بسم الله الرحمن الرحيم abdullah a.al- khorayef s olving assignment-selection...
TRANSCRIPT
الرحمن الله بسمالرحيم
Abdullah A.Al- khorayef
Solving assignment-selection problems with verbal information
Dr. Mohamed Z. Ramadan
Presentation steps
Introduction to Fuzzy AHP model for assignment –selection problem
The case study Applying the method Results conclusion
Fuzzy set theory
Was introduced by ZADEH in 1965.
Deals with vague ,uncertain problems.
Used as a modeling tool for systems hard to define precisely, but can be controlled and operated by humans based on knowledge and experience.
Ahp Method
AHP method uses pair wise comparison of attributes in the decision making process
It is called the importance intensity of the reasons (attributes).
It is useful for finding the weight factor of each reason.
Fuzzy AHP model
Step1. Defining The value of fuzzy synthetic extent with respect to the I’th object.
Step2. The degree of possibility.
Step3: The degree of possibility for a convex fuzzy number M to be greater than k .
Step4. Via normalization .
The case study
The method will be applied on an employee selection problem in Al-Khorayef Group.
The group started its activities more than 45 years ago.
manufacture and trade of industrial & agricultural equipments .
Al-Khorayef Group Activities extended to many countries such as USA, Britain,, Oman, Egypt & Iraq.
The Group has a team of more than 1800 group employees
Al-khorayef Company
مجموعة شركات الخريف
شركةعبر
الشرق لآلالتالحديثة
شركة بيت
التقسيطالسعودي
شركة الخريفللخدماتاإلدارية
شركةالخريف للصيانة والتشغيل
شركةالخريف
للمشاريع الزراعية
شركة المركز اآللي
السعودي
القطاعالزراعي
قطاع البترول
قطاع زيوت
كاسترول
القطاعالبحري
مصانعالخريف
للمضخات الغاطسة
مصانعالخريفألنظمة
الري
مصنعالنخيل
لصناعة الورق
الوحدات قسم
الصيانة ورشةالغيار قطع قسم
والمستودعات المخازن
الخريف مصانع التجارية الخريف شركة قطاعاتالقابضة
APPLIYING THE METHOD
Job positions:1. Purchasing specialist.
2. Agriculture department manager.
3. Sales engineer.
4. Computer programmer.
Skills:
1. Office software experience.
2. Foreign language (English).
3. Communication skills.
4. Flexibility.
5. Analyzing problems.
6. Strategic vision.
7. Authorization.
8. Mathematical ability.
The ranking
jobs
required skills
purchasing specialist
department manager
sales engineer
computer programmer
1HMHV.H
2HHV.HV.H
3LV.HV.HM
4HV.HV.HM
5V.HV.HHH
6MHML
7LHLL
8HHHH
The ranking
candidateRequired
skill12341MLV.HV.H
2HHV.HV.H
3V.HMLM
4V.HV.HMM
5V.HLMH
6HMLL
7HLHL
8HHV.HH
Pair wise comparison
Intensity importanc
e aij
Definition of the comparisons
123456789
Equal importance of i and j Between equal and weak importance of i over j
Weak importance of i over j Between equal and strong importance of i over j
Strong importance of i over j Between strong and demonstrated importance of i over j
Demonstrated importance of i over j Between demonstrated and absolute importance of i over j
Absolute importance of i over j .
Pair wise comparison
pair wise comparison
skill compariso
npurchasing specialist
branch manager
sales engineer
computer programmer
1,22599
1,33329
1,43339
1,59332
1,65399
1,79399
1,82999
2,32322
2,43329
Step 1
Job (1)12345678
1
2
3
4
5
6
7
8
Every number of the skills required for job 1 is converted into a Fuzzy number .
1~
1~
1~
1~
1~
1~
1~
1~
1~
1~
2~
2~
2~
2~
2~
9~
9~
9~
9~
9~
9~
9~
9~
9~
9~
9~
9~
3~
3~
3~
3~
3~
3~
5~
6~
4~
4~
21~
21~
21~
21~
21~
31~
31~
31~
31~
31~
31~
91~
91~
91~
91~
91~
91~
91~
91~
91~
91~
91~
91~
61~
51~
41~
41~
Step 1
Every fuzzy number is changed in to a membership function based on the table
21~
31~
4~
41~
5~
51~
6~
61~
7~
71~
8~
81~
9~
91~
Fuzzy no
Membership
functionReciprocal no
Membership
function
(1,1,2)(1,1,2)
(1,2,3)(1/3,1/2,1)
(2,3,4)(1/4,1/3,1/2)
(3,4,5)(1/5,1/4,1/3)
(4,5,6)(1/61/5,1/4)
(5,6,7)(1/7,1/6,1/5)
(6,7,8)(1/8,1/7,1/6)
(7,8,9)(1/9,1/8,1/7)
(8,9,9)(1/9,1/9,1/8)
1~
1~
2~
3~
Step 1
1 ,21,
31
21,
31,
41
51,
61,
71
41,
51,
61
81,
91,
91
31,
41,
51
1 ,21,
31
12345678
1(1, 1, 2) (1, 1, 2)(2, 3, 4)(2, 3, 4)(8,9,9)(4,5,6)(8,9,9)(1, 1, 2)
2(1, 1, 2)(1, 2, 3)(2, 3, 4)(5, 6,7)(8,9,9)(8,9,9)(1, 1, 2)
3(1, 1, 2)(2, 3, 4)(8,9,9)(8,9,9)(8,9,9)(1, 1, 2)
4(1, 1, 2)(8,9,9)(8,9,9)(8,9,9)(8, 9, 9)
5(1,1,2)(3,4,5)(8,9,9)(1, 1, 2)
6(1,1,2)(3,4,5)(2, 3, 4)
7(1,1,2)(2, 3, 4)
8(1,1,2)(1, 1, 2)
1 ,21,
31
1 ,21,
31
21,
31,
41
21,
31,
41
21,
31,
41
21,
31,
41
21,
31,
41
81,
91,
91
81,
91,
91
81,
91,
91
81,
91,
91
81,
91,
91
81,
91,
91
81,
91,
91
81,
91,
91
81,
91,
91
81,
91,
91
81,
91,
91
81,
91,
91
31,
41,
51
Step 1
12345678
1(1, 1, 2) (1, 1, 2)(2, 3, 4)(2, 3, 4)(8,9,9)(4,5,6)(8,9,9)(1, 1, 2)
1 ,21,
31
21,
31,
41
21,
31,
41
81,
91,
91
41,
51,
61
81,
91,
91
1 ,21,
31
2
3
4
5
6
7
8
n , ... 2, 1,i , ,,jl 1 1 1
m
1j
m
j
m
jjujmM j
gi
n
j
ijuijmijlj
giMmn
m jijiji
m
1
n
1
mnm
1
n
1
1
1,
1j
1jM gi
n
Ij
n
Ii =
,
1
1 ,1
1 ,1
1
ilniimn
iiuni
Step 1
The value of Fuzzy synthetic for job 1 skill 1
S1= (27, 34, 40) =(0.188, 0.202, 0.199 )
S2=(26.3, 32.6,38)
S3 =(28.6, 33.8, 37.5)
S4 = (33.7, 38, 39.5 )
S5 =( 13.5, 15.5, 18.5)
S6 =(6.7, 8.8, 12 )
S7 = (3.75, 4.8, 7 )
S8 = (3.6, 4.2, 8.12)
(0.00698, 0.00597, 0.00498)
(0.00698, 0.00597, 0.00498)
(0.00698, 0.00597, 0.00498)
(0.00698, 0.00597, 0.00498)
(0.00698, 0.00597, 0.00498)
(0.00698, 0.00597, 0.00498)
(0.00698, 0.00597, 0.00498)
= (0.183, 0.194, 0.189 )
= (0.199, 0.201, 0.186)
= (0.235, 0.226, 0.196 )
= (0.094, 0.092, 0.0921)
=(0.0399, 0.0525,0.0597)
=(0.0261, 0.0286, 0.0348)
= (0.025, 0.0250, 0.0404)
1-
M 1
* jgi
m
11
j
nj
gi
m
j iMiS
6.200
1 ,5.167
1 ,15.143
1
Step 2: Degree of possibility
)11()22(21
2u 10,1m 21,
(d) 2)2M 1()12(
lmum
ul
lif
mif
MMhgtMMV
M ( S1 ≥ S2 ) =1
M ( S2 ≥ S1 ) =0.11
M ( S1 ≥ S3 ) =1
M ( S3 ≥ S1 ) = 0
M ( S1 ≥ S4 ) = 0
M ( S4 ≥ S1 ) = 1
M ( S1 ≥ S5 ) = 1
M ( S5 ≥ S1 ) = 0
M ( S1 ≥ S6 ) = 1M ( S6 ≥ S1 ) = 0
M ( S1 ≥ S7 ) = 1M ( S7 ≥ S1 ) = 0
M ( S1 ≥ S8 ) = 1M ( S8 ≥ S1 ) = 0
Step 3
Job ( 1 )
S1≥ S2= 1 S1≥ S3= 1S1≥ S4= 1S1≥ S5= 1S1≥ S6= 1S1≥ S7= 1S1≥ S8= 1
S2≥ S1= 0.11S2≥ S3= 0.11S2≥ S4= 0S2≥ S5= 0S2≥ S6= 1S2≥ S7= 1S2≥ S8= 1
S3≥ S1= 0S3≥ S2= 0S3≥ S4= 0S3≥ S5= 0S3≥ S6= 1S3≥ S7= 1S3≥ S8= 1
Assume that d’ (Ai )= Min V (Si Sk )
For k =1 , 2, … , n; K = i. Then the weight vector is given by
W’ = (d’ (A1) , d’ (A’2)… , d’ (An))
Where AI (I = 1, 2, … , n )are n elements .
Step 4:normalization
W’ = (d’ (A1) , d’ (A’2)… , d’ (An)T)
Where W is a non-fuzzy number
JOB 1
JOB 2
JOB 3
JOB 4
00.7211
0000
0000
10.2700
0000
0000
0000
0000
TOTAL1111
Step 1: candidate--candidate
candidate
qualification
qualification needed for the job
V.LLMHV.H
V.LAIUXX
LEAIUX
MIEAIU
HOIEAI
V.HUOIEA Where:
AEIOUX
654321
1234Job (1)
1
Skill (1)2
3
4
1~
1~1~
1~
1~
1~
1~
54~
54~
21~
21~
45~
25~
52~
52~
52~
step 11234Job (1)
1)1 ,1 ,2()1 ,2 ,3(
Skill( 1 )2)1 ,1 ,2(
3)1 ,1 ,2()1 ,1 ,2(
4)1 ,1 ,2(
Job 1
S1= (3.3, 4.6, 7)
S2= (2 , 2.3, 4 )
S3=( 4.6 , 5.75, 10,66)
S4=(5 ,6. 41, 11, 166 )
(0.0671 , 0.0524, 0.0304 ) = (0.22, 0.241 , 0.469)
(0.0671 , 0.0524, 0.0304 ) = (0.134,0.12,0.121)
(0.0671 , 0.0524, 0.0304 ) = (0.308,0.301,0.324)
(0.0671 , 0.0524, 0.0304 ) = (0.335,0.336,0.339)
1 ,21 ,
31
1 ,54 ,
64
1 ,54 ,
64
42 ,
52 ,
62
42 ,
52 ,
62
5 ,25 ,
35
5 ,25 ,
35
35 ,
45 ,
55
35 ,
45 ,
55
25 ,
35 ,
45
Steps 2,3,4
Step 4normalization for Candidat1- skill 1
0.4
0
0
0.6
Total1
Step 2M ( S1 ≥ S2 ) = 1M ( S1 ≥ S3 ) = 0.727M ( S1 ≥ S4 ) = 0.585
M ( S2 ≥ S1 ) = 0M ( S3 ≥ S1 ) = 1M ( S4 ≥ S1 ) = 1
M ( S2 ≥ S3 ) = 0
M ( S3 ≥ S2 ) = 1
M ( S2 ≥ S4 ) = 0
M ( S4 ≥ S2 ) = 1
M ( S3 ≥ S4 ) = 0
M ( S4 ≥ S3 ) = 1
Step 3
S1 ≥ S2 = 1S1 ≥ S3 = 0.727S1 ≥ S4 = 0.585
S2 ≥ S1 = 0S2 ≥ S3 = 0S2 ≥ S4 = 0
S3 ≥ S1 = 1S3 ≥ S2 = 1S3 ≥ S4 = 0
S4 ≥ S1 = 0S4 ≥ S2 = 1S4 ≥ S3 = 1
job # 1normalizationjob # 3
normalization
12345678 12345678
weight00010000 weight10000000
candidate 10.4000.51000.330.5
candidate 1000
0.50000.330
candidate 20000.5010.50.330.5
candidate 2000
0.5010.50.330
candidate 3000000000
candidate 3
0.510.5000000.5
candidate 40.6010000.50.330
candidate 4
0.500.50100.50.330.5
job # 2normalizationjob # 4
normalizatio
n
12345678 12345678
weight.7300.270000 weight10000000
candidate 11
0.51111.50.4731
candidate 100000000.330
candidate 20.5000000.210
candidate 20010000.50.330
candidate 3000000.500
candidate 3.5
0.50
0.50
0.5001
candidate 400000000.3150
candidate 4
0.5
0.50
0.51
0.50.50.330
results
results
Candidate 1 is assigned to job 2
Candidate 2 is assigned to job 1
Candidate 3 is assigned to job 4
Candidate 4 is assigned to job 3
conclusion
The model proved its capability to deal with verbal terms in staff selection problems.
It is recommended to develop a computer software in the future to deal with the problems in a freindly way.
Thank you for listening