CODAS METHOD FOR 2-TUPLE LINGUISTIC PYTHAGOREAN FUZZY MULTIPLE ATTRIBUTE GROUP DECISION MAKING AND ITS APPLICATION TO FINANCIAL MANAGEMENT PERFORMANCE ASSESSMENT

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Introduction
The numbers 0 and 1 are used to deliver the "no" and "yes" of the depiction of the thing in the exact mathematical set, but there is often an ambiguous state in the depiction of the real world. On the basis of this, (Zadeh, 1965) presented the theory of fuzzy set which used the membership degree to describe things' ambiguity, but it fail to depict both support and opposition ideas (Wei, 2019a(Wei, , 2019bWu et al., 2019aWu et al., , 2019bWu et al., 2018). Thus, Atanassov (1986) designed the intuitionistic fuzzy sets (IFSs) which could conquer this limitation. Reformat and Yager (2014) Zeb et al., 2019;Zhu et al., 2018). Based on the PFSs, Reformat and Yager (2014) presented a novel recommendation system which was collaborative oriented. Peng and Yang (2015) studied Pythagorean fuzzy numbers' division and subtraction algorithms. Garg (2017a) researched the confidence level's statistical concept into the PFSs. Ren et al. (2016) extended the Pythagorean fuzzy TODIM method on the basis of the prospect theory. Garg (2017b) improved scoring function calculation method for PFNs. Zeng et al. (2016) connected the distance measure with the PFSs. Li et al. (2018) defined some operators of Pythagorean Fuzzy Hamy Mean to address MAGDM issues. Zhang et al. (2017) combined the generalized Bonferroni mean with PFNs. Garg (2016) linked the PFSs with the Einstein operator. Li and Lu (2019) proposed some similarity and distance measures under PFSs. Wang et al. (2019b) designed the generalized Dice similarity measures for MAGDM with PFNs. Zhang (2016) extended the PFSs to the form of interval PFSs. Zhang and Jiang (2010) designed entropy for PFNs. Wei (2019c) defined the Hamacher power operators for PFNs. Zhang et al. (2016) presented a model which was about rough set under PFSs by means of multi-granular rough set. Deng et al. (2018a) gave the concept of 2TLPFSs and proposed various Hamy mean operations under 2TLPFSs. Deng et al. (2018) developed some Bonferroni mean operations under 2TLPFSs.
The CODAS method was defined by Keshavarz Ghorabaee et al. (2016). Panchal et al. (2017) employed integrated MCDM framework on the basis of AHP and CODAS method. Badi et al. (2018) made use of CODAS approach to choose the desalination plant's best location in Libya's northwestern coast. Ghorabaee et al. (2018) extended the CODAS method to fuzzy environment to choose the most desirable suppliers. Pamucar et al. (2018) introduced new CODAS method with linguistic Neutrosophic Numbers (LNN). Therefore, the above research failed to concern about the MAGDM issue with 2TLPFNs in terms of CODAS approach. In this essay, we utilize the 2TLPFNs to expand the CODAS method to design a novel MAGDM method. An example is used to display the proposed model's applicability. To illustrate the 2TLPF-CODAS method's stability, we make a comparison between 2TLPF-CODAS method & 2TLPF-TODIM method (Deng & Gao, 2019). The calculating results demonstrate that the presented approach is stability and validity. This paper's remainder is arranged subsequently. Some fundamental concepts of P2TLSs are given in Section 1. The CODAS method is built to handle MAGDM issues with 2TLPFNs in Section 2. A case study for FMPE is given to illustrate the presented approach in Section 3. In last section, the essay is made a conclusion.
 is designed to be a linguistic term set (LTS) with odd integer. s i was employed to depict the possible value in a LTS, and the set S could be depicted as:

PFSs
The PFSs A in a ordinary fixed set X can be depicted underneath (Reformat & Yager, 2014):

( )
A v x denoted the membership degree and the non-membership degree, which meet such condition:
Definition 1. (Deng et al., 2018a). Suppose that depict the membership and non-membership by 2TLSs, then the definition of 2TLPFSs could be defined: Then, Deng et al. (2018a) gave some novel operations on the 2TLPFNs.

The CODAS method for MAGDM with 2TLPFNs
The subsequently assumptions or notations are utilized to denote the MAGDM issues with 2TLPFNs. Assume   Table 1.  Then, an extended CODAS method with 2TLPFNs is proposed to tackle the MAGDM issues. The calculating steps are involved as follows:

{ }
Step 1. Switch the linguistic information k ij l into 2TLPFNs , , , Step 2. According to 2TLPFN , , , Step 3. Calculate the 2TLPF weighted matrix. Step 4. Get the negative ideal solution with score and accuracy functions of 2TLPFNs (if score functions are equal, the accuracy functions are chosen to rank the 2TLPFNs): Step 5. Determine the weighted ED i and HD i : Step 6. Build the relative assessment matrix RA in subsequently equations: where k ∈ {1, 2, …, m} and g means an important function which could be designed: where 0.01,0.05 τ∈     given by DMs. In current study, τ = 0.02.
Step 8. All the alternatives can be ranked on the basis of the computing results of AS i .The best alternative has the highest assessment score.

Case study and comparative analysis
The financial management performance issue is a classical MAGDM issue (Erdogan et al., 2019;Lu et al., 2019;Roy et al., 2019;Tabatabaei et al., 2019;Wang et al., 2019a;Wang, 2019;Wei et al., 2019aWei et al., , 2019b. In this chapter, we shall give a case study of the financial management performance to choose the most desirable enterprise which has the best financial performance by utilizing CODAS method with 2TLPFNs. Assume that an enterprise identified an investment chance with enterprise financial performances, and in order to maximize the expected profit, we need to determine the enterprise financial performances of the five enterprises so as to choose the optimal one. The investment company has to make a decision in terms of the subsequently four benifical attributes: G 1 is the enterprise innovation ability; G 2 is the enterprise resource utilization capability; G 3 is the internal process; G 4 is the corporate credit rating. There are five potential enterprises ( )  Following that, the developed approach is utilized to assess financial management performance of five possible enterprises.
Step 1. Transform the linguistic decision matrixes which are recorded in Tables 2-4 into 2TLPF decision matrix. The results are recorded in Tables 5-7.  ,0 , ,0 s s Table 6. The assessing matrix with 2TLPFNs by second expert   Step 2. According to , the experts' individual evaluations can be fused into the collective assessing matrix with 2TLPFNs (Table 8). Step 3. Compute the weighted assessing matrix with 2TLPFNs (Table 9). Step 4. Obtain the NIS by Eq. (22).The calculating results are recorded in Table 10. Step 5. Compute the ED i and HD i : Step 6. Compute the RA matrix (Table 11).  Table 8 Step 7. Compute the value of AS i by utilizing Eq. (28). A A A A A > > > > . As can be seen, the 2TLPF-CODAS method's ranking result is totally consistent with 2TLPF-TODIM method. What's more, two distance formulas' combination is used in 2TLPF-CODAS method, which is more exact than the single one.

Conclusions
Financial management performance evaluation has a significant effect on the identifying an investment chance. Because this process can be regarded as a MAGDM issue, it is necessary to utilize an efficient MAGDM method for it. Besides, since the group decision-making process is within uncertain environment, it makes this assessment complex. In this paper, the expanding CODAS method has been developed to tackle MAGDM issues under 2TLPFNs. The weighted Euclidean and weighted Hamming distances of 2TLPFNs have been employed to decide the alternatives' desirability with regard to a negative-ideal solution. Also, we extend the crisp CODAS method utilizing the linguistic variables which are defined by 2TLPFNs. In the developed 2TLPF-CODAS method, the application of an example of financial management performance assessment problem is given. The comparative analysis demonstrates that the 2TLPF-CODAS method is effective and practical with 2TLPF-TODIM method. For further researches, the proposed method's application will be conducted in many other unpredictable and ambiguous environments.