Dear ,

AHP and TOPSIS are two MCDM methods as you have said. Say for example there are 10 students and you have to select the best student among them on the basis of 5 criteria. What AHP does is that it takes 2 students at a time and compare their criteria one by one which is called comparison matrix. By doing so AHP finds out the best among the 10 students. Total no of combination becomes 10C2 = 55 i.e. you have to make a total of 55 comparison matrix. The criteria also need some weightage because each criteria shall not contribute equally in choosing the best student. Hence a comparison matrix of the criteria is also needed. As a result a total of 56 comparison matrix is created which is a lengthy process. If in case, there are 60 students in the class, the no of comparison matrices would become (60C2 + 1). Moreover of the lengthy calculation there is one more problem in AHP is selecting of decision makers.

In case of TOPSIS, all the students will be taken at a time as alternatives and they would be given score on the basis of the criteria which is called the decision matrix. By using TOPSIS method, from the decision matrix we can find out the best alternative. The calculation part is lessen as we can compute the best alternative from the decision matrix. But one problem encountered in TOPSIS or other MCDM method is computation of the weightage of the criteria. This problem is tackled by various ways like AHP, cross-entropy, fuzzy preference programming etc etc. As I have already mentioned in the first para that we can compute the weightage of the criteria by forming a comparison matrix for the criteria and following the steps of AHP.

As per the second part of your question, we can use the two method separately for the same problem but again in TOPSIS for criteria weight computation we have to depend on AHP. We can use some other methods for weight computation but as we have already computed the criteria weights by AHP so, it is useless to go for some other method once again for the same step.

For more you can go through the links:

Conference Paper A Hybrid Approach of AHP-Cross Entropy Model to Select Beari...

Conference Paper Entropy based MCDM approach for Selection of material

Chapter A Holistic-Based Multi-Criterion Decision-Making Approach fo...

Conference Paper Developing a Decision Making Model Using Interval Valued Int...

Article Decision Maker Priority Index and Degree of Vagueness Couple...