APPLYING FUZZY MULTIPLE CRITERIA DECISION MAKING

TO EVALUATE AND IDENTIFY OPTIMAL EXPLOSIVE

DETECTION EQUIPMENTS

Ying Bai

Dept. of Computer Science and Engineering, Johnson C. Smith University, North Carolina, U.S.A.

Dali Wang

Dept. of Physical, Computer Science and Eng., Christopher Newport University, Virginia, U.S.A.

Keywords: Fuzzy multi-criteria decision making, Optimal evaluations, Explosive detection equipments.

Abstract: The purpose of this research is to develop a universal model with a practical system to evaluate, identify and

select an optimal system or device to perform the desired task from a large collection of available systems

that have multiple objectives based on a fuzzy multiple criteria decision making model (FMCDMM). As an

example, here we are using this research to identify and select an optimal detection system or device to

detect hazardous chemical materials.

1 INTRODUCTION

Continuously check and detect high-threat chemical

materials to provide early warning and control are

critical parts in protecting chemical threats to our

territory.

Chemical detection equipment (CDE) is an

essential component of hazardous material

(HAZMAT) emergency response. It can be found

that the main challenge with these detection

technologies is to select and identify the best

equipment from a large of collections of available

detection devices based on a quite few of factors or

criteria. Dena et al (Bravata et al., 2004) reported a

review for over 24,000 citations and identified 55

detection systems and 23 diagnostic decision support

systems. Only 35 systems have been evaluated: 4

reported both sensitivity and specificity, 13 were

compared to a reference standard, and 31 were

evaluated for their timeliness. Most evaluations of

detection systems and some evaluations of

diagnostic systems for bioterrorism responses are

critically deficient. Because false-positive and false-

negative rates are unknown for most systems,

decision making on the basis of these systems is

seriously compromised.

Multiple criteria decision making (MCDM) was

introduced as a promising and important field of

study in the early 1970'es. Since then the number of

contributions to theories and models, which could be

used as a basis for more systematic and rational

decision making with multiple criteria, has

continued to grow at a steady rate. A number of

surveys, cf e.g. Bana e Costa (Bana e Costa and

Vincke, 1990), show the vitality of the field and the

multitude of methods which have been developed.

When Bellman and Zadeh, and a few years later

Zimmermann, introduced fuzzy sets into the field,

they cleared the way for a new family of methods to

deal with problems which had been inaccessible to

and unsolvable with standard MCDM techniques.

There are many variations on the theme MCDM

depending upon the theoretical basis used for the

modeling. Zeleny (Zeleny, 1982) shows that

multiple criteria include both multiple attributes and

multiple objectives, and there are two major

theoretical approaches built around multiple attribute

utility theory (MAUT) and multiple objective linear

programming (MOLP), which have served as basis

for a number of theoretical variations. Bana e Costa

and Vincke (Bana e Costa, 1990) argue that with

MCDM the first contributions to a truly scientific

approach to decision making were made, but find

fault with the objectives to carry this all the way as

118

Bai Y. and Wang D..

APPLYING FUZZY MULTIPLE CRITERIA DECISION MAKING TO EVALUATE AND IDENTIFY OPTIMAL EXPLOSIVE DETECTION EQUIPMENTS.

DOI: 10.5220/0003396701180124

In Proceedings of the 13th International Conference on Enterprise Information Systems (ICEIS-2011), pages 118-124

ISBN: 978-989-8425-54-6

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

we have to deal with human decision makers who

can never reach the degree of consistency needed.

When fuzzy set theory was introduced into

MCDM research the methods were basically

developed along the same lines. There are a number

of very good surveys of fuzzy MCDM (cf Chen and

Hwang, 1993); (Fodor and Roubens, 1994);

(Sakawa, 1993) and Ribeiro's contribution in this

issue), which is why we will not go into details here

but just point to some essential contributions. One of

the good surveys is done by Chen and Hwang (Chen

and Hwang, 1993): they make distinctions between

fuzzy ranking methods and fuzzy multiple attribute

decision making methods, which contain all the

families (i) - (iv) listed above.

Cheng and Mon (Cheng and Mon, 1994) propose

a new algorithm for evaluating weapon systems by

the Analytical Hierarchy Process (AHP) based on

fuzzy scales. The systematic procedures used by

Saaty's AHP method (Saaty, 1980) results in a

cardinal order, which can be used to select or rank

alternatives. Cheng and Mon derive a simple and

general algorithm for fuzzy AHP by using triangular

fuzzy numbers, α-cuts and interval arithmetic.

Triangular fuzzy numbers ~1 to ~9 are used to build

a judgment matrix through pair-wise comparison

techniques. They estimate the fuzzy eigenvectors of

the judgment matrix by using an "index of

optimism", indicating the degree of satisfaction of

the decision maker. The proposed technique is

illustrated with the selection of an anti-aircraft

artillery system from several alternatives.

In this study, we will design and implement a

FMCDM algorithm with a real system to improve

the evaluation and selection process of the optimal

detection devices for the CAs to enable users to

identify and select the optimal CAs devices from a

large of collections of candidates in more accurate

and convenient ways.

An introduction to this study and a technique

review of MCDM are given in section 1. The

detailed description of the FMCDM model is

described in section 2. The proposed FMCDM

algorithm used to estimate the weight to the

associated criteria or objectives is provided in

section 3. A case study with an example of

evaluating and assessing the optimal CDE is given

in section 4. Section 5 provides the conclusion.

2 FUZZY MCDM MODEL

Normally, a triangular fuzzy number A can be

defined by a triplet (a, b, c) shown in Fig.1a. An

example of a fuzzy member of an equipment cost is

shown in Fig.1b. The membership function is

defined as Eq. (1).

The general multi-attribute decision making

(MADM) model can be described as (Zhu et al.,

2008):

(a) Let X = {X

|i = 1, . . .,m} denote a finite

discrete set of m (≥2) possible alternatives;

(b) Let A = {A

| j = 1, . . ., n} denote a finite set of

n (≥2) criteria according to which the

desirability of an alternative is to be judged,

, ω

, . . . , ω

)

be the vector of

weights, where

∑

, ω

≥ 0, j = 1, . . ., n,

and ω

denotes the weight of criterion A

(d) Let R = (r

i j

)

m×n

denote the m × n decision

matrix, where r

i j

(≥0) is the performance rating

of alternative X

with respect to criterion A

⎪

⎩

⎪

⎨

⎧

≤≤

−

≤≤

−

.,0

,,0

)(

cxb

bxa

(1)

(a) (b)

Figure 1: A representation of a triangular fuzzy member.

Step 1. Representation of Fuzzy Requirement

When evaluating and assessing the optimal CDE

from a number of similar alternatives, a decision

maker normally develops in his/her mind some sort

of ambiguity. Representation of fuzzy requirements

has been introduced in the beginning of this section.

Step 2. Similarity Measure

In step 1, the requirements of selecting optimal CDE

have been described as the triangular fuzzy number

with respect to different criteria. In this step, we will

take the requirement vector as the ideal CDE, with

the purpose to measure the similarity degree with the

existing candidate CDE vectors, in which the

specification values are known and determinate. As

we know, a fuzzy number cannot be compared with

a crisp one directly unless a non-fuzzy number has

to be transformed into the form of fuzzy number

APPLYING FUZZY MULTIPLE CRITERIA DECISION MAKING TO EVALUATE AND IDENTIFY OPTIMAL

EXPLOSIVE DETECTION EQUIPMENTS

119

firstly. For example, for a crisp number b, the form

of its triangular fuzzy can be written as the Eq. (2).

b = (b

, b

) (2)

where b

= b

, and Similarity measure between

two triangular fuzzy numbers can be calculated with

Eq. (3) (Xu, 2002).

])()()(,)()()max[(

),(

222222 UMLUML

UUMMLL

bbbaaa

bababa

bas

++++

(3)

where two triangular fuzzy numbers are a = (a

) that represents the ideal number and b = (b

, b

) that represents the real number, respectively.

Step 3. Construction of Decision Matrix

Calculation result of similarity measure between

alternate CDEs and the ideal CDE can be concisely

expressed in a matrix format, which is called a

decision matrix in MCDM problems, and in which

columns indicate CDE criteria and rows alternate

CDEs. Thus, an element s

in the in Eq. (4) denotes

the similarity degree to the ideal CDE of the ith

CDE with respect to the jth criterion.

⎥

⎦

⎤

⎢

⎣

⎡

mnmmm

ssss

........

...................................

..........

.........

321

2232221

1131211

(4)

Step 4. Normalization

In order to eliminate the difference of dimension

among different criteria, the operation of

normalization is needed to transform various criteria

dimensions into the non-dimensional criteria. Eqs.

(5) and (6) are utilized to perform this normalization

(Zhu et al., 2008)

⎟

⎠

⎞

⎜

⎝

⎛

∧= 1,,

maxmaxmax

for benefit criteria

(5)

⎟

⎠

⎞

⎜

⎝

⎛

∧= 1,,

minminmin

for cost criteria

(6)

where (●)

max

= max{(●)

} and (●)

min

= min{(●)

Step 5. Rank of the Alternate Products

The element s

in the decision matrix reflects the

closeness degree of the ideal CDE with the ith

alternate CDE with respect to the jth criterion. In

this step, we can use the simple additive weighting

(SAW) method, which is widely used in MCDM, to

calculate the relative importance value with respect

to all criteria, with which the ranking order of

alternate CDEs according to the relative importance

value can be obtained. And we can consider the

CDE with the highest relative importance value as

the closest one to that of the decision maker

requires. The relative importance value of ith

alternate CDE can be calculated with Eq. (7).

(7)

And the maximum of relative importance value

can be written as Eq. (8).

(8)

3 ALGORITHM OF WEIGHT

ASSIGNMENT

Compared with most MCDM methods, the FMCDM

model reported by Bin Zhu et al. is one of the

simplest and most effective methods (Zhu et al.,

2008). A similarity measure method is utilized to

build the decision matrix. However, one problem of

this method is that the weight associated with each

alternative is estimated or determined by the

decision maker or an evaluation team based on their

experience. Generally, this kind of weight estimation

is acceptable for a small set of alternatives, such as 5

or less than 10. However, for a large set of

alternatives, which is a popular situation, this weight

estimation is not accurate and correct based only on

the decision make’s experience.

There are some different weight estimation

methods reported by researchers, such as Saaty who

developed a paired comparison matrix and then an

eigenvector that is equivalent to the weight for an

associated alternative can be calculated based on that

paired comparison matrix (Saaty, 1977). Yager

multiplied the normalized eigenvector by the order

of the system to obtain exponents for weighting the

fuzzy criteria in a decision problem (Yager, 1977).

However, both methods need a lot of mathematical

operations and therefore make the process very

complicated and time consuming.

In this paper, we adopted a weight estimation

method based on the paired comparison matrix to

simplify this estimation process. The operational

procedure is completed by the following steps:

1. List the degree of importance or importance

level of each criterion relative to another

criterion based on Table 1 (Dagdeviren, 2008).

2. Construct a paired comparison matrix W based

on the importance levels in step 1. Each

element w

in the matrix W is a ratio of the

ICEIS 2011 - 13th International Conference on Enterprise Information Systems

120

importance level of the ith criterion over to the

jth criterion.

3. Add each row

∑

iji

ωω

; where i = 1 ~ n.

4. Calculate the normalized weight factor for each

criterion

; where

∑

ωω

5. These weight factors can be used to build the

decision matrix based on the similarity

measure method.

Table 1: Weight assignment to a paired comparison.

In the following section, we will use an example

to illustrate this weight estimation method.

4 CASE STUDY

In this section, we use a group of CDEs (Fatah et al.,

2007) that is collected by the National Institute of

Standards and Technology (NIST) and the National

Homeland Security Research Center (NHSRC),

which contains the updated evaluation results for all

equipments used to detect CAs and Toxic Industrial

Chemicals/Toxic Industrial Materials (TICs/TIMs),

as an example to illustrate the weight estimation

method we developed in this proposal with the

Fuzzy MCDM model we discussed in section 3 to

evaluate and select the optimal CDE currently used

in the U.S. Homeland Security system.

According to (Derringer et al., 2006), the CDEs

can be divided into seven (7) categories based on the

usage:

1. Handheld-portable detection equipment

2. Handheld-stationary detection equipment

3. Vehicle-mounted detection equipment

4. Fixed-site detection systems

5. Fixed-site analytical laboratory systems

6. Standoff detection systems

7. Detection systems with limited data

For each category, the CDEs can be further

grouped into three sub-categories: the CDEs that

capable of detecting CAs only, the CDEs that

capable of detecting TICs/TIMs only, and the CDEs

that capable of detecting both CAs and TICs/TIMs.

To make our research simple and easy to be

understood, in this study, we will concentrate on the

handheld-portable chemical detectors that capable of

detecting CAs only.

Refer to 16 selection factors or criteria used to

evaluate all kinds of CDEs in section 5 in (Fatah et

al., 2007), it can be found that one of the most

important properties is that the evaluation factors are

not given by crisp or accurate values, instead they

are categorized and provided by different ranges. An

example of the first criterion (unit cost of each CDE)

is shown in Fig.2.

Unit Cost

Less than $500 per unit

Between $500 and $2K per unit

Between $2K and $5K per unit

More than $5K per unit

Figure 2: The criteria for evaluating the unit cost.

This kind of criterion did not provide very

accurate or crisp evaluation values, but it does

provide some vague or ambiguous values. Just

because of these vague or ambiguous evaluation

values, it is very suitable to be assessed and

analyzed by using a FMCDM system, and that is the

objective and key points of this proposal.

Because we are using a triangular shape as a

fuzzy member (Fig.1) in this study, therefore we

need to perform a little modification to all 16 criteria

used for this optimal selection process.

Let us create a evaluation table for those

handheld-portable chemical detectors based on the

modified fifteen (15) criteria (detect CAs only, no

criterion), which is shown in Table 2. The blank

evaluation results in Table 2 indicate that no

information available for that criterion for the

selected CDEs. In order to utilize FMCDM system

to evaluate and select the optimal handheld-portable

chemical detectors that capable of detecting CAs

only, we need to perform the following fuzzification

operations to all criteria listed in Table 2.

First let’s use the following letters to represent all

15 criteria as (the number following each criterion

indicates the relative important level of that

criterion):

 C

: Unit Cost (10)

 C

: CAs Detected (1)

 C

: Sensitivity (2)

 C

: Resistance to Interference (3)

 C

: Response Time (5)

APPLYING FUZZY MULTIPLE CRITERIA DECISION MAKING TO EVALUATE AND IDENTIFY OPTIMAL

EXPLOSIVE DETECTION EQUIPMENTS

121

 C

: Start-Up Time (7)

 C

: Detection States (6)

 C

: Alarm Capability (13) (9)

 C

: Portability (9)

 C

: Battery Needs (11)

 C

: Power Capability (12)

 C

: Operational Environment (4)

 C

: Durability (8)

 C

: Operator Skill Level (14)

 C

: Training Requirements (15)

Next we need to use the following three fuzzy

levels to represent those three graphical levels

shown in Table 2:



: HIGH

 : MID

 : LOW

Table 2: Handheld-Portable Detection Equipment (CAs).

ID #

Detector Name

Technology

Unit Cost

CAs Detected

Sensitivit

Resistance to Interferences

Res

onse Time

Start-U

Time

Detection States

Alarm Ca

abilit

Portabilit

Batter

Needs

Power Ca

abilities

erational Environment

Durabilit

Operator Skill Level

Trainin

uirements

AP2C Vapor

and Liquid

Agent

Flame

Spectro

Photo

AP2Ce Vapor

and Liquid

Agent

Flame

Spectro

Photo

APACC

Chemical

Control Alarm

Portable

Apparatus

Flame

Spectro

130

Advanced

Portable

Detector (APD)

IMS

138

M90-D1-C

Chemical

Warfare Agent

Detector

IMS

162

SAW MiniCAD

mkII

SAW

The evaluation results for six (6) handheld-

portable chemical detectors that capable of detecting

CAs only is shown in Table 3 when using those new

definitions described above.

Also those fuzzy levels can be represented by

three numbers, which are defined as:

HIGH – 4, MID – 2 and LOW – 1

Now we need to build the relative important levels

for all criteria. This level is represented by a ratio

between two or a paired of criteria. The ratio

between the same criteria is 1 and a number

represented in the intersection of a row and a column

represnets the importance ratio between that row and

that column. For example, the number in the

intersection cell of row C

and column C

is 2,

which means that the criterion C

(CAs Detected) is

2 times more important than that of criterion C

(Sensitivity). This relative important levels is

obtained based on the experience and real

knowledge of evaluators or decision makers. A

completed importance level of this example based

on Eq. (9) is calculated by comparing two criteria

and based on the following equations:

The important level in cell

CofLeveltpor

tanIm

(10)

Table 3: Evaluation Results (CAs).

Detector

L HMHHHHHM H M H H H H

L HMHHHHHM H H H H H H

130

H L M M M L H L H H H H M M

138

L H M L M L M H L H H H H M M

162

L HMMMM L H H H M M M

Next let’s calculate the overall weight for each

row by adding each row

∑

iji

ωω

; where i = 1 ~ n

and n=15 is the total number of the criteria. The

result of this calculation is shown in Table 4.

Table 4: The Overall Weight for Each Criterion.

c1 c2 c3 c4 c5 c6 c7

12.03 120 60 39.50 24.10 17.11 20

c8 c9 c10

C12 C13 C14 C15

9.23 12.34 10.99 10 30 15.02 8.55 8.00

The total weight is obtained by adding all

weights of criteria together, which is 396.87. The

normalized weight is shown in Table 5.

Table 5: The Normalized Weight for Each Criterion.

c1 c2 c3 c4 c5 c6 c7

0.03 0.30 0.15 0.10 0.06 0.04 0.05

c8 c9 c10 c11 C12 C13 C14 C15

0.02 0.03 0.027 0.025 0.076 0.038 0.02 0.02

Now we can perform step 4 in section 3 to add

these normalized weight for each criterion with all

criteria to construct the ideal and criteria weight

ICEIS 2011 - 13th International Conference on Enterprise Information Systems

122

table, which is shown in Table 6.

The vector of the ideal CDEs can be represented

as the following form of the triangualr fuzzy number

(Table 6):

T = [(1 4 8), (1 4 8), (1 4 8), (1 4 8), (1 4 8), (1 4 8),

(1 4 8), (1 4 8), (1 4 8), (1 4 8), (1 4 8), (1 4 8),

(1 4 8), (1 4 8), (1 4 8)];

Table 6: The Ideal CDEs and Criteria Weight.

Criterion

Ideal

Lower

Upper

Normalized

Weight

c1 4 1 8 0.030

c2 4 1 8 0.300

c3 4 1 8 0.150

c4 4 1 8 0.100

c5 4 1 8 0.060

c6 4 1 8 0.040

c7 4 1 8 0.050

c8 4 1 8 0.020

c9 4 1 8 0.030

c10 4 1 8 0.027

c11 4 1 8 0.025

c12 4 1 8 0.076

c13 4 1 8 0.038

c14 4 1 8 0.020

c15 4 1 8 0.020

The corresponding vector of the criteria weight

can be expressed as:

ω = (0.03, 0.30, 0.15, 0.10, 0.06, 0.04, 0.05, 0.02,

0.03, 0.027, 0.025, 0.076, 0.038, 0.02, 0.02);

The corresponding vector of the criteria weight

can be expressed as:

ω = (0.03, 0.30, 0.15, 0.10, 0.06, 0.04, 0.05, 0.02,

0.03, 0.027, 0.025, 0.076, 0.038, 0.02, 0.02);

The decision matrix, which can be calculated

based on the similarity degree with respect to each

criterion between the ideal CDE and the alternatives,

is shown in Table 7 by using Eqs (3) – (6). The

relative importance value of ith alternate CDE with

respect to all criteria can be computed by equation

(7), and the final calculating results are shown in

Table 8.

When calculate the decision matrix, the ideal

CDE vector is [LOW MID HIGH] = [1 4 8] and the

real CDE vector is selected as [LOW MID HIGH] =

[1 2 4], respectively. The ideal criterion in Table 6,

which is 3, is equal to the HIGH in the real criterion

in Table 2 for this selection.

The relative importance level of ith alternate

CDE can be calculated with equation (7) as:

iji

∑

i = 1, 2, … m

(m is the number of total alternatives)

Table 7: Decision Matrix



Table 8: The Important Level of Each Alternative CDE.

CDE ID# 90 91 93 130 138 162

 0.5027 0.5027 0.5107 0.3887 0.4032 0.3996

The maximum important level of CDEs can be

obtained as:

∑

max

i = 1, 2, … m (m is the number of total alternatives)

The CDE that has the maximum important level

can be found from Table 8, which is the APACC

Chemical Control Alarm Portable Apparatus

(Detector ID#: 93) with the most important level of

0.5107.

The results obtained from this research are based

on the CDE data collected by the NIST and NHSRC

in 2007. More updated evaluations can be achieved

by using updated information on CDEs in the future.

5 CONCLUSIONS

Decision making is one of the most important and

popular research and application topics in the

Detector ID

0.1605

0.6420

0.3210

0.6420

0.3210

0.6420

0.3210

0.6420

0.1605

0.6420

0.3210

0.6420

0.3210

0.6420

0.3210

0.6420

0.1605

0.6420

0.3210

0.6420

0.3210

0.6420

130

0.000

0.6420

0.1605

0.3210

0.1605

0.6420

0.1605

0.6420

0.3210

138

0.1605

0.6420

0.3210

0.1605

0.3210

0.1605

0.3210

0.6420

0.1605

0.6420

0.3210

162

0.1605

0.6420

0.3210

0.1605

0.6420

0.3210

0.000

0.3210

APPLYING FUZZY MULTIPLE CRITERIA DECISION MAKING TO EVALUATE AND IDENTIFY OPTIMAL

EXPLOSIVE DETECTION EQUIPMENTS

123

national defense and homeland security. To assess

and evaluate the optimal Chemical Detecting

Equipment (CDE) system from a large group of

alternatives that contain multiple criteria is a

challenging, sometimes may be a headach task to

decision makers in the defense and the homeland

security system. To correctly pridict and effectively

protect our nationa’s safety, accurately evaluate and

correctly assess the optimal CDE system is the

prerequsite and critical task. In this paper, we used a

collection of CDE information reported by different

agencies in recent years with a target example to

illustrate how to use FMCDM model to simplify this

assessing process.

ACKNOWLEDGEMENTS

The data used in this paper are originally published

by the National Institute of Justice, U.S. Department

of Justice.

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