# Compromise between Short- and Long-Term Financial Sustainability: A Hybrid Model for Supporting R&D Decisions

## Abstract

**:**

## 1. Introduction

## 2. Preliminary and Multidisciplinary Methods for the Hybrid Model

#### 2.1. Rough Machine Learning Mechanism

**IF**antecedent

**THEN**consequence”, which can support DMs to identify (learn) the changes of financial patterns from historical data. This approach is also termed multiple-rules-based decision making (MRDM), which is an emerging field in the research of MCDM.

**Step 1**: Define and discretize the conditional and decision attributes. To form the subsequent bipolar framework, ${d}_{h}^{t+1}$ is defined only in three DCs: positive (POS), neutral ($NEU$), and negative (NEG) ($C{l}_{POS}\succ C{l}_{NEU}\succ C{l}_{NEG}$). The details of discretization in the case study will be explained in Section 4.**Step 2**: Associate each alternative’s conditional attributes’ values at time t with its decision attribute at time t + 1. The step of associations can form a set of DRSA IS.**Step 3**: Divide all the available data from**Step 2**into two groups: the training and testing sets. Once a training set’s classification result is regarded as acceptable, an untouched testing set will be used to examine it. The training set is used to induct the decision rules associated with the positive and negative DCs, termed as the positive and negative rules, to form the associated bipolar model.

#### 2.2. Bipolar Framework

**Step 3**—by a DM selected threshold [25,26]. The threshold ($\mathsf{\Omega}$) is defined as the minimal or required percentage of the instances (objects or alternatives) that satisfy the dominance relation of DRSA in the two groups (i.e., the positive and negative groups), which are defined in Equations (9) and (10).

**Step 4**: Define a threshold $\mathsf{\Omega}$ to select the covered positive and negative rules (refer to Equations (9) and (10)).**Step 5**: Rank the positive and negative rules (new criteria) based on their supports, and calculate their raw support weights according to Equations (9)–(14); the raw support weights should be normalized to sum up to unity as the normalized support weights in a bipolar model.

#### 2.3. Intuitionistic Fuzzy Set Evaluation

**Step 5**. The aforementioned operations of the IFS are shown in Equations (17) and (18) [28].

**Step 6**: Request DMs to indicate their judgments regarding the belongingness and non-belongingness of an alternative on the antecedents (requirements) of a new criterion.**Step 7**: Synthesize the IFS performance scores of an alternative on each new criterion, and the IFS performance scores on all new criteria are to be synthesized at the last stage.

## 3. Empirical Case and Ranking Experiments

#### 3.1. Data

#### 3.2. Forming the Hybrid Bipolar Decision Model

#### 3.3. Ranking of Four Example Companies with Consistency Check

## 4. Discussions on Selecting New R&D Projects and Improvement Planning

## 5. Concluding Remarks

## Acknowledgments

## Conflicts of Interest

## Appendix A. Calculations of the Modified VIKOR Method on Ranking

_{p}-matrix-based aggregators, the modified VIKOR [35,36,37], is referenced and served to test the robustness of the hybrid bipolar model. The original idea of VIKOR is inspired by the works of Yu [38] and Zeleny [39], and it was modified by setting the aspired level as the benchmark for an alternative while calculating its performance score on a criterion. In the present study, the modified VIKOR method is adopted by setting p = 1 in Equation (A1).

_{p}-matrix of this hybrid model is shown in Equation (A1):

Companies | N.S.Weight | S_PR1 | S_PR2 | S_NR1 | S_NR2 | ${\mathit{S}}_{\mathit{t}}^{\mathit{S}}$ | ${\mathit{R}}_{\mathit{t}}^{\mathit{S}}$ | ${\mathit{Q}}_{\mathit{t}}^{\mathit{S}}$ |
---|---|---|---|---|---|---|---|---|

A | 28.13% | 37.50% ^{1} | 50.00% | 100.00% | 100.00% | 71.48% | 28.57% | 50.03% |

B | 21.88% | 50.00% | 50.00% | 100.00% | 87.50% | 72.32% | 28.57% | 50.45% |

C | 28.57% | 12.50% | 12.50% | 66.67% | 62.50% | 38.69% | 19.05% | 28.87% |

D | 21.43% | 37.50% | 50.00% | 83.33% | 0.00% | 45.29% | 23.81% | 34.55% |

^{1}Refer Table 6, 37.50% denotes the performance gap of A on S_PR1: $37.50\%=(1-62.50\%)/(100\%-0)$.

Companies | N.S.weight | L_PR1 | L_PR2 | L_NR1 | L_NR2 | ${\mathit{S}}_{\mathit{t}}^{\mathit{L}}$ | ${\mathit{R}}_{\mathit{t}}^{\mathit{L}}$ | ${\mathit{Q}}_{\mathit{t}}^{\mathit{L}}$ |
---|---|---|---|---|---|---|---|---|

A | 26.32% | 50.00% ^{1} | 37.50% | 83.33% | 83.33% | 63.69% | 25.46% | 44.57% |

B | 23.63% | 50.00% | 37.50% | 100.00% | 100.00% | 72.02% | 30.56% | 51.29% |

C | 30.56% | 33.33% | 25.00% | 50.00% | 66.67% | 42.92% | 15.28% | 29.10% |

D | 19.44% | 16.67% | 37.50% | 83.33% | 83.33% | 54.91% | 25.46% | 40.19% |

^{1}Refer Table 6, 50% denotes the performance gap of A on L_PR1: $50\%=(1-50\%)/(100\%-0)$.

Weights of Expectation (Short-Term:Long-Term) | |||||||
---|---|---|---|---|---|---|---|

Companies | (1.0:0.0) | (0.8:0.2) | (0.6:0.4) | (0.5:0.5) | (0.4:0.6) | (0.2:0.8) | (0.0:1.0) |

A | 50.03% | 45.66% ^{1} | 46.76% | 47.30% | 47.85% | 48.94% | 44.57% |

B | 50.45% | 51.12% | 50.95% | 50.87% | 50.78% | 50.61% | 51.29% |

C | 28.87% | 29.05% | 29.01% | 28.98% | 28.96% | 28.92% | 29.10% |

D | 34.55% | 39.06% | 37.93% | 37.37% | 36.81% | 35.68% | 40.19% |

^{1}It weights 80% on ${Q}_{t}^{S}$ and 20% on ${Q}_{t}^{L}$ (i.e., $45.66\%=0.8\times 50.03\%+0.2\times 44.57$).

## Appendix B. Averaged IFS Assessments of the Three Projects by the DMs

Rule Types | Requirements | Project 1 | Project 2 | Project 3 |
---|---|---|---|---|

Long_Positive | $Tasset\_turn\underset{\_}{\succ}H$ | (0.76, 0.21) ^{1} | (0.59, 0.22) | (0.34, 0.47) |

Long_Positive | $ROA\underset{\_}{\succ}H$ | (0.53, 0.44) | (0.52, 0.31) | (0.51, 0.43) |

Long_Positive | $CF\_reinv\underset{\_}{\succ}H$ | (0.29, 0.28) | (0.25, 0.24) | (0.29, 0.28) |

Long_Positive | $ARturn\underset{\_}{\succ}M$ | (0.81, 0.14) | (0.59, 0.17) | (0.57, 0.17) |

Long_Positive | $SaleDay\underset{\_}{\prec}L$ | (0.76, 0.20) | (0.61, 0.20) | (0.70, 0.20) |

Long_Positive | $Tasset\_turn\underset{\_}{\succ}M$ | (0.85, 0.12) | (0.62, 0.16) | (0.49, 0.33) |

Long_Negative | $SaleDay\underset{\_}{\succ}H$ | (0.60, 0.21) | (0.56, 0.24) | (0.54, 0.22) |

Long_Negative | $Tasset\_turn\underset{\_}{\prec}L$ | (0.62, 0.15) | (0.45, 0.22) | (0.56, 0.16) |

Long_Negative | $ROA\underset{\_}{\prec}L$ | (0.65, 0.26) | (0.57, 0.26) | (0.54, 0.26) |

Long_Negative | $Quick\underset{\_}{\prec}L$ | (0.56, 0.36) | (0.54, 0.41) | (0.52, 0.34) |

Long_Negative | $Inventory\underset{\_}{\prec}M$ | (0.65, 0.31) | (0.58, 0.31) | (0.57, 0.30) |

Long_Negative | $Tasset\_turn\underset{\_}{\prec}M$ | (0.65, 0.26) | (0.59, 0.28) | (0.48, 0.26) |

Short_Positive | $LongCap\underset{\_}{\succ}M$ | (0.13, 0.13) | (0.11, 0.12) | (0.13, 0.13) |

Short_Positive | $SaleDay\underset{\_}{\prec}L$ | (0.81, 0.14) | (0.52, 0.15) | (0.39, 0.15) |

Short_Positive | $Fasset\_turn\underset{\_}{\succ}H$ | (0.75, 0.20) | (0.65, 0.20) | (0.51, 0.20) |

Short_Positive | $CF\underset{\_}{\succ}H$ | (0.81, 0.19) | (0.60, 0.15) | (0.58, 0.19) |

Short_Positive | $NetP\underset{\_}{\succ}H$ | (0.73, 0.27) | (0.56, 0.20) | (0.64, 0.27) |

Short_Positive | $CF\_reinv\underset{\_}{\succ}H$ | (0.14, 0.12) | (0.13, 0.11) | (0.14, 0.13) |

Short_Negative | $SaleDay\underset{\_}{\succ}H$ | (0.74, 0.24) | (0.65, 0.24) | (0.48, 0.28) |

Short_Negative | $Tasset\_turn\underset{\_}{\prec}M$ | (0.69, 0.27) | (0.63, 0.27) | (0.46, 0.27) |

Short_Negative | $CF\_reinv\underset{\_}{\prec}L$ | (0.16, 0.16) | (0.13, 0.14) | (0.16, 0.16) |

Short_Negative | $ARturn\underset{\_}{\prec}M$ | (0.64, 0.36) | (0.58, 0.36) | (0.49, 0.36) |

Short_Negative | $Inventory\underset{\_}{\prec}M$ | (0.58, 0.38) | (0.54, 0.34) | (0.53, 0.39) |

Short_Negative | $Fasset\_turn\underset{\_}{\prec}L$ | (0.73, 0.25) | (0.57, 0.25) | (0.49, 0.29) |

Short_Negative | $NetP\underset{\_}{\prec}L$ | (0.72, 0.22) | (0.59, 0.19) | (0.49, 0.27) |

^{1}It denotes the averaged opinions of the DMs, and $\left({\mu}_{j},{\varpi}_{j}\right)$ = (0.76, 0.21) denotes the averaged IFS assessment of Project 1 on the requirement “$Tasset\_turn\underset{\_}{\succ}H$” for the long-term.

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Conditional Attributes ^{1} | Symbol | Definition |

Debt to total asset | Debt | $\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{d}\mathrm{e}\mathrm{b}\mathrm{t}/\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{t}$ |

Long-term capital to total asset | LongCap | $\mathrm{L}\mathrm{o}\mathrm{n}\mathrm{g}-\mathrm{t}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{c}\mathrm{a}\mathrm{p}\mathrm{i}\mathrm{t}\mathrm{a}\mathrm{l}/\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{t}$ |

Liquidity ratio | Liquidity | $\mathrm{C}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{t}/\mathrm{C}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{l}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{i}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y}$ |

Quick ratio | Quick | $\left(\mathrm{C}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{t}-\mathrm{I}\mathrm{n}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{y}\right)/\mathrm{C}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{l}\mathrm{i}\mathrm{a}\mathrm{b}\mathrm{i}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{y}$ |

Accounts receivable ratio | ARturn | $\mathrm{N}\mathrm{e}\mathrm{t}\mathrm{c}\mathrm{r}\mathrm{e}\mathrm{d}\mathrm{i}\mathrm{t}\mathrm{s}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{s}/\mathrm{A}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{e}\mathrm{d}\mathrm{A}\mathrm{R}$ |

Days for collecting AR | ARdays | $\left(\mathrm{D}\mathrm{a}\mathrm{y}\mathrm{s}\times \mathrm{A}\mathrm{R}\right)/\mathrm{C}\mathrm{r}\mathrm{e}\mathrm{d}\mathrm{i}\mathrm{t}\mathrm{s}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{s}$ |

Inventory turnover rate | Inventory | $\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{o}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{l}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t}/\mathrm{A}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{e}\mathrm{i}\mathrm{n}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{y}$ |

Average days for sales | SaleDay | $\left(\mathrm{A}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{e}\mathrm{e}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{i}\mathrm{n}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{y}/\mathrm{O}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{l}\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{t}\right)\times 365$ |

Fixed asset turnover | Fasset_turn | $\mathrm{Total}\text{}\mathrm{revenue}/\mathrm{Total}\text{}\mathrm{fixed}\text{}\mathrm{asset}$ |

Total asset turnover | Tasset_turn | $\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{r}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{u}\mathrm{e}/\mathrm{A}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{t}$ |

Return on total asset | ROA | $\mathrm{N}\mathrm{e}\mathrm{t}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{i}\mathrm{t}\mathrm{b}\mathrm{e}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{t}\mathrm{a}\mathrm{x}/\mathrm{A}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{t}$ |

Net profit to total capital | NetP_to_cap | $\mathrm{N}\mathrm{e}\mathrm{t}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{i}\mathrm{t}\mathrm{b}\mathrm{e}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{t}\mathrm{a}\mathrm{x}/\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{c}\mathrm{a}\mathrm{p}\mathrm{i}\mathrm{t}\mathrm{a}\mathrm{l}$ |

Net profit ratio | NetP | $\mathrm{N}\mathrm{e}\mathrm{t}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{i}\mathrm{t}/\mathrm{N}\mathrm{e}\mathrm{t}\mathrm{s}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{s}$ |

Earnings per share | EPS | $\frac{\left(\mathrm{N}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{e}-\mathrm{D}\mathrm{i}\mathrm{v}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{d}\mathrm{s}\mathrm{o}\mathrm{n}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{f}\mathrm{e}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{d}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{c}\mathrm{k}\mathrm{s}\right)}{\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{o}\mathrm{u}\mathrm{t}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{s}\mathrm{h}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{s}}$ |

Cash-flow | CF | $\frac{\left(\mathrm{N}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{e}-\mathrm{D}\mathrm{i}\mathrm{v}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{d}\mathrm{s}\mathrm{o}\mathrm{n}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{f}\mathrm{e}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{d}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{c}\mathrm{k}\mathrm{s}\right)}{\mathrm{W}\mathrm{e}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}\mathrm{e}\mathrm{d}\mathrm{a}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{e}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{t}\mathrm{y}}$ |

Cash-flow adequacy | CF_adq | $\mathrm{C}\mathrm{a}\mathrm{s}\mathrm{h}\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w}\mathrm{f}\mathrm{r}\mathrm{o}\mathrm{m}\mathrm{o}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}/\mathrm{A}\mathrm{n}\mathrm{n}\mathrm{u}\mathrm{a}\mathrm{l}\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{e}\mathrm{s}$ |

Cash-flow Reinvestment | CF_reinv | $\frac{\left(\mathrm{I}\mathrm{n}\mathrm{c}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{s}\mathrm{e}\mathrm{d}\mathrm{f}\mathrm{i}\mathrm{x}\mathrm{e}\mathrm{d}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{t}+\mathrm{I}\mathrm{n}\mathrm{c}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{s}\mathrm{e}\mathrm{d}\mathrm{w}\mathrm{o}\mathrm{r}\mathrm{k}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{c}\mathrm{a}\mathrm{p}\mathrm{i}\mathrm{t}\mathrm{a}\mathrm{l}\right)}{\left(\mathrm{N}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{e}+\mathrm{n}\mathrm{o}\mathrm{n}\mathrm{c}\mathrm{a}\mathrm{s}\mathrm{h}\mathrm{e}\mathrm{x}\mathrm{p}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{e}-\mathrm{n}\mathrm{o}\mathrm{n}\mathrm{c}\mathrm{a}\mathrm{s}\mathrm{h}\mathrm{s}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{s}-\mathrm{d}\mathrm{i}\mathrm{v}\mathrm{i}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{d}\mathrm{s}\right)}$ |

Decision Attribute ^{1} | Symbol | Definition |

Return on equity | ROE | $\mathrm{N}\mathrm{e}\mathrm{t}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{i}\mathrm{t}\mathrm{b}\mathrm{e}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{t}\mathrm{a}\mathrm{x}/\mathrm{A}\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{g}\mathrm{e}\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{t}\mathrm{y}$ |

^{1}The values of the conditional attributes are at time t, the decision attribute is at t + 1.

Experiments | Short-Term | Long-Term |
---|---|---|

1st | 75.38% ^{1} | 69.38% |

2nd | 76.35% | 74.64% |

3rd | 78.41% | 72.41% |

4th | 79.13% | 74.82% |

5th | 77.76% | 74.45% |

Average | 77.41% | 73.14% |

Standard Deviation | 1.53% | 2.32% |

^{1}It denotes the CA of the short-term model using a five-fold validation at the first time.

Rules ^{1} | Antecedents (Requirements) | Consequence | Supp ^{2} |
---|---|---|---|

S_PR1 | $\left(LongCap\underset{\_}{\succ}M\right)\wedge \left(SaleDay\underset{\_}{\prec}L\right)\wedge \left(Fasset\_turn\underset{\_}{\succ}H\right)\wedge \left(CF\underset{\_}{\succ}H\right)$ | $ROE\underset{\_}{\succ}POS$ | 27 |

S_PR2 | $\left(SaleDay\underset{\_}{\prec}L\right)\wedge \left(Fasset\_turn\underset{\_}{\succ}H\right)\wedge \left(NetP\underset{\_}{\succ}H\right)\wedge \left(CF\_reinv\underset{\_}{\succ}H\right)$ | $ROE\underset{\_}{\succ}POS$ | 21 |

S_NR1 | $\left(SaleDay\underset{\_}{\succ}H\right)\wedge \left(Tasset\_turn\underset{\_}{\prec}M\right)\wedge \left(CF\_reinv\underset{\_}{\prec}L\right)$ | $ROE\underset{\_}{\prec}NEG$ | 24 |

S_NR2 | $\left(ARturn\underset{\_}{\prec}M\right)\wedge \left(Inventory\underset{\_}{\prec}M\right)\wedge \left(Fasset\_turn\underset{\_}{\prec}L\right)\wedge \left(NetP\underset{\_}{\prec}L\right)$ | $ROE\underset{\_}{\prec}NEG$ | 18 |

^{1}S_PR and S_NR denote the positive and negative rules in the short-term sub-model;

^{2}Supp denotes the number of supports of each rule.

Rules ^{1} | Antecedents (Requirements) | Consequence | Supp ^{2} |
---|---|---|---|

L_PR1 | $\left(Tasset\_turn\underset{\_}{\succ}H\right)\wedge \left(ROA\underset{\_}{\succ}H\right)\wedge \left(CF\_reinv\underset{\_}{\succ}H\right)$ | $ROE\underset{\_}{\succ}POS$ | 20 |

L_PR2 | $\left(ARturn\underset{\_}{\succ}M\right)\wedge \left(SaleDay\underset{\_}{\prec}L\right)\wedge \left(Tasset\_turn\underset{\_}{\succ}M\right)\wedge \left(ROA\underset{\_}{\succ}H\right)$ | $ROE\underset{\_}{\succ}POS$ | 18 |

L_NR1 | $\left(SaleDay\underset{\_}{\succ}H\right)\wedge \left(Tasset\_turn\underset{\_}{\prec}L\right)\wedge \left(ROA\underset{\_}{\prec}L\right)$ | $ROE\underset{\_}{\prec}NEG$ | 22 |

L_NR2 | $\left(Quick\underset{\_}{\prec}L\right)\wedge \left(Inventory\underset{\_}{\prec}M\right)\wedge \left(Tasset\_turn\underset{\_}{\prec}M\right)$ | $ROE\underset{\_}{\prec}NEG$ | 14 |

^{1}L_PR and L_NR denote the positive and negative rules in the long-term sub-model;

^{2}Supp denotes the number of supports of each rule.

Short-Term | Long-Term | |||||||
---|---|---|---|---|---|---|---|---|

(Original/After_$\mathsf{\Omega}$) | POS (50/40) | NEG (48/38) | POS (43/34) | NEG (40/32) | ||||

Decision rule | S_PR1 | S_PR2 | S_NR1 | S_NR2 | L_PR1 | L_PR2 | L_NR1 | L_NR2 |

Supports | 27 | 21 | 24 | 18 | 20 | 18 | 22 | 14 |

Support weights | 67.50% ^{1} | 52.50% | 63.16% | 47.37% | 52.63% | 47.27% | 61.11% | 38.89% |

N.S.weights | 28.13% ^{2} | 21.88% | 28.57% | 21.43% | 26.32% | 23.63% | 30.56% | 19.44% |

^{1}Support weight is calculated by Support/After_$\mathsf{\Omega}$ (e.g., $27/40=67.50\%$);

^{2}N.S.weight denotes the normalized support weight, and the sum of normalized support weights in each sub-model (short or long-term) should be 100.00%.

Timeframes | Short-Term | Long-Term | ||||||
---|---|---|---|---|---|---|---|---|

POS | NEG | POS | NEG | |||||

Companies | S_PR1 | S_PR2 | S_NR1 | S_NR2 | L_PR1 | L_PR2 | L_NR1 | L_NR2 |

A | 62.50% | 50.00% | 0.00% | 0.00% | 50.00% | 62.50% | 16.67% | 16.67% |

B | 50.00% | 50.00% | 0.00% | 12.50% | 50.00% | 62.50% | 0.00% | 0.00% |

C | 87.50% | 87.50% | 33.33% | 37.50% | 66.67% | 75.00% | 50.00% | 33.33% |

D | 62.50% | 50.00% | 16.67% | 100.00% | 83.33% | 62.50% | 16.67% | 16.67% |

Weights of Expectation (Short-Term:Long-Term) | |||||||
---|---|---|---|---|---|---|---|

Companies | (1.0:0.0) | (0.8:0.2) | (0.6:0.4) | (0.5:0.5) | (0.4:0.6) | (0.2:0.8) | (0.0:1.0) |

A | 28.52 ^{1} | 30.07 | 31.61 | 32.39 | 33.16 | 34.71 | 36.26 |

B | 27.68 | 27.73 | 27.78 | 27.80 | 27.83 | 27.88 | 27.93 |

C | 61.31 | 60.45 | 59.60 | 59.17 | 58.74 | 57.89 | 57.03 |

D | 54.71 | 52.77 | 50.84 | 49.87 | 48.90 | 46.97 | 45.04 |

^{1}The final score of A was calculated by putting 100% weighting on the short-term expectation: ${f}_{A}=\left\{1.0\times \left[\left({\displaystyle \sum _{i=1}^{2}{}^{S}w_{i}^{POS}\times {}^{S}f_{iA}^{POS}}\right)+\left({\displaystyle \sum _{j=1}^{2}{}^{S}w_{j}^{NEG}\times {}^{S}f_{jA}^{NEG}}\right)\right]+0.0\times \left[\left({\displaystyle \sum _{i=1}^{2}{}^{L}w_{i}^{POS}\times {}^{L}f_{iA}^{POS}}\right)+\left({\displaystyle \sum _{j=1}^{2}{}^{L}w_{j}^{NEG}\times {}^{L}f_{jA}^{NEG}}\right)\right]\right\}\times 100$, where ${}^{S}w_{i}^{POS}$ denotes the normalized support weight of the i-th positive rule in the short-term model and ${}^{S}f_{iA}^{POS}$ represents the associated performance score of company A on this rule; the other symbols follow the similar logic.

2013 | 2014 | 2015 | 2013–2015 ^{1} | |
---|---|---|---|---|

A | −3.90 | −1.48 | 0.14 | −1.75 |

B | −37.36 | −86.65 | 30.47 | −31.18 |

C | 19.27 | 25.54 | 22.44 | 22.42 |

D | −5.59 | 7.56 | 7.13 | 3.03 |

^{1}It denotes the averaged ROE, from 2013 to 2015 (i.e., long-term).

Weights of Expectation (Short-Term (2013):Long-Term (2013–2015)) | |||||||
---|---|---|---|---|---|---|---|

c-ROE ^{1} (Rank) | (1.0:0.0) | (0.8:0.2) | (0.6:0.4) | (0.5:0.5) | (0.4:0.6) | (0.2:0.8) | (0.0:1.0) |

A | −3.90(2) | −3.47(2) | −3.04(3) | −2.83(3) | −2.61(3) | −2.18(3) | −1.75(3) |

B | −37.36(4) | −36.13(4) | −34.89(4) | −34.27(4) | −33.65(4) | −32.42(4) | −31.18(4) |

C | 19.27(1) | 19.90(1) | 20.53(1) | 20.85(1) | 21.16(1) | 21.79(1) | 22.42(1) |

D | −5.59(3) | −3.87(3) | −2.14(2) | −1.28(2) | −0.42(2) | 1.31(2) | 3.03(2) |

^{1}c-ROE denotes the combined ROE in different weights of expectation of the short- and long-term. For instance, while putting 80% weight on the short-term and 20% the long-term (i.e., (0.8:0.2) in this table), c-ROE of company A was calculated as: $-3.47\%=0.8\times (-3.90\%)+0.2\times (-1.75\%)$.

Timeframes | Short-Term | Long-Term | ||||||
---|---|---|---|---|---|---|---|---|

POS | NEG | POS | NEG | |||||

Rules | S_PR1 | S_PR2 | S_NR1 | S_NR2 | L_PR1 | L_PR2 | L_NR1 | L_NR2 |

Project 1 | (0.70, 0.16) | (0.67, 0.17) | (0.59, 0.22) | (0.67, 0.29) | (0.56, 0.30) ^{1} | (0.73, 0.20) | (0.62, 0.21) | (0.62, 0.31) |

Project 2 | (0.50, 0.15) | (0.50, 0.16) | (0.51, 0.21) | (0.57, 0.27 | (0.47, 0.26) | (0.58, 0.20) | (0.53, 0.24) | (0.56, 0.34) |

Project 3 | (0.42, 0.17) | (0.45, 0.18) | (0.38, 0.23) | (0.50, 0.33) | (0.39, 0.39) | (0.55, 0.26) | (0.54, 0.21) | (0.52, 0.30) |

^{1}The IFS-based assessments of the three projects on each rule were calculated by using IFS OWA; ${\mu}_{1}^{\mathrm{L}\_\mathrm{P}\mathrm{R}\mathrm{1}}=1-{\left(1-0.76\right)}^{1/3}\times {\left(1-0.53\right)}^{1/3}\times {\left(1-0.29\right)}^{1/3}=0.56$ and ${\varpi}_{1}^{\mathrm{L}\_\mathrm{P}\mathrm{R}\mathrm{1}}={\left(1-0.21\right)}^{1/3}\times {\left(1-0.44\right)}^{1/3}\times {\left(1-0.28\right)}^{1/3}=0.30$, where the averaged degree of satisfaction and dissatisfaction of the three projects, on each requirement, can be found in Appendix B.

**Table 11.**M(A) values and the final scores (ranking) of the three projects by SAW method (while equally weighted on the short- and long-term prospects).

Timeframes | Short-Term | Long-Term | |||||||
---|---|---|---|---|---|---|---|---|---|

POS | NEG | POS | NEG | ||||||

Rules | S_PR1 | S_PR2 | S_NR1 | S_NR2 | L_PR1 | L_PR2 | L_NR1 | L_NR2 | Scores |

N.S.Weight | 28.13% | 21.88% | 28.57% | 21.43% | 26.32% | 23.63% | 30.56% | 19.44% | (Ranking) |

Project 1 | 0.54 | 0.50 | 0.37 | 0.38 | 0.26 | 0.53 | 0.41 | 0.30 | 41.42 (1) ^{1} |

Project 2 | 0.35 | 0.34 | 0.30 | 0.29 | 0.21 | 0.38 | 0.28 | 0.23 | 29.91 (2) |

Project 3 | 0.26 | 0.27 | 0.15 | 0.17 | 0.00 | 0.29 | 0.33 | 0.22 | 21.13 (3) |

^{1}The final score of project 1, while equally weighted on the short- and long-term prospect, calculated as: $41.42=\left[\begin{array}{l}0.5\times \left(0.54\times 28.13\%+0.50\times 21.88\%+0.37\times 28.57\%+0.38\times 21.43\%\right)\\ +0.5\times \left(0.26\times 26.32\%+0.53\times 23.63\%+0.41\times 30.56\%+0.30\times 19.44\%\right)\end{array}\right]\times 100$.

Timeframes | Short-Term | Long-Term | ||||||
---|---|---|---|---|---|---|---|---|

POS | NEG | POS | NEG | |||||

Rules | S_PR1 | S_PR2 | S_NR1 | S_NR2 | L_PR1 | L_PR2 | L_NR1 | L_NR2 |

N.S.Weight | 28.13% | 21.88% | 28.57% | 21.43% | 26.32% | 23.63% | 30.56% | 19.44% |

(Short:Long = 0.8:0.2) | 3.03% ^{1} | 2.19% | 2.09% | 1.62% | 5.57% | 10.08% | 10.11% | 4.69% |

Top 3 priority | 3rd | 2nd | 1st | |||||

(Short:Long = 0.5:0.5) | 7.57% | 5.47% | 5.22% | 4.05% | 3.48% | 6.30% | 6.32% | 2.93% |

Top 3 priority | 1st | 3rd | 2nd | |||||

(Short:Long = 0.2:0.8) | 12.12% | 8.74% | 8.35% | 6.48% | 1.39% | 2.52% | 2.53% | 1.17% |

Top 3 priority | 1st | 2nd | 3rd |

^{1}It denotes the weighted performance score of Project 1 while 80% and 20% expectation are placed on the short- and long-term, which is calculated as: $3.03\%=28.13\%\times 0.8\times 0.54$.

© 2017 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ( http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Shen, K.-Y.
Compromise between Short- and Long-Term Financial Sustainability: A Hybrid Model for Supporting R&D Decisions. *Sustainability* **2017**, *9*, 375.
https://doi.org/10.3390/su9030375

**AMA Style**

Shen K-Y.
Compromise between Short- and Long-Term Financial Sustainability: A Hybrid Model for Supporting R&D Decisions. *Sustainability*. 2017; 9(3):375.
https://doi.org/10.3390/su9030375

**Chicago/Turabian Style**

Shen, Kao-Yi.
2017. "Compromise between Short- and Long-Term Financial Sustainability: A Hybrid Model for Supporting R&D Decisions" *Sustainability* 9, no. 3: 375.
https://doi.org/10.3390/su9030375