GONG Jun,HU Tao,and YAO Lu
Department of Management Engineering and Equipment Economics,Naval University of Engineering,Wuhan 430033,China
Abstract:To cope with multi-directional transmission coupling,spreading,amplification,and chain reaction of risks during multiproject parallel construction of warships,a risk transmission evaluation method is proposed,which integrates an intuitionistic cloud model with a fuzzy cognitive map.By virtue of expectancy Ex,entropy En,and hyper entropy He,the risk fuzziness and randomness of the knowledge of experts are organically combined to develop a method for converting bi-linguistic variable decision-making information into the quantitative information of the intuitionistic normal cloud (INC) model.Subsequently,the threshold function and weighted summation operation in the traditional fuzzy cognitive map is converted into the INC ordered weighted averaging operator to create the risk transmission model based on the intuitionistic fuzzy cognitive map (IFCM) and the algorithm for solving it.Subsequently,the risk influence sequencing method based on INC and the risk rating method based on nearness are proposed on the basis of Monte Carlo simulation in order to realize the mutual conversion of the qualitative and quantitative information in the risk evaluation results.Example analysis is presented to verify the effectiveness and practicality of the methods.
Keywords:risk evaluation,multi-project parallel,intuitionistic fuzzy cognitive map (IFCM),intuitionistic normal cloud (INC)model,warship construction.
With the expansion of combat missions and the leaping development of warship equipment,the navy requines that equipment and all types of warships must be constructed upon design completion,leading to the new normal of parallel construction of multiple projects.However,the risks are transmitted in a different way and mechanism during parallel construction of multiple warship projects.Moreover,a large number of sub-projects and processes must be accomplished simultaneously and alternately.As projects proceed,the risks are transmitted in various directions within each project and across multiple projects,such that they could amplify and spread very easily causing a chain reaction.In such a case,it is more difficult to analyze and evaluate the risk transmission path.If at any level,the risks cannot be identified or effectively controlled in a timely manner,they could cause unacceptable consequences and losses to the construction quality,schedule,and cost of warships.For instance,risks in the construction of new warships may be caused by the extensive application of new technologies,new techniques,or new materials.If these risks are not addressed during the construction of the first warship,they may be transmitted and expanded in the construction process to other warships.Meanwhile,the losses caused by these hazards may further increase due to the delayed development of detection methods for such risks.Under such circumstances,a supervisory quality authority should employ more effective evaluation methods to identify and analyze the mechanism and regularity of risk transmission in multiple projects to accurately judge and locate the main risks and vulnerable links and to enhance the capability of risk management.
Since Pritsker first proposed the concept of multiprojects in 1969 [1],many foreign scholars have engaged in the research of multi-project management.However,there are few studies on multi-project risk transmission and particularly its application in complex equipment.In China,the studies on multi-project risk transmission are represented mainly by Li et al.[2].In 2004,Li et al.put forward the concept of the project risk element for the first time,and they extensively studied multi-project risk element transmission theory [2],the multi-project risk element transmission model,and risk evaluation methods[3].They gradually developed a theoretical system for the study of multi-project risk transmission,which has been extensively explored and applied in different fields.Li et al.[2] described longitudinal and transverse risk transmission processes.The longitudinal risk transmission process happened upwards in a single project.A moment generating function was utilized to construct the longitudinal transmission model for accumulated risks subject to gain or loss.The transverse risk transmission process occurred between projects or different project nodes.Relevance analysis was carried out to build a transverse transmission model.The resulting comprehensive risk transmission model was proposed.Liu [4] defined fuzzy risk elements to represent highly subjective risk events.On this basis,Liu [4] proposed an analytic model for project chain risk element transmission and a risk sequencing method based on the possibility degree of interval numbers in order to effectively identify the variation of key risks.Li et al.[5] took into account the evaluation uncertainty and fuzziness arising from experts ’ different perceptions and experiences and put forward a VIKOR multiproject risk cluster evaluation method based on the prospect theory and cloud model.Combining the maximum deviation with the subjective weight,Li et al.[5]constructed an optimized model for solving the criteria weights,achieving higher sequencing reliability.After fully considering the randomness,fuzziness,and uncertainty of risk information,Chen [6] and Li [7] employed risk transmission theory to present,respectively,the risk prediction model based on the recurrent neural network and the evaluation method based on the similarity between fuzzy numbers.
Many studies in recent years have focused on the application of risk transmission theory for complex equipment risk evaluation.Sun et al.[8] and Wang et al.[9] utilized the graphical evaluation and review technique (GERT)and the opportunity theory to develop the uncertain random multiple parameter transmission network model as well as the evaluation and review technique model.These models can be used to analyze the occurrence mechanism for equipment risks more comprehensively.Li et al.[10] and Tao et al.[11] applied the system coupling theory and the maximum entropy method in the optimization of parameters and variables for the GERT model in order to indicate the equipment risk coupled transmission process more clearly and accurately.Sun et al.[12] built the risk transmission network model to explore the risk transmission mechanism among repairmen by conducting a simulation analysis on the factors affecting the process of risk transmission.Bai et al.[13] proposed risk transmission evaluation steps based on the fuzzy cloud model and completed refined evaluation of equipment development risks after comparing and sequencing the risk quantities obtained from comprehensive computation with the cloud model of risk factors against the twodimensional normal cloud scale obtained from the generator.In [14],causal Bayesian networks were applied in the identification of risk factors and the analysis of the risk transmission mechanism.On this basis,a quality risk evaluation method was proposed for complex equipment based on the cloud model and the influence diagram.The method can illustrate the quality risk transmission process of complex equipment in practice.By classifying and calculating different coupling relationships of risks,it can facilitate identification of key factors and nodes affecting the quality hazards.
These studies on risk transmission have limitations as follows: (i) there are no methods directly applicable to the analysis and evaluation of the risk transmission path in the production process of large complex weaponry and equipment under multi-project conditions;(ii) the risk transmission models based on GERT and the influence diagram request that the system,equipment,or component failures are subject to normal distribution,which restricts their promotion and application to some extent;and (iii) the process of integrating the risk evaluation information given by experts on the basis of experience and past data cannot effectively resolve the problem that accurate membership is unable to represent fuzzy matters thoroughly,which significantly undermines the precision and accuracy of risk evaluation.In the meantime,the conventional risk rating method uses the rough scale of classification and overlooks the fuzzy and uncertain boundary of risk evaluation,making it difficult to qualitatively identify the aggregated risk information.
Addressing this situation,this paper builds a risk transmission model for the multi-project parallel construction of warships based on an intuitionistic fuzzy cognitive map (IFCM);proposes conversion methods and operation rules of bi-linguistic variables and the intuitionistic normal cloud;and develops an algorithm for solving the model.On this basis,a risk comparison and rating method is presented following the ideas of Monte Carlo and nearness to develop multi-project parallel construction risk transmission evaluation methods for warship manufacturing.This paper not only enriches the theoretical system of multi-project risk evaluation but also provides guidance for the quality supervision department’s effective risk analysis of multi-project parallel construction.
2.1 Risk in multi-project parallel construction of warships
The multi-project parallel construction of warships is affected by a variety of complicated risk events.They occur at different probabilities and cause consequences of different severity levels.Moreover,they affect each other within a project and across projects.Risk events must be attributed to the joint effect of multiple hazard factors.If risk factors are addressed in the risk analysis and evaluation,the analysis will be more complicated and difficult,and the accuracy of hazard evaluation will be undermined.For this reason,risk factors are unsuitable for the risk evaluation of large weaponry equipment such as warships.Risk events are therefore closely examined in this paper.
The risk in multi-project parallel construction of warships means that all kinds of risk events caused by technology,management,resources,and the environment during the multi-project parallel construction of warships could lead to consequences and losses including unacceptable construction quality,delayed scheduling,and cost increase,which affects the multi-project objectives [14].The form of function is represented as follows:
whereRis the value of risk influence;Pis the probability of risk event;andCis the risk loss that may be caused by some consequences arising from the risk event.The risk loss may be related to qualityCQ,scheduleCS,or costCP.
2.2 Bi-linguistic variable and its definition
The traditional evaluation of linguistic variables often uses mono-linguistic variables.This implies that the membership of an evaluation result to the evaluated information is 1,making it difficult to demonstrate how well a decision-maker is certain about and confident in the judgment.Moreover,it is also difficult to quantitatively describe such certainness in an accurate way.Therefore,some scholars put forward the concept of the bi-linguistic set.A bi-linguistic set contains a pair of linguistic information.One piece of information describes the evaluation result given by the decision-maker following specific criteria and reflects the fuzziness and randomness of the evaluation object.The other piece of information describes the confidence level for such evaluation result and indicates the membership of linguistic scalar.The bilinguistic variables could be used to better represent all kinds of uncertain,fuzzy,incomplete,and complex information and to make the evaluation result closer to the actual condition for higher accuracy.
Definition 1 [15]is a bi-linguistic set in the finite domainX,and,wheresθ:X→S,xsθ(x)∈S,hσ:X→H,xhσ(x)∈H.Two ordered linguistic scales areSandH;the linguistic evaluation ofxissθ;andhσ(x)is the linguistic membership tosθ.During the process of actual evaluation,the suitable linguistic scales may be selected to beSandHaccording to actual needs.
2.3 Fuzzy cognitive map (FCM)
The FCM was proposed by Kosko in 1986 after integrating Zadeh’s fuzzy set theory and Axelord’s cognitive map,expanding the three-valued relationship of the two concepts into the fuzzy membership relationship in [-1,1][16].An FCM utilizes directed arc,node,state value,and other elements to describe and express their causal relations and mutual effects with the concepts or nodes in the network system.It can effectively combine qualitative reasoning and quantitative expression by constructing the reasoning network and conducting the simulation,reasoning,and prediction of the network system based on the existing knowledge and expert experience.Compared with neural networks and other reasoning methods,FCM has a reasoning process and knowledge expression closer to the cognitive manner of human beings,so it is strongly semantic and greatly capable of involving expert opinions and processing fuzzy information [17].
2.4 Intuitionistic normal cloud
2.4.1 Operation rules of intuitionistic normal cloud
Among the cloud models,the normal cloud is most universal and its random membership to the distribution in the corresponding domain shows the characteristic of normal distribution.Nevertheless,the normal cloud model cannot handle the non-membership and hesitation of some concepts.On the basis of the normal cloud,Yang et al.[15,18] proposed the intuitionistic normal cloud (INC)model.The probability theory,the fuzzy set theory,and other basic principles were alternately applied to design the algorithm for efficient integration of qualitative concepts such as fussiness,randomness,and hesitation.At present,the bi-linguistic decision-making method based on the INC model has been successfully applied in various fields.
Definition 2[18] IfU={x} is set as a quantitative domain denoted by a certain value,andCis a qualitative concept in the domainU,the INC corresponding toCinUisY=(〈Ex,ρ,ν〉,En,He),where three numerical characteristics Ex,En,and He denote the expectancy,entropy,and hyper entropy,respectively.It is used to quantitatively reflect the overall characteristic of the qualitative concept.Moreover,ρ and ν indicate membership limit and non-membership limit,respectively,representing the upper limit and lower limit of the possible value for the corresponding membership atx=Ex.
The positive real number λ is given,and the INCs in the domainUareY1=(〈Ex1,ρ1,ν1〉,En1,He1) andY2=(〈Ex2,ρ2,ν2〉,En2,He2).Following the calculation principles of cloud model and intuitionistic fuzzy number and the operation rules of INC based on [18-20],the results are given in Table 1.⊕ is the addition of the cloud,and⊗is the multiplication of the cloud.
Table 1 Aggregation operation of intuitionistic normal cloud
2.4.2 INC ordered weighted averaging operator
Definition 3If there is a set of INCsYi(i=1,2,···,n)with the IN C ordered weighted averaging (INCOWA)operator Ωn→Ω,
The multi-project parallel construction of warships is affected by a variety of complicated risk events.The risk events have different probabilities of occurrence and cause consequences of varying severity levels.The risk events affect each other within each project and across projects.Risk events must be attributed to the joint effect of multiple risk factors.If risk factors are addressed in the risk analysis and evaluation,the analysis on risk transmission will be more complicated,making it more difficult for experts to conduct.Additionally,the calculation will increase exponentially,which affects the accuracy of evaluation.For this reason,risk factors are unsuitable for the risk evaluation of large weaponry equipment,such as warships.In the process of risk identification,the risk events in each project are taken as the basic elements.Experts comprehensively take into account the mutual effect of risk factors while analyzing the transmission of risk events.
Risk evaluation requires the collection,conversion,and processing of basic data.While building a risk transmission model for the multi-project parallel construction of warships,the experts are required to qualitatively determine the probability for occurrence of each risk event as well as the losses caused thereby and the degree of coupling,based on their experience and prior data.Meanwhile,these events and factors are fuzzy and stochastic.At the time of grading,the experts may hesitate with regard to the given evaluation information.Hence,risk evaluation is preconditioned on determining the specific form in which qualitative linguistic information can be obtained from experts and how it can be accurately converted into quantitative information for scientific processing.
The INC model may be used for conversion between qualitative and quantitative uncertainties regarding linguistic values and their denotations to efficiently integrate fuzziness,randomness,and hesitation.If the qualitative linguistic information of experts can be converted into the INC,it could effectively resolve the inability of the accurate membership to represent risks and relevant information thoroughly.This could further enhance the accuracy of risk evaluation.Meanwhile,experts should present risk evaluation information in the form of the bilinguistic variable=〈s,h〉 to ensure the best compliance of such information with personal cognitive processing and actual conditions,to lower the difficulty of risk evaluation,and to facilitate accurate conversion of linguistic information into the INC model.
To convert the bi-linguistic variable decision-making information of the experts=〈s,h〉 into the quantitative information of the INC modelY=(〈Ex,ρ,ν〉,En,He),the method for the linguistic information conversion of risk evaluation is proposed as follows:
(i) Completing the conversions→(Ex,En,He) with the golden section search method
The golden section search method could be used to accurately and conveniently convert the qualitative linguistic information of the experts into the quantitative information of the INC model.Its basic principles [16] are as follows: the interval [Xmin,Xmax] is equally divided into two parts.Among them,n′is the number of linguistic scales inS.In the interval,n′clouds are generated in correspondence with the linguistic scales.IfY0(Ex0,En0,He0) is the cloud in the middle,the neighboring clouds areY-1(Ex-1,En-1,He-1),Y+1(Ex+1,En+1,He+1),Y-(2(Ex-2,En-2,He-2),Y+2(Ex+2,) En+2,He+2),( ···,Y-(n-1)/2Ex-(n-1)/2,En-()n-1)/2,He-(n-1)/2,andY+(n-1)/2Ex+(n-1)/2,En+(n-1)/2,He+(n-1)/2.
The golden section search method is originated from the division of the line segment.The two ends of the line segment are set as Ex of the previous cloud and the next cloud.Moreover,Ex of the next cloud is close to 0.382 times the value of the line segment of the cloud in the middle.For the previous and subsequent clouds,the ratio of En and He is 0.618.In this way,the numerical characteristics of the clouds can be generated.
(ii) Completing the conversionh→(ρ,ν)
InH={h1,h2,···,hk′,···,hn′},n′is the number of linguistic scales inH.The linguistic membership variablehk′should be converted into a membership interval(ρk′,νk′) .The linguistic scales inHare evenly distributed,so the corresponding membership range could be divided inton′intervals.Then,there is [21]
These two steps are taken to complete the collection and conversion of the basic data for risk evaluation.
On this basis,we obtain: (i) the influence of quality risk,schedule risk,and cost risk when the risk events in the project β happen;and (ii) the overall risk influence.Hence,a risk transmission model for multi-project parallel construction of warships should be built for quantitative analysis of risk transmission.
4.1 Construction of risk transmission model
After the INCOWA operator is defined,the threshold function in the traditional (FCM) is transformed into INCOWA by virtue of weighted summation to obtain the risk transmission model based on the IFCM.
Definition 4IFCM is a quaternary ordered group:
Fig.1 Schematic diagram of IFCM topology
4.2 Algorithm for solving the model
During multi-project parallel construction of warships,the occurrence probability and influence of the risk events are considered in the process of risk evaluation [23].This paper intends to verify the calculation of the data in the risk transmission process.For convenience of calculation,it is assumed that the risk events have the same weight.At this time,I NCOWAλdegenerates into I NCAAλ,and there is the following:
The risk events clearly have mutual effect by virtue of the causal relationship reflected in the directed arc.Each risk event imposes influence on another risk event by virtue of the directed arc and is,in turn,influenced by another risk event,which eventually leads to dynamic conversion of those risk events.In the IFCM model,the time variable is introduced into both the occurrence capability of the risk events and the correlation between the risk events,so that the real-time dynamics of the entire system can be demonstrated in the reasoning process.
4.3 Steps for solving the model
Based on the IFCM model and the algorithm for solving it,the following steps are taken to solve the model:
These steps are taken to build the risk transmission model for multi-project parallel construction of warships by converting the initial occurrence probability of the risk events of multiple projectsinto the actual occurrence probability of those risk events whose mutual effect is taken into account.
In the above steps and calculation of the risk transmission model,the mutual effect and correlation of the risk events in each project and among multiple projects are fully considered to provide the data and methodological guarantee for accurate calculation of the risk influence.
5.1 Steps for calculating the risk influence
After obtaining the actual occurrence probability of the risk events in each projectfrom the risk transmission model,the corresponding data,including quality loss,schedule loss,and cost loss,must be integrated.
Step 1Integrate the data of risk losses given by experts.
From (8) and Table 1,the following equation is obtained to effectively integrate the data of quality lossschedule loss,and cost lossas given by the experts:
5.2 Risk comparison and rating
5.2.1 Risk influence comparison method
Definition 5[21] For this purpose,(x,o) is a cloud droplet in the INC;z=xois one score of the droplet for the conceptV,andzadjusts dynamically to the change of(x,o) .Ifis set as the mathematical expectancy ofz,zis the total score of the cloud for the conceptV.WhenY1andY2are set as two clouds in the same domain,if their total scores have≥,there isY1≥Y1.
For risk evaluation in the multi-project parallel construction of warships,the influence of the risk events at all levels belongs to the INC information.The regularity of risk occurrence is often inconsistent with the common probability distribution function,so that the dropletzin the INC information is not subject to the common probability distribution function either.For this reason,it is difficult to analyze and determinezˆ.Following the idea of the Monte Carlo simulation,a computer program can be employed to obtain enough droplet samples by virtue of the droplet generation algorithm for the INC [21].Based on the statistics of these samples,the estimation ofzˆ can be obtained.In this way,many droplet samples (N) are generated.The average value of these samples is taken as the optimal estimation ofzˆ and as the criterion for risk rating and influence sequencing.The calculation ofzˆ is as follows:
Based on Definition 5 and the preceding equation,the influence of the risk events represented by two INCs can be compared.
5.2.2 Risk rating method
It is assumed thatRd=(〈Exd,ρd,νd〉,End,Hed) represents the risk influence of the risk events to be rated.The risks are categorized intot′levels from low to high,that is,f1,f2,···,ft′.The steps of risk rating are as follows:
6.1 Data collection and conversion for risks during shipway construction
The shipway is the most important production facility of a shipbuilder.Shipway construction involves the largest number of projects in parallel construction,the most difficult organization of construction activities,and the largest amount of manpower and resources.Because of the cross operation of numerous processes,all kinds of risks may be transmitted in various directions along with the progress of projects,which could easily expand,conceivably causing chain reactions.In a case with four projects in parallel construction,it is urgent that the quality supervision department analyzes and evaluates the quality,schedule,and cost risks before shipway construction begins.
For this purpose,three experts are invited to classify the risks in terms of cause while considering the actual progress of warship construction.The risk events were classified into nine distinct risk variables: technical state changeA1,new technology applicationA2,technical indicatorA3,plan conflictA4,inspection and acceptanceA5,onsite managementA6,personnel arrangementA7,equipment and materialsA8,and site conditionsA9.The risk events identified in Projects 1-4 are given in Table 2,wherestands for the risk eventAin Projectj.
Table 2 Results of risk identification
Three expertse={e1,e2,e3} are asked to evaluate the initial probability of the risk events as well as the quality,schedule,and cost losses caused thereby.According to the actual condition of the task,the weight vector of the experts is determined to beq={0.3,0.4,0.3},and the weight of Projects 1,2,3,and 4 is{α1,α2,α3,α4}={0.35,0.25,0.20,0.10}.This is now illustrated with the process of converting the initial occurrence probability of the risk.The bi-linguistic evaluation information given by the three experts on the initial occurrence probability of the riskis as follows:
It is assumed that the five-scale method is employed to describe the probability and consequence levels of the risk events in this paper.The given interval is [0,1],and He0=0.01.The numerical characteristics of clouds are calculated with the golden section search method to obtain the cloud model for the correspondence between linguistic evaluation scale and semantic information,as shown in Table 3.
Table 3 Cloud model for the correspondence between linguistic evaluation scale and semantic information
Based on the conversion methodh→(ρ,ν),the linguistic membership scale description is obtained,as shown in Table 4.
Table 4 Linguistic membership scale description
6.2 Risk transmission evaluation
After the data of risks is collected and converted,the risk transmission model for shipway construction based on the IFCM is built using Table 2.The topology of IFCM is shown in Fig.2.
Fig.2 Schematic diagram of IFCM topology during the shipway construction
Following Steps 1-5 in Subsection 4.3,the initial occurrence probabilityof the riskin each project is input into the Matlab for simulation to obtain the actual occurrence probability of.For instance,the actual occurrence probability ofis=(〈0.882,0.532,0.901〉,0.040,0.010).
It is assumed that the risk events have the same weight.Steps 1-3 in Subsection 5.1 are taken to determine the influence of the risk events on quality,schedule,and cost as follows:
The risk rating method in Subsection 5.2.2 is employed to convert the linguistic information of the risk levelsf1f2,···,f5into the quantitative information of the normal cloud modelYl,respectively.Using Table 4,Ylis then converted into the INC information when the experts have the highest level of confidence in the evaluation results=(〈Exl,0.667,1〉,Enl,Hel).Based on Monte Carlo simulation,we takeN=10 000,generateNdroplet samples of,and solveto obtain the risk rating results as given in Table 5.
Table 5 Risk rating based on Monte Carlo simulation
Based on Table 5 and the influence of the risks at different levels,theand level of the risks are determined as given in Table 6.
Table 6 Risk levels
The cloud model for overall risk evaluation is as given in Fig.3 withXandOas the coordinate axes of the droplet (x,o).
Fig.3 Cloud model for overall risk evaluation
6.3 Comparison and discussion
6.3.1 Analysis of calculation results
The quality supervision department sequences the risk events above Level 3 in Table 6 to be controlled in particular.The risks with higher influence on the quality are sequenced from high to low as follows:A1,A3,A6,A8,andA5.The risks with higher influence on the schedule are sequenced from high to low as follows:A3,A1,andA6.The risks with higher influence on the cost are sequenced from high to low as follows:A3,A4,andA6.The overall risk influence is Level 3.Hence,the quality supervision department should strengthen the supervision and control over those risks above Level 3 during the construction of warships,particularly the risksA1andA3.
As revealed in Fig.2,the risksA1andA3are transmitted in each project and between projects.To verify the influence of risk transmission,the initial occurrence probability and actual occurrence probability ofA1andA3in Project 1 are comparatively analyzed in the simulation,as shown in Fig.4 and Fig.5,where the left cloud model represents the initial occurrence probability,while the right cloud model indicates the actual occurrence probability.Clearly,the risks are spread and amplified to cause a chain reaction because of the longitudinal risk transmission.The occurrence probability in the simulation of the risksincreases from 0.158 and 0.168 to 0.162 and 0.205,respectively.The actual occurrence probabilities of the riskA1in Project 1 and Project 2 are compared,as shown in Fig.6.As revealed in the figure,has a higher actual occurrence probability thanbecause of the risk transmission between the projects,and the occurrence probability in the simulation of the risksincreases from 0.158 to 0.181.Hence,particular attention should be paid to the transmission and coordination of other risks withA1andA3,based on Fig.2,while strengthening the supervision and control of the main risks.
Fig.4 Comparison of initial and actual occurrence probabilities of
Fig.5 Comparison of initial and actual occurrence probabilities of
Fig.6 Comparison of actual occurrence probabilities of and
Table 7 Scoring statistical results
Table 8 Results of 20 simulations
Fig.7 Cloud model for resource risk evaluation level
6.3.2 Comparative analysis of methods
(i) Comparison without considering risk transmission
As revealed in Figs.4-6,the risks are indeed transmitted extensively within and among projects,which increases the occurrence probability of risks to different degrees.If risk transmission is not considered,the evaluation results will become inaccurate.Hence,the risk transmission evaluation method proposed in this paper allows the quantitative analysis of risk transmission under the parallel conditions of multiple projects,which provides the data and methodological support for risk management.The proposed method demonstrates significant advantages over traditional risk evaluation methods that ignore such transmission.
(ii) Comparison without considering linguistic membership
To prove the superiority of bi-linguistic information,the information on the linguistic membership revealing the confidence level of evaluation results is deleted from the comments given by experts.Assuming that the corresponding value ofiswhen the linguistic membership is not considered.The simulation is then carried out with the data when the model and other conditions remain unchanged.Table 9 shows thatincreases to different degrees when the linguistic membership is not considered.This causes the variation of risk level judgment.It clearly reveals that the bi-linguistic evaluation method considering the linguistic membership of experts can better tolerate the uncertainties from different sources in the process of evaluation than the traditional evaluation methods.Moreover,it effectively integrates fuzziness,randomness,and hesitation.When an expert has insufficient confidence in his personal comment,his influence on the overall evaluation result can be lowered in the process of integrating linguistic information,in order to make the evaluation result more authentic and reliable.
Table 9 Comparison of risk levels without considering linguistic membership
(iii) Simulation comparison of risk transmission model
The influence diagram of risk transmission in Section 5 of [14] is taken with its algorithm (hereinafter referred to as Method 1) to compare with the proposed method.To ensure effectiveness,the bi-linguistic information in the example and its operation rules are taken as the inputs for calculation.For example,the occurrence probability ofis calculated with Method 1 to be=(〈0.862 2,0.492,0.895〉,0.032,0.009).Following Steps 1-5 in Subsection 4.3,the initial probability ofis input into the Matlab for simulation to eventually obtain the occurrence probability=(〈0.882,0.532,0.901〉,0.040,0.010).The simulation process is shown in Fig.8 withNas the number of simulations.Obviously,the risk events affect each other at the beginning of simulation,so that the values of elements in the intuitionistic normal clouds increase dynamically.After 25 iterations,the values become stable.Since Method 1 requires no simulation or deduction,the calculated values of the elements inare closer to the initial values obtained with the proposed method.
Fig.8 Simulation of occurrence probability
The risk values are calculated and presented in Table 9 wheredecreases to different degrees.Clearly,the risk transmission model based on the IFCM has stronger data reasoning and calculation capability than Method 1.Through the mutual effect and impact of nodes in the entire network,it can simulate the risk transmission process more vividly.In the meantime,it can enhance the utilization efficiency of expert knowledge,achieving effective integration of qualitative reasoning and quantitative expression,while providing higher calculation capability and greater flexibility.
Table 10 Comparison with Method 1
(iv) Risk comparison and rating method
The bi-linguistic method is a new concept.It may not be pragmatically meaningful to compare its evaluation results with the existing risk evaluation methods.However,the proposed method for risk comparison and rating is quite significantly superior.Firstly,Table 7,Table 8 and Fig.7 reveal the high degree of effectiveness and stability of the proposed method as well as the firm reliability of its data.Secondly,the proposed method can be used not only for risk evaluation and rating but also to scientifically sequence the risks at the same level.
(v) Application
The risk transmission evaluation method proposed in this paper requires a complicated calculation.As revealed in the study results,the proposed method can effectively overcome the inaccuracies in the identification of major risks and vulnerable aspects,while providing guidance to the Military Representative Office for more effective analysis of contract performance risks.
During the multi-project parallel construction of warships,all kinds of risks could very easily undergo multidirectional transmission coupling,spreading and amplification,and chain reactions.For this reason,a risk transmission evaluation method is put forward for the multiproject parallel construction of warships.First of all,a method is proposed to convert the bi-linguistic variable decision-making information into the quantitative information of the INC model.The method can aid experts in their efforts to provide the most suitable risk evaluation information based on personal cognition and actual conditions.Moreover,it effectively resolves the problem that accurate membership cannot represent the risks and their relevant information thoroughly,so as to further enhance the accuracy of risk evaluation.Secondly,the threshold function and weighted summation operation in the traditional fuzzy cognitive map is converted into the INC ordered weighted averaging operator.The risk transmission model based on the IFCM is put forward together with the algorithm for solving it.With the benefit of knowledge representation and the mechanism of logical reasoning,the model can facilitate the analysis and evaluation of the risk transmission path during the multi-project construction of warships.Additionally,it can improve the utilization efficiency of experts’ intuitionistic fuzzy information and offer higher calculation capability and flexibility.Thirdly,the risk influence sequencing method based on INC and the risk rating method based on nearness are put forth to achieve the mutual conversion of qualitative and quantitative risk evaluation results.Moreover,it resolves some problems of the conventional rating methodR=P×C,such as using the rough scale of classification and overlooking the fuzziness and uncertainness of the evaluation boundary.Example analysis is conducted to verify the effectiveness and practicality of the methods.While there remains some difficulties in the application of the model and methods proposed in this paper in the accurate calculation for nonlinear risk coupling and transmission and their dynamic changes,this will be addressed in future research.