# A Consistent Fuzzy Preference Relations Based ANP Model for R&D Project Selection

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Related Literature

#### 2.1. Mathematical Programming Methods

#### 2.2. Economic Methods

#### 2.3. Artificial Intelligence Optimization Methods

#### 2.4. MADA Methods

## 3. Proposed Integrated Hybrid Model

#### 3.1. The DEMATEL Approach

**E**through Equations (1) and (2). The diagonal elements equal zero in normalized relation matrix $\mathit{B}$.

_{ij}represent the element of full (or total) relation matrix $\mathit{Z}$. The matrix can be calculated using Equations (3) and (4):

_{ij}of matrix $\mathit{Z}$ provides a degree of influence about how component i affects component j. The direction of influence can be decided from the total matrix $\mathit{Z}$, if the degree of influence from i to j is larger than the degree of influence from j to i. An arrowhead is used to indicate the direction of influence from i to j. The rows and columns are summed separately to define vectors $\mathit{s}$ and $\mathit{o}$ within the full relation matrix $\mathit{Z}$ by

_{i}denotes the sum of the ith row of the full or total relation matrix $\mathit{Z}$ that represents the full effects of criterion i on the other elements. Likewise, o

_{j}is the sum of the jth column in matrix $\mathit{Z}$ which represents the full effects obtained by criterion j from the other criteria. In addition, the method proposed two critical indexes for understanding the influential network relation structure within the evaluation system. The first number (s

_{i}+ o

_{i}) is an index of the influence degree passed and obtained by criterion i. The second number (s

_{i}− o

_{i}) is an index of the influenced degree of the total influence.

#### 3.2. The CFPR-Based ANP Method

#### 3.3. Modified COPRAS-G Method

## 4. Empirical Example: Brand-Name Company

#### 4.1. Criteria and Dimensions for R&D Project Selection

- (1)
- Research and development: A successful project relies on the probability of technical success, availability of resources, and applicability to other products and processes.
- (2)
- Manufacturing: The project needs to fit the firm’s manufacturing capability, facility and equipment requirements, and raw materials and components available.
- (3)
- Marketing and distribution: The potential markets and possible channels for distribution must be viable for company sustainability. Considerations include potential size of the market, competitors’ efforts in similar areas, probability of market success of the product, and product life.
- (4)
- Financial considerations: It is impossible for a project to be launched without considering financing. The capital investment required, rate of return on investment, and unit price of the product are the criteria considered within the financial dimension.

#### 4.2. Measuring Relationships among Dimensions

**E**obtained through pairwise comparisons as well as the influences and direction of influence between dimensions. From the initial influence matrix

**E**(Table 2), the normalized relation

**B**can be calculated using Equations (1) and (2). Then, using Equations (6) and (7), we can determine the full or total influence

**Z**, as shown in Table 4.

#### 4.3. Weighting of Criteria for R&D Project Selection

_{21}) over facility and equipment requirements (C

_{22}).” They were asked to score pairwise comparisons on the nine-point scale, ranging from 1 indicating equal importance to 9 indicating extreme importance. ANP is the generalized form of AHP to solve the interdependent problems between criteria. Because the ANP discusses complex interrelationships between clusters/attributes, it needs n(n − 1)/2 pairwise comparisons for n criteria in a cluster. However, our proposed CFPR-ANP model only requires n − 1 comparisons, thereby avoiding spending too much time on the pairwise comparisons process. Calculating the eigenvectors of each matrix, we can derive the local weights of criteria to form the unweighted super-matrix. In addition, the original ANP needs to check the consistent index, and the CFPR-ANP resolves the shortcoming. The inconsistency is resolved based on the additive transitivity property of the consistent fuzzy preference relation using Equations (8) to (14) to construct the pairwise comparison matrices. In this hybrid CFPR-ANP method, consistency checks are not required and all pairwise comparisons are consistent [38]. Therefore, using the proposed CFPR-ANP can generate consistent results with less time and greatly improves decision efficiency. The unweighted super-matrix is generated as in Table 5 after which, the weight calculation can be derived by the Equation (15) to a limit power. The process is continued until each row reaching a constant value. Table 6 shows the weights of criteria after each row converged to a constant value. The probability of technical success (C

_{11}) is deemed to be the most important criterion followed by the availability of R&D resources (C

_{12}).

#### 4.4. Using the COPRAS-G Method to Measure R&D Project Selection Levels

## 5. Discussion

_{11}), availability of R&D resources (C

_{12}), and applicability to other products and processes (C

_{13}) are the top three criteria with values of 12.8%, 12.7%, and 11.6%, respectively. The results are consistent with the INRM results. The probability of technical success is the most important issue in R&D development, because if the technology is beyond the capabilities of R&D personnel or the technology capability is not mature, the percentage of failure will be high. This high risk can be minimized by setting up an in-house R&D team for advance evaluation. The lowest priority factor is raw materials or components (C

_{23}) at 5.1%. Inside the enterprise, material and component selection from a shared parts library is standard operation procedure. Once part selection has been approved, the firm will decide what is needed from the standard parts library ready. With such a mechanism, the chance of project failure is minimal. The rate of return on investment (C

_{42}) is the most important criterion within the finance dimension. Profit is the ultimate goal for a firm to pursue, reflecting overall performance and efficiencies in terms of marketing, innovation, as well as productivity. In the dimension of marketing, the potential size of the market (C

_{31}) is the most important factor to consider possible market size before the launch of a new project.

## 6. Concluding Remarks

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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Dimension | Literature | Criteria | Literature |
---|---|---|---|

R&D (C_{1}) | [9,11,37] | Probability of technical success (C_{11}) | [9,11,37] |

Availability of R&D resources (C_{12}) | [11,37] | ||

Applicability to other products and processes (C_{13}) | [11] | ||

Manufacturing (C_{2}) | [9,37] | Fits manufacturing capability (C_{21}) | [37] |

Facility and equipment requirements (C_{22}) | [37] | ||

raw material/ component (C_{23}) | [9] | ||

Marketing (C_{3}) | [1,9,11,37] | Potential size of market (C_{31}) | [9,11,37] |

Competitor efforts in similar areas (C_{32}) | [9,11] | ||

Probability of market success of product (C_{33}) | [11,37] | ||

Product life (C_{34}) | [9] | ||

Finance (C_{4}) | [11,37] | Capital investment required (C_{41}) | [37] |

Rate of return on investment (C_{42}) | [11,37] | ||

Unit price of product (C_{43}) | [37] |

R&D | Manufacturing | Marketing | Finance | |
---|---|---|---|---|

R&D (C_{1}) | 0 | 0.37 | 0.35 | 0.28 |

Manufacturing (C_{2}) | 0.30 | 0 | 0.21 | 0.24 |

Marketing (C_{3}) | 0.31 | 0.20 | 0 | 0.26 |

Finance (C_{4}) | 0.27 | 0.25 | 0.28 | 0 |

R&D | Manufacturing | Marketing | Finance | |
---|---|---|---|---|

R&D (C_{1}) | 1.26 | 1.48 | 1.49 | 1.38 |

Manufacturing (C_{2}) | 1.25 | 0.98 | 1.17 | 1.14 |

Marketing (C_{3}) | 1.27 | 1.16 | 1.01 | 1.16 |

Finance (C_{4}) | 1.27 | 1.21 | 1.25 | 0.97 |

Dimensions | ${\mathit{s}}_{\mathit{i}}+{\mathit{o}}_{\mathit{i}}$ | ${\mathit{s}}_{\mathit{i}}-{\mathit{o}}_{\mathit{i}}$ |
---|---|---|

R&D (C_{1}) | 10.64 | 0.56 |

Manufacturing (C_{2}) | 9.36 | −0.29 |

Marketing and distribution (C_{3}) | 9.52 | −0.32 |

Finance (C_{4}) | 9.34 | 0.04 |

${\mathit{C}}_{11}$ | ${\mathit{C}}_{12}$ | ${\mathit{C}}_{13}$ | ${\mathit{C}}_{21}$ | ${\mathit{C}}_{22}$ | ${\mathit{C}}_{23}$ | ${\mathit{C}}_{31}$ | ${\mathit{C}}_{32}$ | ${\mathit{C}}_{33}$ | ${\mathit{C}}_{34}$ | ${\mathit{C}}_{41}$ | ${\mathit{C}}_{42}$ | ${\mathit{C}}_{43}$ | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

${C}_{11}$ | 0 | 0 | 0 | 0.39 | 0.37 | 0.31 | 0.39 | 0.34 | 0.41 | 0.30 | 0.28 | 0.30 | 0.33 |

${C}_{12}$ | 0 | 0 | 0 | 0.30 | 0.32 | 0.37 | 0.35 | 0.36 | 0.36 | 0.32 | 0.39 | 0.34 | 0.32 |

${C}_{13}$ | 0 | 0 | 0 | 0.31 | 0.31 | 0.32 | 0.26 | 0.30 | 0.23 | 0.38 | 0.33 | 0.36 | 0.35 |

${C}_{21}$ | 0.43 | 0.35 | 0.35 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.29 | 0.35 | 0.32 |

${C}_{22}$ | 0.29 | 0.36 | 0.35 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.37 | 0.34 | 0.32 |

${C}_{23}$ | 0.29 | 0.29 | 0.29 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.34 | 0.32 | 0.36 |

${C}_{31}$ | 0.20 | 0.28 | 0.27 | 0.26 | 0.27 | 0.25 | 0 | 0 | 0 | 0 | 0.28 | 0.29 | 0.24 |

${C}_{32}$ | 0.24 | 0.25 | 0.23 | 0.23 | 0.24 | 0.21 | 0 | 0 | 0 | 0 | 0.24 | 0.24 | 0.28 |

${C}_{33}$ | 0.29 | 0.26 | 0.25 | 0.26 | 0.27 | 0.25 | 0 | 0 | 0 | 0 | 0.24 | 0.26 | 0.23 |

${C}_{34}$ | 0.26 | 0.22 | 0.25 | 0.25 | 0.22 | 0.29 | 0 | 0 | 0 | 0 | 0.25 | 0.22 | 0.25 |

${C}_{41}$ | 0.36 | 0.38 | 0.34 | 0 | 0 | 0 | 0.36 | 0.32 | 0.35 | 0.39 | 0 | 0 | 0 |

${C}_{42}$ | 0.35 | 0.33 | 0.37 | 0 | 0 | 0 | 0.37 | 0.37 | 0.36 | 0.37 | 0 | 0 | 0 |

${C}_{43}$ | 0.30 | 0.28 | 0.29 | 0 | 0 | 0 | 0.27 | 0.31 | 0.29 | 0.24 | 0 | 0 | 0 |

${\mathit{C}}_{11}$ | ${\mathit{C}}_{12}$ | ${\mathit{C}}_{13}$ | ${\mathit{C}}_{21}$ | ${\mathit{C}}_{22}$ | ${\mathit{C}}_{23}$ | ${\mathit{C}}_{31}$ | ${\mathit{C}}_{32}$ | ${\mathit{C}}_{33}$ | ${\mathit{C}}_{34}$ | ${\mathit{C}}_{41}$ | ${\mathit{C}}_{42}$ | ${\mathit{C}}_{43}$ | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

DEMATEL and CFPR-ANP | 0.128 | 0.127 | 0.116 | 0.058 | 0.056 | 0.051 | 0.065 | 0.059 | 0.064 | 0.060 | 0.077 | 0.078 | 0.061 |

Reasoning maps and CFPR-ANP | 0.142 | 0.132 | 0.112 | 0.060 | 0.055 | 0.049 | 0.085 | 0.077 | 0.085 | 0.081 | 0.044 | 0.043 | 0.036 |

Criteria | ${\mathit{C}}_{11}$ | ${\mathit{C}}_{12}$ | ${\mathit{C}}_{13}$ | ${\mathit{C}}_{21}$ | ${\mathit{C}}_{22}$ | ${\mathit{C}}_{23}$ | ${\mathit{C}}_{31}$ | ${\mathit{C}}_{32}$ | ${\mathit{C}}_{33}$ | ${\mathit{C}}_{34}$ | ${\mathit{C}}_{41}$ | ${\mathit{C}}_{42}$ | ${\mathit{C}}_{43}$ | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Weight | 0.13 | 0.13 | 0.12 | 0.06 | 0.06 | 0.05 | 0.07 | 0.06 | 0.06 | 0.06 | 0.08 | 0.08 | 0.06 | |

Project A | u | 5.15 | 6.25 | 7.00 | 7.44 | 6.30 | 6.37 | 6.54 | 7.10 | 7.33 | 7.30 | 8.05 | 6.73 | 7.13 |

l | 3.19 | 4.86 | 5.11 | 5.67 | 4.70 | 4.41 | 4.58 | 4.90 | 5.67 | 5.37 | 5.95 | 4.71 | 5.98 | |

Project B | u | 9.30 | 9.08 | 7.46 | 7.94 | 8.44 | 8.70 | 9.56 | 9.65 | 9.17 | 9.43 | 8.56 | 9.85 | 9.27 |

l | 6.93 | 6.81 | 4.65 | 5.39 | 6.56 | 6.52 | 7.99 | 8.02 | 7.49 | 7.57 | 6.11 | 8.60 | 6.84 | |

Project C | u | 7.11 | 8.21 | 7.92 | 8.37 | 7.82 | 8.28 | 7.75 | 7.10 | 8.33 | 7.26 | 7.33 | 7.41 | 6.86 |

l | 5.44 | 6.79 | 6.30 | 6.63 | 6.29 | 6.38 | 5.92 | 5.46 | 6.67 | 5.74 | 5.67 | 6.04 | 4.91 | |

Project D | u | 7.26 | 7.27 | 7.48 | 7.65 | 7.70 | 7.54 | 6.16 | 6.85 | 7.54 | 6.80 | 7.23 | 6.61 | 6.58 |

l | 5.52 | 5.84 | 6.41 | 6.35 | 5.86 | 5.69 | 4.51 | 5.04 | 5.69 | 5.42 | 4.99 | 5.39 | 5.20 | |

Project E | u | 7.16 | 7.30 | 6.47 | 7.00 | 7.56 | 6.75 | 5.70 | 7.93 | 7.50 | 6.51 | 6.87 | 5.98 | 8.42 |

l | 5.17 | 5.03 | 4.53 | 4.22 | 5.55 | 4.36 | 3.08 | 5.73 | 5.17 | 4.49 | 4.46 | 3.35 | 6.80 |

Criteria | ${\mathit{C}}_{11}$ | ${\mathit{C}}_{12}$ | ${\mathit{C}}_{13}$ | ${\mathit{C}}_{21}$ | ${\mathit{C}}_{22}$ | ${\mathit{C}}_{23}$ | ${\mathit{C}}_{31}$ | ${\mathit{C}}_{32}$ | ${\mathit{C}}_{33}$ | ${\mathit{C}}_{34}$ | ${\mathit{C}}_{41}$ | ${\mathit{C}}_{42}$ | ${\mathit{C}}_{43}$ | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Weight | 0.13 | 0.13 | 0.12 | 0.06 | 0.06 | 0.05 | 0.07 | 0.06 | 0.06 | 0.06 | 0.08 | 0.08 | 0.06 | |

Project A | u | 0.43 | 0.5 | 0.56 | 0.6 | 0.5 | 0.51 | 0.52 | 0.57 | 0.59 | 0.59 | 0.67 | 0.54 | 0.57 |

l | 0.35 | 0.42 | 0.43 | 0.46 | 0.41 | 0.4 | 0.41 | 0.42 | 0.46 | 0.45 | 0.48 | 0.41 | 0.48 | |

Project B | u | 0.87 | 0.83 | 0.6 | 0.65 | 0.72 | 0.76 | 0.93 | 0.95 | 0.84 | 0.9 | 0.74 | 1 | 0.86 |

l | 0.55 | 0.54 | 0.41 | 0.45 | 0.52 | 0.52 | 0.66 | 0.66 | 0.61 | 0.61 | 0.49 | 0.74 | 0.55 | |

Project C | u | 0.57 | 0.69 | 0.65 | 0.71 | 0.64 | 0.7 | 0.63 | 0.57 | 0.7 | 0.58 | 0.59 | 0.6 | 0.55 |

l | 0.45 | 0.54 | 0.5 | 0.53 | 0.5 | 0.51 | 0.48 | 0.45 | 0.53 | 0.47 | 0.46 | 0.49 | 0.42 | |

Project D | u | 0.58 | 0.58 | 0.6 | 0.62 | 0.63 | 0.61 | 0.49 | 0.55 | 0.61 | 0.54 | 0.58 | 0.53 | 0.52 |

l | 0.45 | 0.47 | 0.51 | 0.51 | 0.48 | 0.46 | 0.4 | 0.43 | 0.46 | 0.45 | 0.43 | 0.45 | 0.44 | |

Project E | u | 0.57 | 0.59 | 0.52 | 0.56 | 0.61 | 0.54 | 0.47 | 0.65 | 0.61 | 0.52 | 0.55 | 0.48 | 0.72 |

l | 0.44 | 0.43 | 0.4 | 0.39 | 0.46 | 0.4 | 0.35 | 0.47 | 0.44 | 0.4 | 0.4 | 0.36 | 0.54 |

$\mathit{\gamma}({\overline{\mathit{u}}}_{\mathit{j}}^{\mathit{a}\mathit{s}\mathit{p}\mathit{i}\mathit{r}\mathit{e}},\overline{{\mathit{u}}_{\mathit{k}\mathit{j}}})$ | $\mathit{\gamma}({\overline{\mathit{u}}}_{\mathit{j}}^{\mathit{a}\mathit{s}\mathit{p}\mathit{i}\mathit{r}\mathit{e}},\overline{{\mathit{l}}_{\mathit{k}\mathit{j}}})$ | ${\mathit{V}}_{\mathit{k}}$ | ${\mathit{H}}_{\mathit{K}}\left(\mathit{\%}\right)$ | Rank | |
---|---|---|---|---|---|

Project A | 0.54 | 0.43 | 0.48 | 70.6 | 5 (5) |

Project B | 0.81 | 0.56 | 0.68 | 100.0 | 1 (1) |

Project C | 0.63 | 0.49 | 0.56 | 81.6 | 2 (2) |

Project D | 0.57 | 0.46 | 0.52 | 75.6 | 3 (3) |

Project E | 0.56 | 0.42 | 0.49 | 71.9 | 4 (4) |

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**MDPI and ACS Style**

Cheng, C.-H.; Liou, J.J.H.; Chiu, C.-Y.
A Consistent Fuzzy Preference Relations Based ANP Model for R&D Project Selection. *Sustainability* **2017**, *9*, 1352.
https://doi.org/10.3390/su9081352

**AMA Style**

Cheng C-H, Liou JJH, Chiu C-Y.
A Consistent Fuzzy Preference Relations Based ANP Model for R&D Project Selection. *Sustainability*. 2017; 9(8):1352.
https://doi.org/10.3390/su9081352

**Chicago/Turabian Style**

Cheng, Chia-Hua, James J. H. Liou, and Chui-Yu Chiu.
2017. "A Consistent Fuzzy Preference Relations Based ANP Model for R&D Project Selection" *Sustainability* 9, no. 8: 1352.
https://doi.org/10.3390/su9081352