The optimization model of whole process engineering consulting consortium members based on Z-number

J OURNAL OF M ECHATRONICS AND A RTIFICIAL I NTELLIGENCE IN E NGINEERING


Introduction
The interest distribution of relevant stakeholders is an important part of the whole process of engineering consultation in the form of a consortium.The interest distribution of all parties in the consortium is crucial to the smooth implementation of the project.Reasonable interest distribution can improve the enthusiasm of all parties for cooperation.Dissatisfaction of any party may lead to the dissolution of the consortium or the reduction of service quality [1].
Xu et al. [2] established a three-stage evaluation model for the selection of members in the design team, and conducted preliminary analysis, fuzzy comprehensive evaluation, and dynamic adjustment of candidate members.Through case studies, it has been verified that this method has strong flexibility and is suitable for various evaluation situations.Fan et al. [3] established a dual objective 0-1 model based on comprehensive consideration of personal information and collaboration ability for the screening problem of R&D team members, and applied it to an example to solve it using genetic algorithm, verifying the feasibility of the model.Watanabe et al. [4] introduced visual analysis methods into the study of member selection.Based on the collected information, they systematically analyzed the basic indicators of candidate members and visualized the evaluation process and prediction results of candidate members.Kumar et al. [5] used the fuzzy analytic hierarchy process to calculate indicator weights, combined with the decision-making method of fuzzy multi-objective optimization, established an optimization model, and obtained the ranking of candidate members.Cheng et al. [6] established a partner selection model in the supplier selection problem, with the constraints of cost, quality, completion time, and service quality in lean systems, and the goal of reducing time consumption.
In summary, research on the selection of consortium members in supply chain, transportation, virtual enterprises, and other fields is extensive and in-depth.However, the acquisition of decision-making information lacks judgment on the reliability of information, and there is a possibility of information loss during the evaluation process.China's whole Process engineering consulting is still in its infancy.For small and medium-sized consulting enterprises to form a consortium, the lead enterprise should also establish a member selection model based on the internal characteristics and development status of the whole Process engineering consulting

The whole process of project consulting consortium member selection index system
The selection index of engineering consulting members in the whole process is screened and the index system is established.Member Member selection indicators are shown in Table 1.The meanings of specific indicators are as follows.

Index weight determination
The sequential method is a subjective weighting method.In the process of implementation, there is no need to construct judgment matrix and consistency test, and expert opinions can be fully expressed.There is no restriction on the number of indicators, and it has a good effect in determining the weight of indicators.The method firstly sorted the whole index, then compared the importance of adjacent indexes from weak to strong in pairs, and finally determined the weight of indexes by quantitative calculation by substituting the formula.3) Calculated weight.According to Eq. ( 1), the weight of the least important index is obtained, and according to formula (2), the weight of other indicators is obtained successively [6]: 3. Whole process engineering consulting consortium member selection model

Modeling idea
The leading unit of the consortium selects the best partners for the whole process engineering consulting project, which is not only conducive to the smooth development of the project, but also conducive to the smooth implementation of the whole process engineering consulting model in the form of a joint body.Therefore, in view of the principle of selecting the best members, several experts were invited to evaluate and score the indicators of the alternative members based on Z-numbers method.The weight of each indicator was calculated by the sequential method.The weight of each expert was obtained by using the information reliability part of Z-numbers combined with the entropy weight method, and the data were summarized and substituted into fuzzy TOPSIS method.The positive and negative ideal distance of each member is calculated, and the member is ranked to determine the consortium cooperative enterprises

The transformation of language variables
Language terms have fuzziness and uncertainty, which conform to the fuzzy limitation and reliability principle of Z-numbers.Studies show that language variables have the best effect between 6-10 partitions.If the score interval of language terms is too small, experts will not consider the relevant information of the evaluation object comprehensively, which will affect the accuracy of data.If the score interval of language terms is too large, experts should have high evaluation experience, evaluation efficiency, knowledge reserve and other conditions, and the amount of evaluation tasks of experts should be increased.Therefore, the 7-point conversion rule of language variables is adopted in this paper to convert the first part and the second part of Z-numbers into trapezoidal fuzzy numbers and triangular fuzzy numbers respectively.The conversion rules of language variables are shown in Table 3

Z-Numbers are converted to classical fuzzy numbers
Kang proposed a method that can approximate Z-Numbers into classical fuzzy numbers under the premise of partial loss of information, which is conducive to improving decision efficiency and practical application.Its basic thinking path is as follows: First, let  = (, ) be a Z-Number, Where A is the restrictive part, and the membership function is 1  = (,  )| ∈ 0,1 ,  is the reliability part.The membership function is expressed as  = (,  )| ∈ 0,1 ; Part  of reliability judgment is transformed according to gravity center method.You get a clear number  for a fuzzy number , As shown in Eq. (3).For triangular fuzzy numbers the results of centroid calculation formula are shown in Eq. ( 4): Then, the barycenter value  of reliability part  can be used as the weight of restriction part .Then  = (, ) can be converted into the classical trapezoidal fuzzy number  .As shown in Eq. ( 5).If the constraint part  is a trapezoidal fuzzy number, it can be expressed as Eq. ( 6):

Expert weight calculation
The initial evaluation data contains the opinions of several experts, which need to be integrated to calculate the weight of each expert opinion.The reliability part of Z-Numbers represents the degree of experts' understanding of the information of evaluation objects.It can be used to calculate the weight of experts by combining the entropy weight method with the reliability part.When an expert has a full understanding of the information of evaluation objects, the accuracy of his evaluation will be higher, so the weight of the expert will be higher.The expert weight is calculated as shown in Eqs. ( 7), (8) and (9): where  represents the weight of the  TH expert,  represents the reliability function of the  TH expert opinion,  represents the reliability value of the evaluation opinion of the  TH expert on the  TH index of the  TH evaluation object.That is, the reliability of Z-Numbers is partially clarified.There are a total of  experts,  evaluation objects and  evaluation indicators.Eqs. ( 10) and (11) were used to integrate the opinions of several evaluation experts into the evaluation matrix of alternative members: (11)

TOPSIS determines the member ordering
1) The index weight obtained by the sequential method is weighted to the evaluation matrix of alternative members, as shown in Eq. ( 12), where  represents the weight of the th index: 2) Determine the most ideal index  and the least ideal index  : When the  indicator is a benefit indicator, it is shown in Eq. ( 15).When the  indicator is a cost-type indicator, it is shown in Eq. ( 16): 3) Solve the positive and negative ideal distance.The distance calculation of two trapezoidal fuzzy numbers is shown in Eqs. ( 17) and ( 18), and the distance calculation of two trapezoidal fuzzy numbers is shown in Eq. ( 19): TH evaluation object and the positive ideal solution: 5) When sorting alternative units, the larger the  value is, the better the evaluation object is and the more it meets the selection demand of the lead unit.The largest  value belongs to the consortium partner.

Example
Currently, a design institute, as the lead enterprise, has formed a consortium to carry out the whole process of CBD construction engineering consulting project of a city business district.The design institute can provide design services and construction cost services.The project owner requires the whole process of engineering consulting services including supervision services.All submitted relevant information about their enterprises.

Determine index weight
The weight of each index is determined by the sequential method, as shown in Table 5.

Evaluation and scoring
4 industry experts are invited to evaluate A, B and C enterprises according to the 7-point scale terms, as shown in Table 6, 7 and 8.

Z-numbers transform
Z-Numbers are converted into classical fuzzy numbers, as shown in Table 9, Table 10 and Table 11.

Calculated expert weight
The reliability part of Z-numbers is clarified according to Eq. ( 7), the expert weight is calculated according to Eqs. (8) and (9), and the member selection evaluation matrix is obtained according to the index weight, as shown in Table 12.

TOPSIS calculates the rankings
Since indexes in this paper are benefit indexes, the values of positive and negative ideal solutions are treated as  .The positive and negative ideal distance of each unit in TOPSIS is shown in Table 13.The value of the alternative units is  = 0.850,  = 0.154,  = 0.625.

Conclusions
To carry out consulting work in a consortium is a necessary way to effectively promote the whole process of engineering consulting.From three aspects of team cooperation, technical ability, organization and management, the whole process of project consulting consortium member selection evaluation index system including 9 indexes is put forward.Z-numbers combined with entropy weight method were used to obtain the weight of expert opinions, and Z-Numbers fuzzy TOPSIS model was introduced to solve the ranking of alternative enterprises.The uncertainty and reliability of decision information were fully considered.Fuzzy TOPSIS was used to calculate the distance between fuzzy numbers, reducing the loss of information.It can reflect the reality well.The applicability of the model is verified by an example.The optimization model of the consortium members in the whole process of engineering consulting provides a feasible method to solve the problem of leading enterprises choosing partners.

Table 1 .
Member 1) Deterministic order relation.Suppose there are  indicators in the index system.Respectively expressed as  ,  … .Its weight is expressed as  ,  … .The importance of indicators is ranked by experts, and after ranking, it is represented by  * >  * ⋯  * .The weight is expressed as  * ,  * ⋯  * ． 2) Comparison of the importance of adjacent indicators.Expert on adjacent indicators  * and  * Compared to the importance of the evaluation, Getting the importance assignment  , =   ⁄ ( = 2,3 ⋯ , ), at the same time must satisfy  > 1  ⁄ , degree of importance.The assignments  are shown in Table2.
* is extremely important than indicator  * and Table4.

Table 3 .
Constraint language variables and trapezoidal fuzzy number conversion rules Serial number Constrains some language variables Corresponding fuzzy number

Table 4 .
Conversion rules of reliability language variables and triangular fuzzy numbers

Table 5 .
Weight of each indicator

Table 10 .
B unit classical fuzzy number

Table 12 .
Alternative enterprise member selection evaluation matrix

Table 13 .
Positive and negative ideal distances in fuzzy topsis