FUZZY DECISION MAKING METHOD BASED ON COCOSO WITH CRITIC FOR FINANCIAL RISK EVALUATION

. The financial risk evaluation is critically vital for enterprises to identify the potential financial risks, provide decision basis for financial risk management, and prevent and reduce risk losses. In the case of considering financial risk assessment, the basic problems that arise are related to strong fuzziness, ambiguity and inaccuracy. q-rung orthopair fuzzy set (q-ROFS), portrayed by the degrees of membership and non-membership, is a more resultful tool to seize fuzziness. In this article, the novel q-rung orthopair fuzzy score function is given for dealing the comparison problem. Later, the $ and % operations are explored and their interesting properties are discussed. Then, the objective weights are calculated by CRITIC (Criteria Importance Through Inter-criteria Correlation). Moreover, we present combined weights that reflects both subjective preference and objec-tive preference. In addition, the q-rung orthopair fuzzy MCDM (multi-criteria decision making) algorithm based on CoCoSo (Combined Compromise Solution) is presented. Finally, the feasibility of algorithm is stated by a financial risk evaluation example with corresponding sensitivity analysis. The salient features of the proposed algorithm are that they have no counter-intuitive case and have a stronger capacity in differentiating the best alternative.


Introduction
Financial risk refers to the possibility that the ultimate financial results achieved by a company in a specified time and within a specified range out of line with the desired business goal due to multiple uncontrollable and unpredictable factors in diverse financial activities, thus resulting in economic losses or greater profits for the enterprise. The financial activities of a company are throughout the all course of operation and production. Raising capital, making long-and short-term investments, and distributing profits may all bring risks. Financial risk is a practical issue that companies must confront in the financial management process.
Financial risks are objective that enterprise manager only takes efficient ways to lower risks and not completely eliminate risks. In today's world, it is not uncommon for companies to fail or go bankrupt due to financial risks, even very large enterprises such as Enron, one of the Fortune Global 500 companies in 2002. Therefore, ignoring financial risks will bring us serious consequences.
Financial risk indicators are financial analysis methods based on broad-based financial activities, from the perspective of dynamics and long-term, setting sensitive financial indicators and observing their changes, and monitoring and forecasting financial risks that the company may or will face. It is the unification of financial indicators and financial early warning models. The former is the embodiment of the financial evaluation system of the enterprise to report the financial risk. The latter is based on the combination of multiple financial indicators, select multiple enterprise samples, establish a multi-variable mathematical model, and conduct a more comprehensive and in-depth analysis of enterprise financial risk, which has the value of macro analysis. The aim of analyzing financial risk indicators is to recognize underlying financial risks of companies by setting financial risk warning and warning index on the basis of detecting the financial status and financial results of enterprises, so as to provide decision basis for financial risk management, and prevent and reduce risk losses. The design principles of financial risk indicators are mainly shown in Figure 1.
In the process of financial risk evaluation (FRE), enterprises are assessed by professional with diverse financial risk indicators can be treated as MCDM (multi-criteria decision making) issue. To evaluate the financial risk of enterprises' performance, diverse effective methods have already been developed. Duan (2019) employed the deep neural networks for assessing and predicting the assessment of financial system. Gerrard et al. (2019) developed a simple communication tool for enabling financial risk of the optimal investment profile. Goda and Tesfamariam (2019) presented the financial risk assessment of buildings in Victoria and Montreal. Nevertheless, these scholars only consider the entire evaluation of financial risk, but fail to consider individual evaluations (assessments of financial risk over diverse indicators). Also, for assessing the financial risk of enterprise, there exists much indeterminate and inconclusive information. Under such environment, the chief financial officer (CFO) Figure 1. The four principles of financial risk indicators Financial risk indicators make decisions with a strong capability in differentiating the best alternative. In addition, the uncertainty of assessing the financial risk of enterprise decides that the CFO fails to provide the pinpoint preference information if they face with various options. While some existing theories such as intuitionistic fuzzy set (IFS) (Atanassov, 1986), and Pythagorean fuzzy set (PFS) (Yager, 2014) have been employed in imitating fuzziness. The above theories possess their intrinsic shortcomings and restrictions (Peng & Selvachandran, 2019).
Lately, q-rung orthopair fuzzy set (q-ROFS), initially developed by Yager (2017), has been served as a resultful means to depict fuzziness in MCDM issues. The q-ROFS is portrayed by the degrees of membership and non-membership, whose sum of the corresponding qth power is less than or equal to 1. It is easy to understand that as the rung q increases, the corresponding acceptable orthopairs space increases, which more orthopairs meet the limited condition. That is to say, the q-ROFS is generic form because IFS and PFS are both its particular form. Consequently, q-ROFS is more appropriate and befitting for the indeterminate environment. In view of such advantage of the q-ROFS, it is fast becoming a hot study topic, containing aggregation operators, information measure, decision making methods and calculus.
-Aggregation operators: In 2018,  developed two q-rung orthopair fuzzy aggregation operators (q-ROFAO) for aggregating the assessment values of potential companies. Xing et al. (2019) brought point operators into q-ROFAO , which can make them more flexible in the decision process. Peng et al. (2018) presented novel aggregation operators (AOs) based on novel exponential operational law under q-rung orthopair fuzzy (q-ROF) environment. For considering interrelationships between criteria, the Bonferroni Mean (BM) operator (Bonferroni, 1950) is taken into consideration by combining the q-ROFS (Liu & Liu, 2018;Liu & Wang, 2018b;Yang & Pang, 2019). Moreover, the Maclaurin symmetric mean (MSM) operator (Laurin, 1729) and Heronian mean (HM) operator (Beliakov et al., 2007) are also resultful approach to seize the correlation among the multi-input arguments, which have been applied them in combining the advantage of q-ROFS (Wei et al., 2019;. Further, Wang et al. (2019) explored a more general form of Muirhead means (MM) operator (Muirhead, 1902) into q-ROF environment that the AOs Liu & Liu, 2018) can be their special cases. -Information measures: Liu et al. (2019) developed cosine similarity measures and distance measures based q-ROFS. Du (2018Du ( , 2019 proposed q-rung orthopair fuzzy distance measures, correlation and correlation coefficient with Minkowski-type and proved their interesting properties. Peng and Liu (2019) explored the scientific transition of information measure (distance measure, entropy, similarity measure, inclusion measure) for q-ROFS, and proposed some new formulae for q-rung orthopair fuzzy information measure. Moreover, they successfully applied q-rung orthopair fuzzy similarity measure to medical diagnosis, clustering analysis and pattern recognition. -Decision making methods: In addition to the AOs Xing et al., 2019) and information measures Du, 2018) mentioned above can be employed in integrating the entire preference information.  presented a MCDM method for disposing of heterogeneous relationship among criteria with uncharted weight information under q-ROF environment.  developed a q-rung orthopair fuzzy TODIM (TOmada de Decisao Interativa e Multicritevio) method based on prospect theory for achieving the optimal green supplier. Peng and Dai (2019) explored the q-rung orthopair fuzzy decision making method based on CODAS (combinative distance-based assessment) and multiparametric similarity measure, and successfully applied them in assessing the classroom teaching quality. -Calculus: Ye et al. (2019) defined the notion of q-rung orthopair single variable fuzzy function (q-ROSVFF) for depicting the fuzzy continuous information. Gao et al. (2019) explored derivatives, continuities and differentials of q-ROSVFF. Shu et al. (2019) presented q-rung orthopair fuzzy definite integrals (q-ROFDIs), constructed the q-ROFDIs, gave their specific values, and discussed their integrability criteria through two perspectives. Figure 2 illustrates the top 5 application fields of q-ROFS. In Figure 2, the fields of colored rectangles show the numbers of applications with q-ROF environment. As can be seen, the most popular application fields are computer science, science technology other topics, and mathematics.
When we handle some q-rung orthopair fuzzy MCDM problems, there are four deficiencies, which form our incentives.
1. The existing AOs Xing et al., 2019) employing in solving MCDM issues have counter-intuitive cases (Peng et al., 2018) and low discernibility degree in differentiating the best alternative. It may be unmerited or impracticable for decision makers (DMs) to select optimal alternative. The CoCoSo (Combined Compromise Solution) method, firstly developed by Yazdani et al. (2018), is an adaptive algorithm to dispose the information in a logical and viable way. Consequently, the 1st incentive is to handle the MCDM problems by presenting novel algorithm without two defects above.   Peng et al., 2018;Peng & Dai, 2019) cannot precisely rank the q-ROFNs in some special cases. Moreover, we can see that the score functions Peng & Dai, 2019) cannot think the impact of hesitation case, which indicates that the corresponding information is incomplete. Consequently, the 2nd incentive is to bring a novel score function that to consider the hesitation case. 3. The existing q-ROF weighting determining methods only think objective weight  or subjective weight Xing et al., 2019). The subjective weight is offered by DMs while they neglect the weight information transmitted by the evaluation matrix. However, the objective weight can be achieved from the evaluation matrix by some effective methods while they cannot consider the DMs' preference information. How to integrate them is a hot topic . Consequently, the 3rd incentive is to bring the combined weight model that to consider both subjective preference and objective preference. 4. The existing operations (Yager, 2017) on q-ROFS are not affluent and their relations are not well discussed. Moreover, some operations (Peng et al., 2018) such as $, % are so complex and many limit conditions, which is hard to deal with decision data. Consequently, the 4th incentive is to present more q-ROF operations and also explore their wonderful relations. Based on the above four incentives and the character of financial risk evaluation, this article presents new q-ROF MCDM method. The innovations of the proposed method is listed in the following.
1. The novel q-ROF financial risk decision making method based on CoCoSo is developed, which can achieve the best alternative out of counter-intuitive case and have a strong capacity in differentiating the most desired alternative. 2. The novel q-ROF score function is developed, which consider the hesitation case that lowering the evaluation information losses. In addition, some desired theorems are explored. 3. The combined weight method is based on CRITIC (Criteria Importance Through Inter-criteria Correlation) and the linear weighted comprehensive method that to simultaneously consider subjective information and objective information. 4. Novel revised operations ($ and %) and their affluent relations are given and proved, respectively. To process our discussion, the remainder of this article is listed as follows: Section 1 reviews the basic notions of q-ROFS. In Section 2, the novel q-ROF score function is presented and its affluent relations are proved. In Section 3, the novel q-ROF operations are presented and explored. In Section 4, we present a new q-ROF financial risk decision making method based on CoCoSo with CRITIC, and the sensitive analysis is shown. In Section 5 gives numerical examples to state the effectiveness of developed algorithm. In last section, some conclusions are derived.

Preliminaries
This section chiefly reviews the notions of q-rung orthopair fuzzy set (q-ROFS).
Definition 1 (Yager, 2017). Let X be domain of discourse. The q-ROFS A in X is expressed as where denote the degrees of membership and nonmembership of the element x ∈ X to the set A, respectively. Its limited condition must meet For simple, Yager (2017) defined a = (m, n) as q-rung orthopair fuzzy number (q-ROFN).

A novel q-rung orthopair fuzzy score function
This section reviews some existing score functions Peng et al., 2018;Peng & Dai, 2019), discusses their drawbacks, and presents a novel score function by taking hesitant attitudinal into consideration.

Some existing q-rung orthopair fuzzy score functions
Assume that a q-ROFN is expressed by a = (m, n), where m, n denote for the pro and con, respectively.  presented the following score function.
where S liu (a) ∈ [-1, 1]. It can be easily seen that the bigger the S liu (a) is, the larger the q-ROFN is.

Example 1.
Given that a = (0.4, 0.4) and b = (0.5, 0.5). If we employ score function S liu  to choose the largest q-ROFN, we can have S liu (a) = S liu (b) = 0. Therefore, we can't differentiate the discrepancy, which reveals that such score function fails to rank in such condition. Notice the drawbacks , they presented the definition of accuracy function: Remark 2. If q = 1, it degrades into H hc (a) = m + n (Hong & Choi, 2000); If q = 2, it degrades into H peng (a) = m q + n q (Peng & Yang, 2015).
The score function S liu can precisely rank the common alternatives. Nevertheless, Peng et al. (2018) discovered that score function S liu and accuracy H liu fail to take the impact of hesitance into consideration, which means that the potential information will not be integrated. So they presented a new score function in the following.
It also can be found that the score function (Peng et al., 2018) also confronted the same case when m = n. In other words, S px will degrade into S liu .
Moreover, Peng and Dai (2019) proposed another score function ( ) p S a λ , which also take the influence of hesitation into consideration.

The novel score function
Definition 4. For any q-ROFN a = (m, n), the novel score function can be denoted as Theorem 1. For any q-ROFN a = (m, n), S pxd (a) monotonically increases and monotonically decreases when the increase of m and n, respectively.
Proof. By means of the Eq. (6), we have corresponding first partial derivative of S pxd (a) with m,  Similarly, we can obtain the corresponding first partial derivative of S pxd (a) with n, Theorem 2. For any q-ROFN a = (m, n), the new score function S pxd (a) abides by the following relations.
Proof. According to Theorem 1, we will find that S pxd (a) monotonically increases and monotonically decreases when the increase of m and n, respectively.
To test the effectiveness of the introduced score function S pxd , Table 1 displays a comparison among the ranking results achieved by the developed score function S pxd and the conditions of the existing score functions induced by S liu , p S λ λ = and S px (The red background color presents illogical results and the blue background color denotes counterintuitive results).
According to Table 1, it can be easily found that the introduced score function S pxd can availably handle some deficiencies of S px (Peng, Dai, & Garg, 2018), p S λ (Peng & Dai, 2019) and S liu  in all Cases. That is to say, the introduced score function can identify the difference of two diverse q-ROFNs while some existing score functions fail to obtain. Moreover, we also find that the ranking results of p S λ (Peng & Dai, 2019) are counterintuitive due to the uncertainty of the λ value. If we keep employing accuracy function S liu of the cases in Table 1, we can conclude that the ultimate results is equal to the introduced score function, which reflects that our introduced score function S pxd is concise and explicit. Hence, the new score function not only can solve the illogical results but also avoid counterintuitive results in simple and clear way.  (Peng et al., 2018)

Two novel q-rung orthopair fuzzy operations
For the operations $ and % in Definition 3, we can find that the limited conditions are so complicated, which greatly affects its application. Hence, we propose some novel $ and % operators to overcome such drawback.
Definition 5. Suppose that a = (m 1 , n 1 ) and b = (m 2 , n 2 ) be q-ROFNs, the $ and % operations are denoted as Remark 3. Obviously, for any two q-ROFNs a and b, the final result of a $ b and a % b are still a q-ROFN. Some simple illustrations are shown as follows: Theorem 4. Suppose that a = (m 1 , n 1 ) and b = (m 2 , n 2 ) be q-ROFNs, then Proof. We just prove the (1), and the (2)-(4) can be similarly obtained.
q q q q q q q q q q q q q   m n n n +m +m −n m −n m −m m + n m m     Hence, it can be proved.
(1) Let a = (m 1 , n 1 ) and b = (m 2 , n 2 ) be two given q-ROFNs, then q q q q q q q q q q q q b = m n − n +m −n m =m n + n m − n +m q q q q q q q q q q q q a = m n − n +m −n m =m n + n m − n +m Further, q q q q q q q q q q q q m n + n m − n +m − m n + n m − n +m = ij ij m n × m n , which is shown in Table 2. The framework of developed method is presented in Figure 3.

Determine objective weights: CRITIC method
For the decision making issues, criteria can be regarded as a significant information source . The vital criteria weights could reveal plentiful information involving in each of them, which is called as "objective weight". The CRITIC (Criteria Importance Through Inter-criteria Correlation) is an approach for computing the objective weights of the given criteria in the MCDM issues (Diakoulaki et al., 1995). The objective weights derived by above approach combine both intensity contrast of each criterion and conflict among criteria. Intensity contrast of criteria is deemed to standard deviation and conflict between them is computed by the correlation coefficient. In current subsection, we branch out this approach into q-ROF environment. Suppose that ij p ( 1,2, , ; 1,2, , ) i m j n = =   denotes the q-ROF preference value of ith alternative according to jth criterion, o j w represents the fuzzy objective weight of jth criterion, C is a series of cost criteria, and B is a series of benefit criteria. Next, it lists the steps of computing q-ROF objective weights based CRITIC.
Step 1: Compute the score function Step 2: Switch the score matrix R into a standard q-ROF matrix ( ) Step 5: Calculate the quantity of information of each criterion as follows: The larger the c j is, the more information a certain criterion contains, so the weight of this evaluation criterion is greater than that of other criteria.
Step 6: Obtain the objective weight of each criterion as follows: (12)

Determine combined weights: linear weighted integrated method
Suppose that subjective weight, given by the DMs or experts, is

The q-rung orthopair fuzzy CoCoSo method
CoCoSo (Combined Compromise Solution) method is a novel and resultful MCDM method, which is presented by Yazdani et al. (2018). The suggested approach is based on an integrated exponentially weighted product (EWP) and simple additive weighting (SAW) model, which can be a compendium of compromise solutions. In order to solve the MCDM issue, we present a q-ROF-CoCoSo approach. Generally speaking, the q-ROF-CoCoSo method includes the steps below.
ij m n P p × = Step 2: Compute the score function ( ) ij m n R r × = of each q-ROFN p ij by Eq. (7).
Step 3: Switch score the matrix ( ) ij m n R r × = into a standard q-ROF matrix ( ) ij m n R r × ′ ′ = by Eq. (8).
Step 5: Compute the total of the weighted comparability sequence for every alternative as S i : Step 6: Compute the whole of the power weight of comparability sequences for each alternative as P i : Step 7: Relative weights of alternatives employing the below aggregation strategies are computed by Eqs (16)-(18): Step 8: Compute the assessment value k i by Eq. (19).

Remark 4.
It must be explained that the q-ROF-CoCoSo approach whose evaluation value in decision matrix is represented by q-ROFNs. The q-ROFNs are very effective in seizing imprecision of experts or DMs in decision making issues. Moreover, the q-ROF-CoCoSo method is a valuable means to deal with the DM issues with q-ROFNs, which has a grand power in differentiating the given alternatives and achieves the most desired alternative out of counter-intuitive case (Without the process of AOs presented by Peng et al. (2018)). However, other MCDM methods in q-ROF environment fail to possess such precious characteristics.

A case study in financial risk evaluation
In today's society, any enterprise will encounter various financial risks in operation and production. Financial risks are not only difficult to achieve financial benefits, but more likely to threaten the normal operation and production of enterprises. At present, enterprise personnel pay little attention to financial risks, but what I want to say is that financial risks are always around you. Enterprises are one-sided in pursuit of profitable products, ignoring market demand. When the sale also blindly pursues the expansion market, causes the buyer to default on the payment for goods the phenomenon to occur from time to time. Corporate balance sheet has been high, these may be the potential financial risks of enterprises. When evaluating the financial risk, it is indispensable to design a logical assessment system to guarantee the effective and scientific evaluation results. We construct and depict an evaluation criteria for financial risk as C j (j = 1, 2, 3, 4, 5, 6, 7).
The description of each criterion is briefly stated in Table 3.
Example 2. Suppose that there are five enterprises A = {A 1 , A 2 , A 3 , A 4 , A 5 } to be considered for the evaluation of financial risk. The Chief Financial Officer selects the criteria set C j (j = 1, 2, 3, 4, 5, 6, 7 ) as C 1 (Asset profitability), C 2 (Debt-paying ability), C 3 (Economic efficiency), C 4 (Enterprise development potential), C 5 (Financial flexibility), C 6 (Earning power), and C 7 (Leverage financial risk). According to the characteristics of the financial risk, we can find that C 1 , C 2 , C 3 , C 4 , C 5 , C 6 are benefit criteria and C 7 is cost criterion. It is the ultimate goal of business operation, and it is also the premise of enterprise survival and development. The profitability is determined by the total return on assets (representing the profit level of each capital, reflecting the profit level of the assets used by the enterprise) and the cost and profit margin (reflecting the higher the profit level of each dollar spent, the stronger the profitability of the enterprise).
Debt-paying ability (C 2 ) Indicators for measuring debt-paying ability have current ratios and assetliability ratios. If the current ratio is too high, it will cause liquidity to lose reinvestment opportunities. The average productive enterprise is about 2, and the asset-liability ratio is generally 40-60%. When the return on investment is bigger than the borrowing rate, the more borrowing, the more profit, and the greater the financial risk.

Economic efficiency (C 3 )
High and low directly reflect the level of business management, including: reflect the asset operating indicators have account receivable turnover rate and production and sales balance rate (product sales value/industrial output value).

Enterprise development potential (C 4 )
Indicators for measuring the development potential of enterprises include sales growth rate and capital preservation and appreciation rate. Several values are specified for each selected evaluation index. The design and calculation of the individual efficiency coefficients of various indicators are used. The Delphi method can quantify the financial status of the enterprise.

Financial flexibility (C 5 )
It refers to the ability of an enterprise to take resultful measures to transform the flow and time of cash flow for adapting to unexpected opportunities and needs. It is principally related to the net cash flow generated by the business activities of enterprises. Indicators reflecting financial elasticity include: working capital and total assets ratio used to measure the liquidity level of all assets of an enterprise, principal repayment ratio of matured debts, ratio of real net asset to tangible long-term asset, accounts receivable and inventory turnover ratio.
Earning power (C 6 ) In the long run, a company can stay away from financial crisis, which must have good profitability, enterprise external financing ability and debt repayment ability to be stronger. It consists of the following aspects: total assets net cash ratio, sales net cash ratio and return on equity.
Leverage financial risk (C 7 ) Enterprise risk is due to debt, all with their own capital in a business enterprise management risk without financial risk. Hence, to weigh the leverage of financial risk to determine the debt ratio, debt should be operating return on assets and the debt capital cost comparison, only the former is greater than the latter, due to return of principal and interest can be ensured, and achieve financial leverage income; At the same time, the debt solvency, that is, the amount of cash the enterprise has or the liquidity of its assets; The reasonable allocation of debt capital among various projects.
Suppose that the DM has the below prior weights w = (0.2,0.1,0.2,0.1,0.14,0.16,0.1). The assessments for enterprises arising from the expert in finance department are given in Table 4. In the following, we employ the developed algorithm (q = 3, λ = 0.5) to choose excellent enterprise.
Step 1: The q-ROF decision matrix is given in Table 4.

The sensitivity analysis of weight information
In order to make sensitivity analysis of parameter q in weight, we present the radar chart and 2D line chart. According to Figure 4, it can be easily seen that the q = 2 is a watershed, which the weights w 1 , w 2 , w 3 , w 4 and w 7 are firstly increasing and later decreasing with the increase in q while w 6 keeps in the opposite part. For w 5 is still decreasing with the increase of q. The w 4 and w 2 are ranked first place and last place from q ∈ [2,9], respectively. With respect to the weights w 3 , w 5 and w 7 are less than w 1 when q ∈ [2,9]. In order to have a better comparison with the weight information, we give the original weight, objective weight , two existing combined weights Peng & Dai, 2019) and the developed combined weight (q = 1, 2, ... 9) in Figure 5. Moreover, for combined weight in , we set the parameter p in comparing the results with original weight because it has no parameter q. According to Figure 5, we can easily find that the developed combined weight method can efficaciously reveal the objective preference (CRITIC) and subjective preference. However, the objective weight presented by  fails to reveal the most difference compared with weight offered by experts such as w 5 and w 6 . For combined weight in , although it can partly reflect the DM's preference (w 3 ), most of them has no difference. In other words, this combined weight determining model fails to effectively describe the law among the decision values transmitted by expert and subjective weight. For combined weight (Peng & Dai, 2019), although it can fully reflect the DM's preference with distinct difference, it loses the meaning of weight information (w 2 , w 3 , w 4 and w 7 ) when q takes other values.

Influence of the parameters q and λ in Algorithm 1
According to Algorithm 1, it can be easily found that the influence of conclusive ranking related the parameters q and λ come from the objective weight method (especially for score function) and CoCoSo method, respectively. Original weight q = 1 q = 2 q = 3 q = 4 q = 5 q = 6 q = 7 q = 8 q = 9 a) The proposed combined weight b) The objective weight by  c) The combined weight by Peng and Dai (2019) d) The combined weight by   Figure 6. The monolithic changing trend of parameters q and λ in Algorithm 1

Decision values
According to diverse pairs of parameters, the corresponding assessment values are shown in Figure 6. From these, the almost all of alternatives can be clearly seen in different levels. In other words, it has the better differentiation. Moreover, two key points have been concluded and listed in the following.
1) For a constant value of λ, it can be found that the decision values with respect to enterprise increase (A 2 , A 3 , A 4 ) or decrease (A 1 , A 5 ) along with the increase in parameter q (Figure 7). Furthermore, it can be observed that the decision values of entire enterprises are quite change slowly when q increases. Meanwhile, the decision values of enterprise A 5 is greater than A 3 and A 4 from (a) to (k) when q = 1. Since then, the ranked positions have without any change. However, no matter what it becomes, the decision values of A 1 and A 2 are ranked the first place and second place, respectively. From (a) to (k), the most of ranking results all hold as The parameter q The parameter q Decision values a) l = 0 b) l = 0.1

Decision values
The parameter q c) l = 0.2

Decision values
The parameter q d) l = 0.3

Figure 7. To be continue
Decision values The parameter q e) l = 0.4

Decision values
The parameter q f) l = 0.5

Decision values
The parameter q g) l = 0.6 Decision values The parameter q h) l = 0.7

Decision values
The parameter q i) l = 0.8

Decision values
The parameter q j) l = 0.9 2) For a constant value of q, as λ increases, the decision values with respect to each enterprise have different variation tendency when λ increases. (Figure 8).

Decision values
The parameter q k) l = 1.0

Decision values
The parameter q a) q = 1 Decision values The parameter q b) q = 2

Figure 8. To be continue
Decision values The parameter q c) q = 3 Decision values The parameter q d) q = 4 Decision values The parameter q e) q = 5 Decision values The parameter q f) q = 6 Decision values The parameter q g) q = 7 Decision values The parameter q h) q = 8 Decision values The parameter q i) q = 9 Figure 8. The changing trend of λ in diverse q

The differentiation degrees of some existing methods
Some existing methods Xing et al., 2019;Liu & Liu, 2018) have lower differentiation degrees for final decision making results of all alternatives. In other words, the decision results obtained from them are not resultful and convincing. For a better comparison with some existing algorithms, the related score functions and weight information are adopted by the developed score function and combined weighted. The comparison results are shown in Figure 9 by employing the Example 2. From Figure 9, we can find that the presented MCDM method based CoCoSo has sky-high differentiation degrees. Figure 9. The comparison with existing methods q-ROFWA q-ROFWG q-ROFPWAD q-ROFPWGD q-ROFPWAF q-ROFPWGF q-ROFPWAG q-ROFPWGG q-ROFPWAH q-ROFPWGH q-ROFWBM q-ROFWGBM q-ROFWMSM q-ROFWDMSM q-ROFGWHM q-ROFWGHM q-ROFWHM TOPSIS CODAS Similarity measure CoCoSo

Remark 5. From
Example 4. Continue to the Example 2. Assume that there has another expert from finance department to give its assessments for enterprises, which is presented in Table 7.