# A TODIM-PROMETHEE Ⅱ Based Multi-Criteria Group Decision Making Method for Risk Evaluation of Water Resource Carrying Capacity under Probabilistic Linguistic Z-Number Circumstances

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## Abstract

**:**

## 1. Introduction

- An information representation, namely probabilistic linguistic Z-numbers (PLZNs), is proposed to describe complex group preferences. Z-numbers constitute a good representation to depict vague and imprecise information. Due to the complexity of group decision-making circumstances, Z-numbers and their extensions make it difficult to meet the requirements of information expression. Considering the advantages of PLTSs for the description of group decision making information, PLTSs are utilized to depict the fuzzy restriction of Z-numbers. This extension of Z-numbers is referred to PLZNs. PLZNs can help decision-makers to express their opinions and preferences more easily and correctly during group decision making.
- A TODIM-PROMETHEE Ⅱ based decision support framework is developed to address MCGDM issues, involving the risk evaluation of WRCC. The TODIM method and PROMETHEE (preference ranking organization method for enrichment evaluation) Ⅱ method are common MCGDM methods. However, the TODIM method has the compensation problem, while the PROMETHEE Ⅱ method cannot distribute the weights of related importance to the criteria in an effective way. Considering their complementarity, TODIM and PROMETHEE Ⅱ methods are combined to overcome their respective restrictions, and the combined method is referred to as the TODIM-PROMETHEE Ⅱ method. The TODIM-PROMETHEE Ⅱ method utilizes the value function of prospect theory as its preference function, which provides a good description for decision behaviors of bounded rationality. It can well reflect decision makers’ preferences in practical decision conditions.

## 2. Literature Review

#### 2.1. Fuzzy Sets

#### 2.2. MCGDM Methods

#### 2.3. WRCC

## 3. Preliminaries

#### 3.1. The Basic Concept of PLTSs

**Definition**

**1.**

- The set is ordered:$\alpha >\beta \iff {s}_{\alpha}>{s}_{\beta}$, and
- A negation operator exists:$neg\left({s}_{\alpha}\right)={s}_{2g-\alpha}$.

**Definition**

**2.**

#### 3.2. The Basic Concept of Linguistic Scale Functions (LSFs)

**Definition**

**3.**

**LSF 1**:${f}_{1}\left({s}_{i}\right)={\theta}_{i}$

**LSF2:**${f}_{2}\left({s}_{i}\right)={\theta}_{i}$

**LSF3:**${f}_{3}\left({s}_{i}\right)={\theta}_{i}$

#### 3.3. The Basic Concept of Linguistic Z-Numbers

**Definition**

**4.**

**Definition**

**5.**

## 4. PLZNs and Their Knowledge

#### 4.1. The Concept of PLZNs

**Definition**

**6.**

#### 4.2. The Comparison Method of PLZNs

**Definition**

**7.**

**Definition**

**8.**

- (1)
- When$E\left({z}_{\alpha}\right)>E\left({z}_{\beta}\right)$,${z}_{\alpha}\succ {z}_{\beta}$
- (2)
- When$E\left({z}_{\alpha}\right)=E\left({z}_{\beta}\right)$,

#### 4.3. The Distance of PLZNs

**Definition**

**9.**

**Definition**

**10.**

**Theorem**

**1.**

- (1)
- $D\left({z}_{\alpha},{z}_{\beta}\right)\ge 0$,
- (2)
- $D\left({z}_{\alpha},{z}_{\beta}\right)=D\left({z}_{\beta},{z}_{\alpha}\right)$, and
- (3)
- $D\left({z}_{\alpha},{z}_{\beta}\right)\le D\left({z}_{\alpha},{z}_{\gamma}\right)+D\left({z}_{\gamma},{z}_{\beta}\right)$.

**Proof.**

- (1)
- $D\left({z}_{\alpha},{z}_{\beta}\right)=\left|d\left({z}_{\alpha}\right)-d\left({z}_{\beta}\right)\right|\ge 0$.
- (2)
- $D\left({z}_{\alpha},{z}_{\beta}\right)=\left|d\left({z}_{\alpha}\right)-d\left({z}_{\beta}\right)\right|=\left|d\left({z}_{\beta}\right)-d\left({z}_{\alpha}\right)\right|=D\left({z}_{\beta},{z}_{\alpha}\right)$.
- (3)
- $D\left({z}_{\alpha},{z}_{\beta}\right)=\left|d\left({z}_{\alpha}\right)-d\left({z}_{\gamma}\right)+d\left({z}_{\gamma}\right)-d\left({z}_{\beta}\right)\right|\le \left|d\left({z}_{\alpha}\right)-d\left({z}_{\gamma}\right)\right|+\left|d\left({z}_{\gamma}\right)-d\left({z}_{\beta}\right)\right|\le D\left({z}_{\alpha},{z}_{\gamma}\right)+D\left({z}_{\gamma},{z}_{\beta}\right)$.

#### 4.4. The Operations of PLZNs

**Definition**

**11.**

**Example**

**1.**

**Definition**

**12.**

## 5. Decision Support Framework

## 6. Case Study

#### 6.1. Calculation Process and Results

#### 6.2. Sensitivity Analysis

#### 6.3. Comparison Analysis

#### 6.4. Discussion

## 7. Conclusions, Limitation and Future Work

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

${c}_{1}$ | ${c}_{2}$ | ${c}_{3}$ | |

${a}_{1}$ | $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.3\right),{s}_{2}\left(0.3\right),{s}_{1}\left(0.3\right)\right),{s}_{4}\right)$ $\left(\left({s}_{4}\left(0.6\right),{s}_{3}\left(0.1\right),{s}_{1}\left(0.3\right)\right),{s}_{3}\right)$ $\left(\left({s}_{4}\left(0.3\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.3\right),{s}_{1}\left(0.1\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.3\right),{s}_{2}\left(0.4\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{4}\left(0.3\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.1\right),{s}_{1}\left(0.3\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.4\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.3\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.3\right)\right),{s}_{2}\right)$ $\left(\left({s}_{4}\left(0.4\right),{s}_{3}\left(0.4\right),{s}_{1}\left(0.2\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.4\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.5\right)\right),{s}_{3}\right)$ $\left(\left({s}_{4}\left(0.3\right),{s}_{3}\left(0.4\right),{s}_{2}\left(0.1\right),{s}_{1}\left(0.2\right)\right),{s}_{2}\right)$ $\left(\left({s}_{4}\left(0.3\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.2\right),{s}_{1}\left(0.4\right)\right),{s}_{1}\right)$ |

${a}_{2}$ | $\left(\left({s}_{5}\left(0.4\right),{s}_{3}\left(0.4\right),{s}_{1}\left(0.2\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.1\right),{s}_{2}\left(0.3\right),{s}_{1}\left(0.4\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.4\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.3\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.2\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.2\right),{s}_{3}\left(0.2\right),{s}_{1}\left(0.4\right)\right),{s}_{4}\right)$ $\left(\left({s}_{4}\left(0.4\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.2\right),{s}_{1}\left(0.1\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.4\right),{s}_{2}\left(0.2\right),{s}_{2}\left(0.2\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.4\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.4\right),{s}_{2}\left(0.4\right)\right),{s}_{4}\right)$ $\left(\left({s}_{4}\left(0.3\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.1\right),{s}_{1}\left(0.4\right)\right),{s}_{3}\right)$ $\left(\left({s}_{4}\left(0.3\right),{s}_{2}\left(0.2\right),{s}_{1}\left(0.5\right)\right),{s}_{2}\right)$ $\left(\left({s}_{4}\left(0.3\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.1\right),{s}_{1}\left(0.4\right)\right),{s}_{1}\right)$ |

${a}_{3}$ | $\left(\left({s}_{4}\left(0.3\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.1\right),{s}_{1}\left(0.3\right)\right),{s}_{4}\right)$ $\left(\left({s}_{4}\left(0.4\right),{s}_{3}\left(0.3\right),{s}_{1}\left(0.3\right)\right),{s}_{3}\right)$ $\left(\left({s}_{4}\left(0.3\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.3\right),{s}_{1}\left(0.1\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.4\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.2\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{4}\left(0.3\right),{s}_{3}\left(0.4\right),{s}_{2}\left(0.2\right),{s}_{1}\left(0.1\right)\right),{s}_{4}\right)$ $\left(\left({s}_{4}\left(0.4\right),{s}_{3}\left(0.3\right),{s}_{1}\left(0.3\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.4\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.4\right)\right),{s}_{2}\right)$ $\left(\left({s}_{4}\left(0.3\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.3\right),{s}_{1}\left(0.1\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.2\right),{s}_{3}\left(0.6\right),{s}_{2}\left(0.2\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.4\right),{s}_{2}\left(0.2\right)\right),{s}_{3}\right)$ $\left(\left({s}_{4}\left(0.3\right),{s}_{2}\left(0.1\right),{s}_{1}\left(0.6\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.6\right),{s}_{2}\left(0.3\right)\right),{s}_{1}\right)$ |

${a}_{4}$ | $\left(\left({s}_{4}\left(0.4\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.1\right),{s}_{1}\left(0.4\right)\right),{s}_{4}\right)$ $\left(\left({s}_{4}\left(0.3\right),{s}_{2}\left(0.4\right),{s}_{1}\left(0.3\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.3\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.5\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.1\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.4\right),{s}_{2}\left(0.4\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.4\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.3\right)\right),{s}_{3}\right)$ $\left(\left({s}_{4}\left(0.4\right),{s}_{2}\left(0.4\right),{s}_{1}\left(0.2\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.3\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.5\right),{s}_{2}\left(0.1\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.2\right),{s}_{1}\left(0.5\right)\right),{s}_{3}\right)$ $\left(\left({s}_{4}\left(0.4\right),{s}_{2}\left(0.3\right),{s}_{1}\left(0.3\right)\right),{s}_{2}\right)$ $\left(\left({s}_{4}\left(0.3\right),{s}_{3}\left(0.3\right),{s}_{1}\left(0.4\right)\right),{s}_{1}\right)$ |

${a}_{5}$ | $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.2\right),{s}_{3}\left(0.4\right),{s}_{2}\left(0.3\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.2\right),{s}_{3}\left(0.5\right),{s}_{2}\left(0.2\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.4\right),{s}_{2}\left(0.4\right)\right),{s}_{2}\right)$ $\left(\left({s}_{4}\left(0.3\right),{s}_{2}\left(0.6\right),{s}_{1}\left(0.1\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{4}\left(0.6\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.1\right),{s}_{1}\left(0.1\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.3\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{2}\left(0.8\right)\right),{s}_{2}\right)$ $\left(\left({s}_{4}\left(0.3\right),{s}_{2}\left(0.3\right),{s}_{1}\left(0.4\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{4}\left(0.5\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.2\right),{s}_{1}\left(0.1\right)\right),{s}_{4}\right)$ $\left(\left({s}_{4}\left(0.4\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.2\right),{s}_{1}\left(0.2\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.4\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.3\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.4\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.3\right)\right),{s}_{1}\right)$ |

${a}_{6}$ | $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.4\right),{s}_{2}\left(0.2\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.4\right)\right),{s}_{3}\right)$ $\left(\left({s}_{4}\left(0.3\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.3\right),{s}_{1}\left(0.3\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.3\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.2\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.4\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{3}\left(0.7\right),{s}_{2}\left(0.1\right)\right),{s}_{3}\right)$ $\left(\left({s}_{4}\left(0.3\right),{s}_{2}\left(0.4\right),{s}_{1}\left(0.3\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.5\right),{s}_{2}\left(0.4\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.3\right)\right),{s}_{4}\right)$ $\left(\left({s}_{4}\left(0.3\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.3\right),{s}_{1}\left(0.1\right)\right),{s}_{3}\right)$ $\left(\left({s}_{4}\left(0.3\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.2\right),{s}_{1}\left(0.3\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.4\right),{s}_{2}\left(0.4\right)\right),{s}_{1}\right)$ |

${c}_{4}$ | ${c}_{5}$ | ${c}_{6}$ | |

${a}_{1}$ | $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.4\right),{s}_{2}\left(0.3\right)\right),{s}_{4}\right)$ $\left(\left({s}_{4}\left(0.5\right),{s}_{2}\left(0.3\right),{s}_{1}\left(0.2\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.2\right),{s}_{3}\left(0.4\right),{s}_{2}\left(0.3\right)\right),{s}_{2}\right)$ $\left(\left({s}_{4}\left(0.7\right),{s}_{1}\left(0.3\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.2\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.3\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.2\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.3\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.4\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.4\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.3\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.1\right),{s}_{3}\left(0.6\right),{s}_{2}\left(0.3\right)\right),{s}_{4}\right)$ $\left(\left({s}_{4}\left(0.6\right),{s}_{2}\left(0.2\right),{s}_{1}\left(0.2\right)\right),{s}_{3}\right)$ $\left(\left({s}_{4}\left(0.4\right),{s}_{2}\left(0.2\right),{s}_{1}\left(0.4\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.2\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.3\right)\right),{s}_{1}\right)$ |

${a}_{2}$ | $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.3\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.3\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.2\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.2\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.3\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.3\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.4\right),{s}_{2}\left(0.4\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.4\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.2\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.5\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.3\right),{s}_{2}\left(0.5\right)\right),{s}_{4}\right)$ $\left(\left({s}_{4}\left(0.4\right),{s}_{3}\left(0.4\right),{s}_{2}\left(0.2\right)\right),{s}_{3}\right)$ $\left(\left({s}_{4}\left(0.5\right),{s}_{2}\left(0.2\right),{s}_{1}\left(0.3\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.5\right)\right),{s}_{1}\right)$ |

${a}_{3}$ | $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.4\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.2\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.4\right),{s}_{2}\left(0.3\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.5\right),{s}_{2}\left(0.2\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.3\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{4}\left(0.5\right),{s}_{3}\left(0.2\right),{s}_{1}\left(0.3\right)\right),{s}_{4}\right)$ $\left(\left({s}_{4}\left(0.5\right),{s}_{1}\left(0.5\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.1\right),{s}_{2}\left(0.6\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.5\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.3\right),{s}_{2}\left(0.4\right)\right),{s}_{4}\right)$ $\left(\left({s}_{4}\left(0.4\right),{s}_{3}\left(0.5\right),{s}_{1}\left(0.1\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.1\right),{s}_{2}\left(0.6\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.6\right)\right),{s}_{1}\right)$ |

${a}_{4}$ | $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.4\right),{s}_{2}\left(0.2\right)\right),{s}_{4}\right)$ $\left(\left({s}_{4}\left(0.6\right),{s}_{2}\left(0.2\right),{s}_{1}\left(0.2\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.4\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.2\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.5\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.3\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{4}\left(0.5\right),{s}_{3}\left(0.1\right),{s}_{1}\left(0.4\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.4\right),{s}_{2}\left(0.4\right)\right),{s}_{3}\right)$ $\left(\left({s}_{4}\left(0.5\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.3\right),{s}_{1}\left(0.1\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.4\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.3\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.6\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.4\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.3\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.4\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.3\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{3}\left(0.5\right),{s}_{2}\left(0.2\right)\right),{s}_{1}\right)$ |

${a}_{5}$ | $\left(\left({s}_{5}\left(0.2\right),{s}_{3}\left(0.8\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.4\right),{s}_{2}\left(0.4\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.3\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.4\right),{s}_{2}\left(0.4\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.5\right),{s}_{2}\left(0.3\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.2\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.6\right),{s}_{2}\left(0.2\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.4\right),{s}_{2}\left(0.4\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.1\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.6\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.7\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.4\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.2\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.5\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.1\right)\right),{s}_{1}\right)$ |

${a}_{6}$ | $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.4\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.2\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.4\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.4\right),{s}_{2}\left(0.6\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.4\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.3\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.4\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.2\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.2\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.4\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.1\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.3\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.3\right)\right),{s}_{4}\right)$ $\left(\left({s}_{4}\left(0.5\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.4\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.1\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.4\right),{s}_{2}\left(0.3\right)\right),{s}_{1}\right)$ |

${c}_{7}$ | ${c}_{8}$ | ${c}_{9}$ | |

${a}_{1}$ | $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.3\right),{s}_{2}\left(0.4\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.4\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.6\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.2\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.4\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.4\right),{s}_{4}\left(0.4\right),{s}_{2}\left(0.2\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.2\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.4\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.4\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.2\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.3\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.3\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.4\right),{s}_{4}\left(0.5\right),{s}_{2}\left(0.1\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.3\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.2\right)\right),{s}_{1}\right)$ |

${a}_{2}$ | $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.2\right)\right),{s}_{4}\right)$ $\left(\left(,{s}_{4}\left(0.2\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.3\right)\right),{s}_{3}\right)$ $\left(\left({s}_{4}\left(0.6\right),{s}_{3}\left(0.2\right),{s}_{1}\left(0.2\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{3}\left(0.4\right),{s}_{2}\left(0.3\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.4\right),{s}_{4}\left(0.4\right),{s}_{2}\left(0.2\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.5\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.1\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.2\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.4\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.2\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.3\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.5\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.3\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.2\right),{s}_{2}\left(0.5\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.4\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.4\right)\right),{s}_{1}\right)$ |

${a}_{3}$ | $\left(\left({s}_{4}\left(0.5\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.2\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.3\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.3\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.2\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.4\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.5\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.1\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.2\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.2\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.3\right),{s}_{2}\left(0.4\right)\right),{s}_{2}\right)$ $\left(\left({s}_{4}\left(0.8\right),{s}_{2}\left(0.2\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.3\right),{s}_{3}\left(0.4\right),{s}_{2}\left(0.3\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.5\right),{s}_{2}\left(0.2\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.5\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.3\right),{s}_{2}\left(0.6\right)\right),{s}_{1}\right)$ |

${a}_{4}$ | $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.3\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.4\right),{s}_{2}\left(0.4\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.4\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.4\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.1\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.4\right),{s}_{2}\left(0.4\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.4\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.1\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.4\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.3\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.5\right),{s}_{2}\left(0.3\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.2\right),{s}_{2}\left(0.6\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.4\right),{s}_{4}\left(0.5\right),{s}_{2}\left(0.1\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.3\right),{s}_{2}\left(0.4\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.3\right)\right),{s}_{1}\right)$ |

${a}_{5}$ | $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.4\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.3\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.4\right),{s}_{2}\left(0.4\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.2\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.5\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.2\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.3\right),{s}_{2}\left(0.5\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.4\right),{s}_{2}\left(0.4\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.2\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.4\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.2\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.5\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.1\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.2\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.3\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.3\right),{s}_{2}\left(0.5\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.5\right),{s}_{2}\left(0.2\right)\right),{s}_{1}\right)$ |

${a}_{6}$ | $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.4\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.3\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.4\right),{s}_{4}\left(0.4\right),{s}_{2}\left(0.2\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.4\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.4\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.4\right),{s}_{2}\left(0.6\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.4\right),{s}_{2}\left(0.3\right)\right),{s}_{3}\right)$. $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.4\right),{s}_{2}\left(0.5\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.4\right),{s}_{2}\left(0.2\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.4\right),{s}_{3}\left(0.4\right),{s}_{2}\left(0.2\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.6\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.6\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.2\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.4\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.2\right)\right),{s}_{1}\right)$ |

${c}_{10}$ | ${c}_{11}$ | ${c}_{12}$ | |

${a}_{1}$ | $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.3\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.5\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.4\right),{s}_{4}\left(0.5\right),{s}_{2}\left(0.1\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.4\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.2\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.4\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.1\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.2\right),{s}_{3}\left(0.2\right),{s}_{2}\left(0.4\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.3\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.4\right),{s}_{2}\left(0.2\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.1\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.5\right),{s}_{2}\left(0.2\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.3\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.1\right),{s}_{4}\left(0.6\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.2\right)\right),{s}_{1}\right)$ |

${a}_{2}$ | $\left(\left({s}_{5}\left(0.1\right),{s}_{3}\left(0.6\right),{s}_{2}\left(0.3\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.3\right)\right),{s}_{3}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.1\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.3\right)\right),{s}_{2}\right)$ $\left(\left({s}_{5}\left(0.2\right),{s}_{4}\left(0.2\right),{s}_{3}\left(0.4\right),{s}_{2}\left(0.2\right)\right),{s}_{1}\right)$ | $\left(\left({s}_{5}\left(0.3\right),{s}_{4}\left(0.3\right),{s}_{3}\left(0.3\right),{s}_{2}\left(0.1\right)\right),{s}_{4}\right)$ $\left(\left({s}_{5}\left(0.3\right),{s}_{3}\left(0.1\right),{s}_{2}\left(0.6\right)\right),{s}_{3}\right)$ $(({s}_{5}\left(0.1\right),{s}_{4}\left(0.5\right),{s}_{3}\left(0.1\right),<$ |