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