USING AHP AND FUZZY MATHEMATICAL PROGRAMMINGFOR PROJECT PORTFOLIO SELECTION Graduate Program of Industrial Management

**

**

(1/2)e- **

** (2/2)

(1/3)Baker and Freeland (1975) **

(2/3) (AHP/ANP) ()LINDOLINGO**

(3/3) **

**

**

(1/4)Archer & Ghasemzadeh (1999) ()**

(2/4) **

(3/4) (i) (ii) (iii) (iv) (v) **

(4/4) (Time-dependent) **

**

**Sharpe and Keelin (1998)

** (Ordinal measure) (Cardinal measure) AHP/ANP

(1/2) (Analytic Hierarchy Process, AHP) Saaty (1986) AHP (Reciprocal comparison) (Homogeneity) (Independence) (Expectations) **

(2/2)AHP (LLSM) (GPM) GPM **

** ( Lee and Kim, 2000)

() () ( )

**

(1/2) (Vagueness) Zadeh (1965) 0 1 **

(2/2)Dubois and Prade (1997) (Similarity) (Preference) (Uncertainty) **

(1/2)

**

(2/2)Zadeh min max min max Zadeh min max (Maximin) **

(1/2) (Sample space) vs. (Pattern space) s- (s-algebra) vs. (Discrete topology) vs. Pos S (Possibility measure) **

(2/2) Nec Pos **

**

Archer and Ghasemzadeh (1999) **

** (1/3) () ()

(2/3)**

(3/3) ()**

**(1/4)

** (2/4)

**(3/4) ( -)

(3-2)-(3-4) (3-2)

**

0-1 (3-9)

(Liu, 1998; Liu and Iwamura, 1998)

(4/4)

** (1/4)

** (2/4) 35 150 250

** (3/4)

** (4/4)

5 (g, b) (1, 1), (1, 0.95), (1, 0.8), (0.9, 0.85), (0.9, 0.7)

** (1/3) AHP LLSM GPM

** (2/3)

** (3/3) () AHP/ANP

**

Liu and Iwamura (1998) maximax Liu (1998) minimax (Klir and Yuan, 1995) maximax 0 minimax (Gray and Larson, 2008)*