1. بسم الله الرحمن الرحيم Abdullah A.Al- khorayef S olving assignment-selection problems with verbal information Dr. Mohamed Z. Ramadan

2. Presentation steps Introduction to Fuzzy AHP model for assignment –selection problem The case study Applying the method Results conclusion

3. 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.

4. 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.

5. 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.

6. 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

7. Al-khorayef Company مصانع الخريفقطاعات شركة الخريف التجارية

8. APPLIYING THE METHOD Job positions: 1. Purchasing specialist. 2. Agriculture department manager. 3. Sales engineer. 4. Computer programmer.

9. S kills: 1. Office software experience. 2. Foreign language (English). 3. Communication skills. 4. Flexibility. 5. Analyzing problems. 6. Strategic vision. 7. Authorization. 8. Mathematical ability.

10. The ranking jobs computer programmersales engineer department manager purchasing specialist required skills V.HHMH 1 HH 2 M L 3 M H 4 HH 5 LMHM 6 LLHL 7 HHHH 8

11. The ranking candidate 4321 Required skill V.H LM 1 HH 2 MLM 3 MM 4 HML 5 LLMH 6 LHLH 7 H HH 8

12. Pair wise comparison Definition of the comparisons Intensity importance a ij 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. 123456789123456789

13. Pair wise comparison pair wise comparison computer programmer sales engineer branch manager purchasing specialist skill comparison 9952 1,2 9233 1,3 9333 1,4 2339 1,5 9935 1,6 9939 1,7 9992 1,8 2232 2,3 9233 2,4

14. Step 1 87654321 Job (1) 1 2 3 4 5 6 7 8 Every number of the skills required for job 1 is converted into a Fuzzy number.

15. Step 1 Every fuzzy number is changed in to a membership function based on the table Membershi p function Reciproc al no Membershi p function Fuzz y no (1,1,2) (1/3,1/2,1)(1,2,3) (1/4,1/3,1/2)(2,3,4) (1/5,1/4,1/3)(3,4,5) (1/61/5,1/4)(4,5,6) (1/7,1/6,1/5)(5,6,7) (1/8,1/7,1/6)(6,7,8) (1/9,1/8,1/7)(7,8,9) (1/9,1/9,1/8)(8,9,9)

16. Step 1 87654321 (1, 1, 2)(8,9,9)(4,5,6)(8,9,9)(2, 3, 4) (1, 1, 2) 1 (8,9,9) (5, 6,7)(2, 3, 4)(1, 2, 3)(1, 1, 2) 2 (8,9,9) (2, 3, 4)(1, 1, 2) 3 (8, 9, 9) (1, 1, 2) 4 (8,9,9)(3,4,5)(1,1,2) 5 (2, 3, 4)(3,4,5)(1,1,2) 6 (2, 3, 4)(1,1,2) 7 8

17. Step 1 87654321 (1, 1, 2)(8,9,9)(4,5,6)(8,9,9)(2, 3, 4) (1, 1, 2) 1 2 3 4 5 6 7 8 =

18. Step 1 The value of Fuzzy synthetic for job 1 skill 1 =(0.188, 0.202, 0.199 )S1= (27, 34, 40) = (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) (0.00698, 0.00597, 0.00498) 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)

19. Step 2: Degree of possibility M ( S 1 ≥ S 5 ) = 1 M ( S 5 ≥ S 1 ) = 0 M ( S 1 ≥ S 4 ) = 0 M ( S 4 ≥ S 1 ) = 1 M ( S 1 ≥ S 3 ) =1 M ( S 3 ≥ S 1 ) = 0 M ( S 1 ≥ S 2 ) =1 M ( S 2 ≥ S 1 ) =0.11 M ( S 1 ≥ S 8 ) = 1 M ( S 8 ≥ S 1 ) = 0 M ( S 1 ≥ S 7 ) = 1 M ( S 7 ≥ S 1 ) = 0 M ( S 1 ≥ S 6 ) = 1 M ( S 6 ≥ S 1 ) = 0

20. Step 3 Job ( 1 ) S 1 ≥ S 8 = 1S 1 ≥ S 7 = 1S 1 ≥ S 6 = 1S 1 ≥ S 5 = 1S 1 ≥ S 4 = 1S 1 ≥ S 3 = 1 S 1 ≥ S 2 = 1 S 2 ≥ S 8 = 1S 2 ≥ S 7 = 1S 2 ≥ S 6 = 1S 2 ≥ S 5 = 0S 2 ≥ S 4 = 0S 2 ≥ S 3 = 0.11 S 2 ≥ S 1 = 0.11 S 3 ≥ S 8 = 1S 3 ≥ S 7 = 1S 3 ≥ S 6 = 1S 3 ≥ S 5 = 0S 3 ≥ S 4 = 0S 3 ≥ S 2 = 0 S 3 ≥ S 1 = 0 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.

21. Step 4:normalization W’ = (d’ (A 1 ), d’ (A’ 2 )…, d’ (A n ) T ) Where W is a non-fuzzy number JOB 4 JOB 3 JOB 2 JOB 1 110.720 0000 0000 000.271 0000 0000 0000 0000 1111 TOTAL

22. Step 1 : candidate--candidate qualification needed for the job candidate qualificatio n V.HHMLV.L XXUIA XUIAE L UIAEI M IAEIO H AEIOU V.H Where: XUOIEA 123456 Job (1)4321 Skill (1) 1 2 3 4

23. step 1 Job (1)4321 Skill( 1 ) (1, 2, 3)(1, 1, 2) 1 2 3 4 Job 1 (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) S1= (3.3, 4.6, 7) S2= (2, 2.3, 4 ) S3=( 4.6, 5.75, 10,66) S4=(5,6. 41, 11, 166 )

24. Steps 2,3,4 Step 4 normalization for Candidat1- skill 1 0.4 0 0 0.6 1Total Step 2 M ( S 1 ≥ S 4 ) = 0.585M ( S 1 ≥ S 3 ) = 0.727M ( S 1 ≥ S 2 ) = 1 M ( S 4 ≥ S 1 ) = 1M ( S 3 ≥ S 1 ) = 1M ( S 2 ≥ S 1 ) = 0 M ( S 3 ≥ S 4 ) = 0 M ( S 4 ≥ S 3 ) = 1 M ( S 2 ≥ S 4 ) = 0 M ( S 4 ≥ S 2 ) = 1 M ( S 2 ≥ S 3 ) = 0 M ( S 3 ≥ S 2 ) = 1 Step 3 S 1 ≥ S 4 = 0.585S 1 ≥ S 3 = 0.727S 1 ≥ S 2 = 1 S 2 ≥ S 4 = 0S 2 ≥ S 3 = 0S 2 ≥ S 1 = 0 S 3 ≥ S 4 = 0S 3 ≥ S 2 = 1S 3 ≥ S 1 = 1 S 4 ≥ S 3 = 1S 4 ≥ S 2 = 1S 4 ≥ S 1 = 0

25. norma lizatio n job # 3 normaliz ation job # 1 87654321 87654321 00000001weight 00001000 0 0.33000 0. 5000 candidate 1 0.5 0.330010.5000.4 candidate 1 0 0.33 0. 510 000 candidate 2 0.5 0.33 0. 510 000 candidate 2 0.5 00000 1 candidate 3 0 00000000 0.5 0.33 0. 5010 0 candidate 4 0 0.33 0. 5000100.6 candidate 4 normali zation job # 4 normaliz ation job # 2 87654321 87654321 00000001weight 0000.2700.73 weight 0 0.330000000 candidate 1 1 0.473.51111 0. 51 candidate 1 0 0.33 0. 5000100 candidate 2 0 0.2100000.50 candidate 2 1 00 0. 50 0.5.5 candidate 3 0 0.5000000 candidate 3 0 0.33 0. 5 1 0 candidate 4 0 0.3150000000 candidate 4 results

26. 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

27. 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.

28. Thank you for listening