Student Name:… Student ID: …
MULTI-CRITERIA DECISION MAKING
Exercises – Fuzzy AHP
Question 1: Supplier Selection Problem
ABC company is going to select their plastic supplier from their three potential candiates (i.e. A1,
A2, and A3). Moreover, the company is considering the selection under three attributes. These
attributes are on-time delivery (C1), years of operations (C2), and product quality (C3). The
decision maker’s opinions about the relative importance of a pair of attributes are shown in Table 1.
Table 1. Comparison of Attributes C1 C2 C3 C1 ~ 1 C2 ~ ~ 5 1 C3 ~ ~ ~ 3 7 1
The alternative’s weights are shown in Table 2.
Table 2. Comparison of Candidates for Three Criteria Alternative C1 C2 C3 A1 (0.037, 0.170, 1.764) (0.059, 0.092, 0.307) (0.301, 0.738, 1.443) A2 (0.175, 0.636, 2.033) (0.033, 0.043, 0.309) (0.071, 0.258, 1.057) A3 (0.071, 0.637, 1.057) (0.176, 0.258, 2.022) (0.037, 0.205, 0.429)
The scales of the pairwise comparison of linguistic variables can be expressed using the fuzzy numbers as shown in Table 3.
Table 3. Triangular Fuzzy Conversion Scale Intensity of fuzzy Linguistic scale Triangular fuzzy scale scale ~ Absolutely important (7, 9, 9) 9 ~ Very strong important (5, 7, 9) 7 ~ Essentially important (3, 5, 7) 5 1 Student Name:… Student ID: … ~ Weak important (1, 3, 5) 3 ~ Equal Important (1, 1, 3) 1 ~−1 Less Important (1/3, 1, 1) 1 ~−1 Less weak important (1/5, 1/3, 1) 3 ~−1 Less essentially important (1/7, 1/5, 1/3) 5 ~−1 Less very strong important (1/9, 1/7, 1/5) 7 ~−1 Less absolutely important (1/9, 1/9, 1/7) 9 Task:
a. Complete the hierarchy tree and the pairwise matrix in Table 1.
b. Determine the fuzzy weight of each criterion by using fuzzy AHP method. c. Rank the candidates.
Question 2: CEO Selection Problem
A company is looking for a CEO. There are three applicants (A1, A2, A3) for this position. The
company is also looking for three attributes from these applicants. These attributes are leadership
(C1), problem-solving skill (C2), and experience (C3). The decision maker opinions about the
relative importance of a pair of attributes are shown in Table 4 to 7.
Table 4. Comparison of Attributes C1 C2 C3 C1 Eq Es Ab C2 Eq Vs C3 Eq
Table 5. Comparison of Candidates for Leadership A1 A2 A3 A1 Eq Wk Vs A2 Eq A3 Wk Eq 2 Student Name:… Student ID: …
Table 6. Comparison of Candidates for Problem-solving skill C1 C2 C3 C1 Eq C2 Vs Eq C3 Ab Wk Eq
Table 7. Comparison of Candidates for Experience C1 C2 C3 C1 Eq Vs C2 Eq C3 Es Wk Eq
Table 8. Triangular Fuzzy Conversion Scale Intensity of Linguistic scale Notation Triangular fuzzy scale fuzzy scale ~ Absolutely important Ab (7, 9, 9) 9 ~ Very strong important Vs (5, 7, 9) 7 ~ Essentially important Es (3, 5, 7) 5 ~ Weak important Wk (1, 3, 5) 3 ~ Equal Important Eq (1, 1, 3) 1 ~−1 Less Important L (1/3, 1, 1) 1 ~−1 Less weak important LWk (1/5, 1/3, 1) 3 ~−1 Less essentially important Les (1/7, 1/5, 1/3) 5 ~−1 Less very strong important LVs (1/9, 1/7, 1/5) 7 ~−1 Less absolutely important LAb (1/9, 1/9, 1/7) 9 Task:
a. Complete the hierarchy tree and four pairwise matrices.
b. Determine the fuzzy weight of each criterion by using fuzzy AHP method. 3 Student Name:… Student ID: …
c. Determine the fuzzy weight of each candidate under each criterion. d. Rank the candidates. Question 3:
Source: Table 12.1-page 148 Textbook Gwo-Hshiung Tzeng, Jih-Jeng Huang - Multiple
Attribute Decision Making_ Methods and Applications (2011, Chapman and Hall _CRC)
Given a Fuzzy AHP problem with the hierarchy presented in the figure below. It is known that the
higher the score given in criterion Price, the better alternative is.
Skincare clinic selection problem hierarchy
Table 1: Pair-wise comparison of alternatives for Price O2 skin Zakka Miss Ba Ga Spa O2 1 3 Zakka 1 Miss Ba 5 7 1 3 4 Student Name:… Student ID: … Ga Spa 3 5 1
Table 2: Pair-wise comparison of alternatives for Technology O2 skin Zakka Miss Ba Ga Spa O2 1 7 5 Zakka 3 1 9 7 Miss Ba 1 Ga Spa 3 1
Table 3: Pair-wise comparison of alternatives for Qualified staffs O2 skin Zakka Miss Ba Ga Spa O2 1 1 3 Zakka 3 1 3 5 Miss Ba 1 1 3 Ga Spa 1
Table 4: Pair-wise comparison of alternatives for Promotion O2 skin Zakka Miss Ba Ga Spa O2 1 5 3 Zakka 1 Miss Ba 3 1 Ga Spa 5 7 7 1 5 Student Name:… Student ID: …
Table 5: Comparison of criteria in fuzzy number Price Technology Qualified staffs Promotion Price 1 3 Technology 3 1 3 Qualified staffs 5 3 1 5 Promotion 1 Task:
a. Develop the weight of criteria in table 5. (Round to 3 digits)
b. Use Fuzzy AHP method to determine the best alternative for this problem (Round to 3 digits) 6