Decision making - ELECTRE method

Question

I need to use a decision making algorithm as a part of a project. After long time research, I decide to use “ELECTRE Method”. Which get a matrix as input and calculate a weight for each row, based on its own method. The problem is that some values in matrix are null and caused inconsistency in calculation the weight of each row. Have anybody any idea about this or may someone know a good forum, where I can ask my question.

thanks in advance

Answer 1

What an interesting challenge you bring here. Thanks for it. Make sure you are comparing alternatives with a consistent criterion.

Indeed, dealing with uncertainty, incomplete information or unmatchable criteria between alternatives are common challenges in multi-criteria decision making (MCDC). Usually, when some criteria values are unknown you can (A) Use a standardization (set a default value for uncertain value). or (B) Apply fuzzy/intuitionistic or neutrosophic logic operators *1.

Now, from what I heard, you have a set of different alternatives that have attributes that do not match with each other. M1 alternative does not have one of the attributes.

However, the way you approach the fix depends on your decision goal. For instance, if your goal is to select the most optimal material, you might find relevant if some material has or not has hardness property. Apart from representing hardness with a range of integers or float numbers you can set a numeric boolean number: 1 for yes, 0 for no. Or a fuzzy number. (A scale from 0 and 1 for example).

Make sure you understand how the ELECTRE method works. *2-3

Try using a boolean or fuzzy operator for those null values and let me know if you have consistent results.

You may want to consider TOPSIS algorithm as well. *4-5

I hope it helps!

REFERENCES:

• 1 Mardani, A., Nilashi, M., Zavadskas, E. K., Awang, S. R., Zare, H., & Jamal, N. M. (2018). Decision-Making Methods Based on Fuzzy Aggregation Operators: Three Decades Review from 1986 to 2017. International Journal of Information Technology & Decision Making, 17(02), 391–466. doi:10.1142/s021962201830001x
• 1 Pramanik, S., Biswas, P., & Giri, B. C. (2015). Hybrid vector similarity measures and their applications to multi-attribute decision making under neutrosophic environment. Neural Computing and Applications, 28(5), 1163 doi:10.1007/s00521-015-2125-3
• 2 Roy, Bernard (1968). "Classement et choix en présence de points de vue multiples (la méthode ELECTRE)". La Revue d'Informatique et de Recherche Opérationelle (RIRO) (8): 57–75.
• 3 Electre method for Multiple Criteria Decision Making. Retrieved from https://www.youtube.com/watch?v=wOwP-EFlcVU
• 4 Hwang, C.L.; Yoon, K. (1981). Multiple Attribute Decision Making: Methods and Applications. New York: Springer-Verlag
• 5 Hwang, C.L.; Lai, Y.J.; Liu, T.Y. (1993). "A new approach for multiple objective decision making". Computers and Operational Research. 20: 889–899

Answer 2

The reference I have for ELECTRE (Multiple Attribute Decision Making: An Introduction) starts from a matrix where rows are possible choices and columns are attributes. It assumes that all attributes of all choices are known, and in fact are positive numbers. Why do you have null entries? Are they unknown values, or irrelevant values? If you want to try and extend ELECTRE you might start by considering what would make sense, for your example, if you only had one attribute. In fact, if you could create an order of preference for each attribute, taken in isolation, you could use this to replace the original values of that attribute, including the nulls, in the input matrix for ELECTRE.

My reference suggests that selection and scoring of the attributes is more important than choice of method, and that a simple additive weighted score may be good enough. If you are looking for something interesting, I refer you to http://homepage3.nifty.com/hiway/dm/franklin.htm.