capacityin dealing with large scale MADA problems with thousands of attributes.

For the car selection example above, the final result generated using the IDS package issummarised 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, theassessment results are interpreted as in Table 3.

The results can also be graphically displayed in different combinations so that thecomparison 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 theassessment results for three of the assessed cars. It displays the overall ranking of the 3cars as well as their rankings on each of the three selected attributes: Price, Performanceand Chassis. You can add or delete cars and attributes to draw different graphs as youwish.

To rank the candidates, the distributed assessments are converted to utilities. The carwith the highest utility value is the best (Figure 9). Infinity I30t is ranked as numberone, 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 selectionproblem using IDS and are shown in Figure 2, Figure 3, Figure 4 and Figure 5.



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Table 1 Original Car Evaluation Data

Acura 3.2

TLPremium

BMW

3251

Infinity

I30t

Lexus

ES300

Mazda

Mellenia

Mercedes

Benz

Price ($) 36020 36420 34200 36453 33760 39332

Cargocapacity

14.1 10.3 14.1 14.3 13.3 13.7

Fuel cap. 17.2 17.2 18.5 18.5 18.0 16.4

Weight/ power

17.6 16.7 16.9 18.0 16.2 17.0

D i m e n s i o n s

Dimension 12.23 10.47 12.06 11.61 11.90 11.04

Acceleration 8.8 8.0 7.7 8.4 8.0 7.9

Braking 128 124 127 134 135 126

Handling B A B B- B+ A

Horsepower 196 152 182 183 138 171

Ride quality A- B- B B+ B+ A-

Powertrain B B+ A B A- A

SpeedthroughSlalom

63.3 61.4 62.0 63.1 65.8 63.2

P e r f o r m a n c e

Fueleconomy 20 20 21 20 19 20

Steering B Nodata

Nodata

C+ B A-

Safetyfeatures

A A A Nodata

A A+ C h a s s i s

Turning 34.8 34.1 34.8 36.7 37.4 35.2

Styling B- Nodata

Nodata

B A- B+

Trunk utility A- B- A B B B+

Ergonomics No data B- B+ B+ B+ B+

Noiseisolation

B+ C+ B+ B+ No data A- G e

n e r a l

Interiorcomfort

A B- A- B+ No data No data



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Cargo capacity (0.3)

Fuel capacity (0.2)

Weight / Power (0.4)Dimension (0.1)

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)

Styling (0.3)

Trunk utility (0.1)Ergonomics (0.1)Noise isolation (0.25)

Interior comfort (0.25)

General dimension

(0.1)

Price (0.15)

Chassis (0.15)

Performance (0.5)

General (0.1)

Car ranking

Level 1 Level 2 Level 3

Figure1. A Hierarchy of Performance Attributes for Car Evaluation

Table 2 Final Evaluations and Ranking of the Cars

Overallassessment

Acura 3.2TL remium BMW 3251 Infinity I30t Lexus ES300

MazdaMellenia S

MercedesBenz C280

Distributed

assessment

{(P, 0.0252)*,

( A, 0.1761),

(G, 0.5883),

( E , 0.1328),

(T , 0.0676)}

{(W, 0.0287),

(P, 0.0866),

( A, 0.2174),

(G, 0.3483),

( E , 0.1408),

(T , 0.1106)}

{(P, 0.0455),

( A, 0.0703),

(G, 0.2109),

( E , 0.5471),

(T , 0.0587)}

{(P, 0.1089),

( A, 0.227),

(G, 0.5149),

( E , 0.054),

(T , 0.0051)}

{(W, 0.0275),

(P, 0.1193),

( A, 0.125),

(G, 0.3323),

( E , 0.3029),

(T , 0.043)}

{(W, 0.035),

(P, 0.0773),

( A, 0.1062),

(G, 0.3501),

( E , 0.2828),

(T , 0.1236)}

Maximumutility

0.6484 0.6285 0.7655 0.5883 0.6403 0.6745

Minimumutility

0.6384 0.561 0.698 0.4983 0.5903 0.6495

Averageutility

0.6434 0.5948 0.7318 0.5433 0.6153 0.662

Ranking 3 5 (4, 6) 1 6 (5) 4 (5) 2

*W: Worst, P: Poor; A: Average, G: Good, E: Excellent, T: Top



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Table 3 Car Assessment Results for BMW 3251

Results Interpretation

(W, 0.0287) Worst, degree of belief is 0.0287

(P, 0.0866) Poor, degree of belief is 0. 0866

( A

, 0.2174) Average, degree of belief is 0. 2174(G, 0.3483) Good, degree of belief is 0. 3483

( E , 0.1408) Excellent, degree of belief is 0. 1408

(T , 0.1106) Top, degree of belief is 0. 1106

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 usedfor 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 averageutility value of the attribute (in case of an qualitative one). Double click on any of thethree 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.



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Figure 3 Attribute Definition Dialogue

Figure 3 is an example of the dialogue window for defining an attribute. It is activatedby 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 thebest 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 isdetermined by the decision makers or the assessors according to their preferences.



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Figure 5 Quantitative Attribute Value Input Dialogue

To input a value for an attribute, double click on the lower right space of the blueboxes. If the attribute is quantitative, a dialogue window similar to Figure 5 will popup. If the attribute is qualitative, the dialogue window will be similar to Figure 6.

Figure 6 Qualitative Attribute Value Input Dialogue



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Figure 7 Graphics Display of Assessment Results

for 3 of the Assessed Cars

Figure 8 Graphical Comparison of Distributed Assessment Results



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Figure 9 Graphics Display of Car Ranking

IV. More Examples

To illustrate the potential application areas of IDS, a few more real life examples arepresented below. They are house selection, bidder selection and organisation self-assessment. These are very simple examples and only used to illustrate what IDS cando and how IDS is used.

4.1. House SelectionThe 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). Fourcandidates are assessed. The ranking is shown in Figure 10, at the lower left corner of each candidate’s box (yellow box).



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Figure 10 Overview Window of the House Selection Problem

Figure 11 Values of Attractiveness Attribute in House Selection Problem



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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):



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• 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 secondlevel attributes. The final ranking is again displayed at the lower left corner of theyellow boxes with its utility function value on its right side (Figure 13).

4.3. 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 examplebelow 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 termsof 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 otherexamples. This tree view style of overview window is especially suitable for MADAproblem with a large number of attributes or alternatives, or attributes and alternativeswith 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 MADAproblems. It is flexible, user friendly and practical. Its application areas could beendless, for example, supplier assessment for superstores and large companies,investment strategy assessment for investment institutes, engineering safety analysis andenvironment risk assessment. It has already generated a lot of interests among some of the blue chip companies in the UK.



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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, 1981.

[2] Saaty, T. L. The Analytic Hierarchy Process. University of Pittsburgh, 1988.

[3] Yang, J. B. and Singh, M. G., “An evidential reasoning approach for multiple attributedecision making with uncertainty”, IEEE Transactions on Systems, Man, and Cybernetics24/1 (1994) 1-18.

[4] Yang, J. B. and Sen, P., “A general multi-level evaluation process for hybrid MADM withuncertainty”, IEEE Transactions on Systems, Man, and Cybernetics 24/10 (1994) 1458-1473.

[5] Yang, J B, “Rule and utility based evidential reasoning approach for multiattributedecision analysis under uncertainties”, European Journal of Operational Research,2000, pp.1-31 (in press and long proof checked, EJOR Paper #98287).

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