EDAS METHOD FOR MULTIPLE ATTRIBUTE GROUP DECISION MAKING UNDER Q-RUNG ORTHOPAIR FUZZY ENVIRONMENT

. Extended q-rung orthopair fuzzy sets (q-ROFSs) is an excellent tool to depict the qualitative assessing information in multiple attribute group decision making (MAGDM) environments. The EDAS method is very effective especially when the conflicting attributes exist in the MAGDM issues in which the optimal alternative should have the biggest value of PDAS and the smallest value of NDAS. In this paper, we put forward the EDAS method for MAGDM issues under q-ROFSs, which makes use of average solution (AS) for assessing the chosen alternatives. The positive distance from AS (PDAS) and negative distance from AS (NDAS) is derived through the score of q-ROFSs. Then, the sorting order or the optimal alternative can be acquired by computing integrative appraisal score. Finally, a numerical example for buying a refrigerator is given to testify our developed EDAS method and some comparative analysis are also raised to further show the precious merits of this method.


Introduction
In recent years, Pythagorean fuzzy sets (PFSs) (Yager, 2014) has appeared as an useful tool for characterizing ambiguity and complexity of the MAGDM Wu, Wang, & Gao, 2019). The PFS is depicted by the functions of membership and non-membership, which satisfies the sum of squares of them are limited to 1. Intuitionistic fuzzy sets (IFSs) Wei, 2019;Wu, G. W. Wei, Gao, & Y. Wei, 2018) are a part of the PFSs Li, Wei, & Lu, 2018;Peng & Dai, 2017), which means the PFS is more useful to solve the MAGDM. Moreover, according to the PFSs, Yager (2017)  In addition, the degree of hesitancy is defined as Definition 2 (Yager, 2017). Let , 1 1 .  Liu and Wang (2018) defined the q-rung orthopair fuzzy WA (q-ROFWA) operator and the q-rung orthopair fuzzy WG (q-ROFWG) operator.

q-rung orthopair fuzzy aggregation operators
On the basis of the definition 6−7, we shall give some other aggregating operators with q-ROFNs.
for any l.
be a set of q-ROFNs, and q-rung orthopair fuzzy OWG (q-ROFOWG) operator is defined: From above, we know that q-ROFWA and q-ROFWG operators only take into account the weight of the q-ROFNs, and the q-ROFOWA and q-ROFOWG operators only considers the ordered positions. To consider both weight of the q-ROFNs and the ordered positions, then, we now define q-rung orthopair fuzzy hybrid aggregation (q-ROFHA) and q-rung orthopair fuzzy hybrid geometric (q-ROFHG) operators.
is the position weights, with  and 1 1 n l l= ϑ = ∑ , and n is the balancing coefficient.
be a set of q-ROFNs, and q-ROFHG is defined: is a permutation of a set of the weighted q-ROFNs Obviously, from Definition 10−11, we know that the q-ROFHA operator and q-ROFHG operator consists of the following computational steps.  into the collective ones. From the above analysis, we can know that: (1) q-ROFWA and q-ROFOWA operators are special cases of q-ROFHA operator; q-ROFWG and q-ROFOWG operators are special cases of the q-ROFHG operator.
(2) The q-ROFHA operator generalizes q-ROFWA and q-ROFOWA operators; the q-ROFHG operator generalizes q-ROFWG and q-ROFOWG operators. (3) The advantages of the q-ROFHA operator and the q-ROFHG operator are that they consider not only the importance of the given q-ROFNs themselves but also the ordered positions of the given q-ROFNs.
Step 4: According to different types of attributes, calculate the PDAS matrix and the NDAS matrix. is the score function.
Step 8: Derive the ordering in accordance with the results of ( )

Case analysis
With development of social and improvement of peoples' living standards, the household refrigerator becomes a necessary appliance. The household refrigerator can provide the low temperature for saving food and simultaneously it consumes a lot of energy during 24-hour running. Improving refrigerator performance, not only can contribute to electricity saving for families, but also contributes to the national advocated motivation of energy-saving emission reduction and low-carbon, even contribute to the environment sustainability. Therefore, it is very important for potential customers to make an overall evaluation of alternative refrigerator through qualitative reviews. To facilitate consumer purchase decisions, ranking the alternative refrigerator based on EDAS method is a worthy research topic which is also regards as a classical MAGDM problem. Let us consider a customer who wants to buy a refrigerator.

Algorithm one:
If we use the q-ROFHA operator to fuse the given q-ROFNs, we can derive the aggregating collective matrix (see Table 4) and the position weight is w = (0.2, 0.5, 0.3). Step 1: According to Table 4, we can compute ( )  Table 4 (see Table 5) based on definition 2. Step 3: According to score values, compute the PDAS (Table 6) and the NDAS (Table 7). Step 4 Step 5: Normalize the values of ( ) Step 6: Compute the values of ( ) Step 7: Derive the ordering of ( ) IAS 1,2,3,4,5 l l = : T T T T T > > > > . Thus, the best refrigerator is T 2 .

Algorithm two:
If we use the q-ROFHG operator to fuse the given q-ROFNs, we can derive the aggregating matrix (Table 8) and the position weight is w = (0.2, 0.5, 0.3). Step 1: According to  Then, we can obtain the score results of Table 8 (see Table 9) based on definition 2. Step 3: According to score values, compute the PDAS (Table 10) and NDAS matrix (Table 11). Step 5: Normalize the results of ( ) Step 6: Derive the results of ( )

T T T T T
> > > > . Thus, the best refrigerator is also T 2 .

Compared with exiting MAGDM methods
To testify the advantages and effectiveness of q-ROF-EDAS method, we compare this method with some operators (Liu & Wang, 2018). According to the results of Table 1 and the attributes weight ( ) 0.20,0.15,0.25,0.17,0.13,0.10 ϑ = , we can compute the ranking of alternatives by these operators are listed in Table 12.

T T T T T > > > >
Comparing the results of the q-ROF-EDAS method with some existing operators, the aggregation results are slightly different. However, the best alternative is same. q-ROF-EDAS method has the precious characteristics of considering the conflicting attributes. And compared with other MAGDM methods, EDAS method has required fewer computations, although it results in the same best alternative. EDAS method is proposed based on the distance measure from the average solution unlike TOPSIS and VIKOR methods.

Conclusions
The q-ROFS provides a new way to accept information and make decisions. Its flexibility and convenience are more and more important in complex group decision making, with broad development prospects and far-reaching social significance. In our manuscript, we build the q-ROF-EDAS method for MAGDM. The specific content is as below: (1)Firstly, we review some basic knowledge of q-ROFNs. (2)Next, based on the q-ROFSs, we review and propose some aggregation operators, for example, q-ROFWA operator, q-ROFWG operator, q-RO-FOWA operator, q-ROFOWG operator, q-ROFHA operator and q-ROFHG operator. (3)The q-ROFSs are a complex form of information expression. How to apply it effectively to our real society is a difficult problem. At present, the application on q-fuzzy sets is still relatively limited. In our manuscript, we build the q-rung orthopair fuzzy EDAS model for MAGDM and develop the computing steps for MAGDM problem with q-ROFNs. (4) Finally, in order to depict the effectiveness of proposed method, an example of purchasing refrigerator in case of sudden power failure is given. Moreover, to show the merits of this new model in detail, we compare proposed method with some existing methods. In our developed opproach, it's more accuracy and useful to consider the conflicting attributes.
Turning a complex, uncertain piece of information into an intuitive, easily-acceptable message is a very complicated task. In the future, more scholars will explore and expand to enrich the content of the q-ROFS and the q-ROF-EDAS method under other MAGDM and many other uncertain and fuzzy environments.