VIKOR multi-criteria decision making with AHP reliable weighting for article acceptance recommendation

Decision Support System (DSS) enables a more efficient decision-making process [1]. It is built to support a problem solution or an opportunity evaluation. One of DSS variety is Multi-Criteria Decision Making (MCDM). MCDM overcomes severe cases [2] with many criteria or attributes [3]. Furthermore, MCDM can solve real-life problems, especially for a problem with contradictory decision criteria [4]. It works as a selection of the best of several mutually exclusive alternatives, determined by the decisionmaker [5].


Introduction
Decision Support System (DSS) enables a more efficient decision-making process [1].It is built to support a problem solution or an opportunity evaluation.One of DSS variety is Multi-Criteria Decision Making (MCDM).MCDM overcomes severe cases [2] with many criteria or attributes [3].Furthermore, MCDM can solve real-life problems, especially for a problem with contradictory decision criteria [4].It works as a selection of the best of several mutually exclusive alternatives, determined by the decisionmaker [5].
AHP method breaks complicated problems of an unstructured situation into variables [27].Variables are organized into a hierarchical order form, provides numerical values for subjective evaluations of each relative importance of variables.Furthermore, the assessment is synthesized according to the variable with the highest influential priority to the solution [28].AHP is independently developed on the use of alternative comparison concerning various criteria and estimated weight criteria [3], uses Saaty theory [28], [29].AHP weighting is not only performed to obtain the weight but also to examine weight consistency.This made AHP weighting is valid and reliable.Furthermore, AHP can manage qualitative attributes as a quantitative analysis [30].Thus, it can be applied in all multi-criteria cases.Instead of its strengths, AHP is very limited in case of development from the predetermined weight of criteria.
In different circumstances, VIKOR aims to derive alternative of the ranking of results as an approximate ideal solution by proposing a compromise solution [31].This method has advantages in compromising the existing alternatives and can solve discrete decision-making on contradictory and noncommensurable criteria; unit differences between criteria [24].It will find the closest solution to the overall weight [3].The disadvantage of the VIKOR method is its subjective initial weighting that is challenging to validate.
The combination of AHP and VIKOR methods is proposed to cover each disadvantage.AHP could improve the validity and reliability of weighting in VIKOR.In other words, the hybrid may produce more consistent weighting criteria.In this paper, AHP and VIKOR will be hybridized for creating a more reliable decision in a manuscript acceptance system.

Method
This paper uses scientific articles to review as a study case.In general, the publication of scientific articles requires several stages: article submission, review process, and the announcement of review results: whether the article deserves to be published, should be revised or must be rejected [17].The article publication consumes a relatively long time.The longest stage could be the review process.This study uses a combination of AHP and VIKOR to recommend the review status of an article based on five acceptance criteria as shown in Table 1.Each criterion was marked using C1 to C5 codes according to the priority order of the article evaluation.This study focused on a review of 18 articles.Five experts assess each article (A1 to A18).Table 2 shows the final decision for each article.This data is valid and used as a baseline of the study.In other words, the best method is an approach with the closest result to the baseline.Experts assess 18 articles and decide the complete decision for each article.This expert judgement is used for comparison with AHP-VIKOR result.Fig. 1 shows the AHP algorithm.The Pairwise Comparison matrix (in step1) is built using Saaty comparison scale, is presented in Table 3.The algorithm stop condition is based on the value of Consistency Ratio (CR).It must be repeated until CR ≤0.1.Fig. 2 presents the VIKOR algorithm [32] which is used to obtain article ranking.In a matrix F (Step 2 on Fig. 2), Ai declared i th alternative i= 1,2,3, ;  xn declared j th criteria  = 1,2,3, … . ij is the alternative response  in the criteria .where   ̅̅̅̅ is the result of pairwise criteria normalization, where  is the relative importance scale between two criteria, n is the number of criteria, and  represented the relative importance scale in one criterion.
Step 4: Calculate the total each column in the normalization matrix (TCNM) and divide it with the number of criteria to obtain the relative priority of each criterion.
Step 5: Measure the criteria consistency by multiplying each element in the column with its representative criterion relative priority (RP).A consistency matrix (CM) is produced as a result of this process.
Step 6: Calculate the total of each row (λ) in CM and divide it by the relevant criterion.
Step 7: Calculate the total of λ and divide it with the number of criteria (n) to produce  = ∑   .
Step 9: Calculate the Consistency Ratio (CR) value by dividing CI value with random generator value (RI).
Step 10: Check the consistency of criteria weight determination by looking at CR value.If CR> 0.1, then repeat step 5 to step 9.If CR ≤0.1, then the process is stopped.
Where   is Here,   is the value of alternative  i in  ℎ criteria.

Fig. 2. VIKOR algorithm
The third step implement the AHP relative priority value as weight.In the step 4, the alternative of the ideal solution of each criterion and decision of the normalization matrix is defined as positive   * or negative  − .Positive   * is the highest value of a is the best,   * =maxjAij.While negative   − is the smallest value of the criteria is the best,   − =maxjAij.Thus, it could be written as the following equation: Afterward, the decision of the normalization matrix is performed by dividing each A* and A - reduction value with initial weight.Then, the actual weight was obtained by multiplying the results of the normalization matrix with the AHP criteria weighting.The utility measure of each alternative (Step 5 on Fig. 2), can be calculated as, In the sixth step, the VIKOR index could be written as, Algorithm 2: VIKOR Step 1: Define the decision-making criteria.
Step 2: Each criterion and alternative is arranged into a matrix F.
Step 3: Perform criteria weighting to differentiate the degree of importance among AHP criteria.
Step 4: Determine the positive and negative values as the ideal solution of each criterion and decision of the normalization matrix.
Step 5: Calculate the utility measure of each alternative.
Step 6: Calculate the value of VIKOR index Step 7: Compromise alternative ranking.
Step 8: Propose the best alternative compromise solution by measuring the minimum VIKOR index.
where S * is Mini (Si), S -for Maxi(Si), R * is Mini(R), and R -as Maxi(R); and  was weight ranging from 0 to 1 (generally 0.5).The smaller VIKOR index (Qi), then the better the alternative solution.After Qi was calculated (Step 7 on Fig. 2), then there would be three types of ranking: Si, Ri, and Qi.Compromise solutions were seen in Qi ranking.Finally, the last step measures the minimum VIKOR index based on the following conditions: 1) Acceptable advantage, a difference between the A (1) and A (2) , the best and the second alternative ranking respectively.
2) Acceptable stability in decision making.This compromise solution is stable in the decision-making process that could be due to: "vote by majority rule" (when v > 0.5), or "by consensus" (v = 0.5), or "by veto" (v < 0.5).
If any of conditions is not met, then two compromise solutions can be proposed.The first solution selects alternative A (1) and A (2) , if only Acceptable stability condition in decision making is not met.The second solution chooses alternative A (1) , A (2) , ... , A (M) , if Acceptable Advantage condition is not met; A (M) is the alternative determined from the relation.
M maximum is an alternative, in which the position on adjacent condition.
The calculation of MAX MIN utility measure is S-of 0.89, S* of 0.04, R-of 0.50, and R* of 0.03.Alternative ranking in this study was an alternative compromise solution or acceptable stability in decision making.The alternative ranking of normal v value at 0.5 is equal to the calculation when the value of v <0.5 is 0.4 and when the value of v> 0.5 was 0.6.These calculations can be seen in Table 4.

Results and Discussion
The results of AHP-VIKOR Alternative ranking can be seen in Table 5.The table also consists of general VIKOR ranking and experts' judgments for comparison.VIKOR and AHP-VIKOR ranking mechanisms are the same.Ranking starts from the smallest value of VIKOR index.It is different from expert ranking, where the ranking is based on the article value.Experts recognize the highest value as the first rank.For instance, A1 is the first rank article with a total score of 14.If there are two or more articles have the same value (e.g., A1 and A18), then the order is based on the ascending order of article code.The experts evaluate the articles based on the five criteria: originality, quality, clarity, significance, relevance.It is the same as AHP-VIKOR and VIKOR ranking criteria.In fact, the expert evaluation is conducted subjectively and does not through any weighting mechanisms.Experts only provide three types of decision scales (1, 2, and 3).The highest value of each criterion is 3, and the lowest value is 1.In this case, the article with a score of fewer than ten score is rejected.Here, the rejected articles are A9, A5, A11, A12, A15, and A10.Following the expert judgment in Table 6, the rejected articles rejected by AHP-VIKOR is ranged from 13th to 18th rank: A2, A9, A10, A12, A15, and A5.On the other hand, general VIKOR rejects five articles: A10, A11, A9, A15, A5, and A12.Table 6 shows a case of comparison between the article's acceptance decision using VIKOR and AHP-VIKOR.In this case, the accuracy of VIKOR is higher than AHP-VIKOR.The result shows that the VIKOR result is identical with the expert recommendation.However, it means that the result is subjective since the initial weighting is decided by the reviewers.Thus, those approaches should be compared with different scenarios of initial weighting.While the initial weighting is different, the VIKOR accuracy could also be changed.AHP may reduce weighting subjectivity.Fig. 3 shows the accuracy comparison between VIKOR and AHP-VIKOR.After tried with ten different scenarios, it seems that the accuracy of AHP-VIKOR is slightly higher than VIKOR.The average accuracy of AHP-VIKOR is 90%, while VIKOR is 87.8%.Moreover, VIKOR's standard deviation (6.3) is higher than AHP-VIKOR (3.5).In short, VIKOR is less stable than AHP-VIKOR.Therefore, AHP-VIKOR outperforms VIKOR in terms of accuracy and stability.

Conclusion
AHP-VIKOR can be used as a method in decision making in the publication of scientific articles.AHP is used as more reliable weighting criteria for VIKOR decision making.AHP refines the accuracy and stability of VIKOR decision making.Therefore, AHP-VIKOR can be used as an alternative decision making for scientific publications acceptance.To create higher quality research, the variety of criteria, review decision and the article subjects should be enriched.In advance, a combination with a fuzzy-based approach or TOPSIS should be performed for more reliable decision-making result.

Table 1 .
The DSS criteria

Table 2 .
Expert decision

Table 3 .
Saaty's Comparison Scale Create a Pairwise Comparison matrix by comparing the degree of importance between criteria using the Saaty comparison scale.Step 2: Calculate the total of each criterion in one column of the pairwise comparison matrix.

Table 6 .
Comparison of Review Recommendation