A Novel Hybrid Fuzzy Grey TOPSIS Method: Supplier Evaluation of a Collaborative Manufacturing Enterprise

Round 1

Reviewer 1 Report

The Multi-Criteria Decision Making (MCDM) approaches are extensively developed and applied to solve real-life problems. I have read the paper on a novel hybrid fuzzy grey TOPSIS method and its application for supplier’s evaluation with great interest.

The paper’s authors made great efforts to overview MCDM methods focusing on a Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS), Grey Comprehensive Evaluation (GCE) approaches and fuzzy set theory. The authors have to look very carefully at the summary given in the tables and context, and the list of references, because a wrong, inappropriate or unsuitable citation blights the quality of a paper. Whereas an excellent bibliography shows off scientific information and knowledge of authors, such a mess as referring to the wrong source or source not included to the references (e.g. Zheng et al. [79], Ahari and Niaki [80] (see Table III), and [79] or [80] in the References), leave a question regarding point of the paper's authors about other MCDM methods lingering in the air. Likewise the classical methods as AHP and TOPSIS (as they described in Table III (see last two rows)), are not based on a fuzzy set theory.

The authors describe the fuzzy grey TOPSIS method and demonstrate how proposed enhancements improve the ability to solve MCDM problems in real decision-making. Finally, an illustrative example for supplier evaluation of a collaborative manufacturing enterprise is given to illustrate the application and effectiveness of the developed method. The matrices in Step 1 (row 331) (see An illustrative example) require additional comments. Mapping rules of linguistic variables and fuzzy number, for example, are given in row 177. For what purpose, authors use criteria marking, i.e. the quality level (x1), if it is not reflected in the paper text? Could the J1, J2, …, J6 matrices named as the fuzzy linguistic value evaluation matrices? (They have quantitative criterion numerical (not linguistic) value). Moreover, how the value of the Pass-rate of production (x12) was obtained? How I need to follow the Step 1.2 (row 208)?

In this paper, the authors propose hybrid decision-making model which provides “a more accurate and reliable method for evaluating the fuzzy system MCDM problems with interaction criteria”. I entirely agree with authors but to prove this, they have to work with demonstration of applicability of the proposed method. Furthermore, if the method could help to solve enterprises’ problems and to develop enterprises better, this must be reflected in the illustrative example. How the proposed method deals with such kinds of issues?

If the authors are developing a new approach and looking at the problem with a different angle of vision, it must be visible both in the framework and in the example. However, the question arises why we need to apply the proposed novel method if it is complicated like others?

In my opinion and looking to the results, “manufacturing” as a keyword is inaccurate.

Author Response

Answer: Thanks for your painstaking comments.

Firstly, we are so sorry for make a mess reference since our careless. We have checked all the reference carefully.

Secondly, we have added more explanation about the mapping rules of linguistic variables and fuzzy numbers for J1 in row 332. As show in follows:

The fuzzy linguistic value evaluation matrices  are shown as follows, in which the mapping rules of linguistic variables and fuzzy number are given in Table IV.

Thirdly, we have added more explanation about the evaluation of criteria x₁₂ (second row in the fuzzy linguistic value evaluation matrix). As show in follows:

where each matrix represents the evaluation data of an alternative, and each row in matrix represents the evaluation data of one qualitative criterion given by 12 experts expect for the second row of each matrix that is the evaluation data of the quantitative criterion and just have one value. In fact, we can give the evaluation of qualitative criteria and quantitative criteria respectively, but for the convenience of writing we give them in one matrix.

Fourthly, we give an illustrative example of proposed method and compare it with the GCE and TOPSIS method. The result shows that the proposed method can reflect both the difference of shape and distance of objects, which overcomes the one-sidedness of the GCE method and TOPSIS method. Thus, the proposed method is applicative to evaluate the fuzzy system MCDM problems with interaction criteria.

Fifthly, the fuzzy system MCDM problems with interaction criteria are often encountered by the enterprise and the reasonable evaluation of it are really crucial to the development of the enterprise. The proposed method can evaluate the fuzzy system MCDM problems with interaction criteria more reasonable, thus can help the enterprise develop better.

Sixthly, in our opinion, it is better to apply the proposed method rather than other exists method to evaluation the fuzzy system MCDM problems with interaction criteria. It is because the proposed method can evaluation the fuzzy system MCDM problems with interaction criteria more reasonable, not because the proposed method is simple than others.

Seventhly, we have remove “manufacturing” from the index terms list. Thank you for your pertinent advice.

Reviewer 2 Report

1) Litterature review is incomple; important contributions related to bipolar analysis, satisficing games, weighted cardinal fuzzy measure (wcfm) are not adressed; please consider comparing your approach to these approaches.

2) There some typo errors to correct

Author Response

Answer: We have cited some related references in the revision. Also, we do the comparing analysis with the general method, e.g., GCE and TOPSIS. Please see the section V-B. 

Answer: Thanks for your careful comments, we have read the paper carefully.

Reviewer 3 Report

I like the paper, its style and also the received results.

Used symbols are explained, Results are supported with the example.

Conclusion section is little short but it gives all necessary information.

Author Response

Answer: Thanks for your positive comments very much.

Reviewer 4 Report

The fuzzy / grey TOPSIS applications are not new and have been omnipresent in the literature. Furthermore, MCDM techniques are well studied in the supplier evaluation and selection domain. Unfortunately, there is no major scientific contribution in this study.

Author Response

Answer: This work develops a novel hybrid MCDM method called the Fuzzy Grey TOPSIS (FGT) and a supplier evaluation case is tested. Our main contribution is presented as follows in the revision:

Firstly, the proposed method combines the GCE and TOPSIS, which improves the one-sidedness of the GCE and TOPSIS methods. Decision makers can make a decision according to their preference through adjusting a parameter that reflects on the weights of the shape and the distance factors.

Secondly, fuzzy measures and fuzzy integral are employed to express and integrate the interaction between the criteria that cannot be properly expressed through the existing methods.

Thirdly, fuzzy numbers are used to help the experts make more reasonably and accurately evaluation of some qualitative criteria.

For supplier evaluation and selection is a merely application work. Also to our best knowledge, this is a first application to this problem by such an integrated approach. We explained them in the revision and thanks for your understanding. 

Round 2

Reviewer 4 Report

The authors have addressed my concerns properly.