I am searching a recently developed new method to find the criteria weight.
If anyone knows about plz suggest me...
Why to look for a new method when there is entropy and standard devation, which are objective, unbiased and permanent?
Why to look for a new method to invent werights?
Sir actually, as per current research situation we have to do or apply new method/technique while solving any unkown problem so that it can be accepted in good journal.
You may see "ordered weighted averaging (OWA)"
here in research gate in 2010
Article A fuzzy MCDM approach for personnel selection
or in
http://dx.doi.org/10.1016/j.eswa.2009.11.067
Do you know that since the 50s. there is a method that does not use weights and however quantifies criteria importance?
This method is LinearProgramming, when omly one objective is used (1948), or SIMUS if multiple objectives are used (2011).
Technically, multi-objective optimization has been around for quite some time* - well before the fashionable MCDM was named.
(*the least could be mentioned: KKT conditions (Karush-Kuhn-Tucker, 1939-1951), Pareto (19-20th cen.), Lagrange multipliers = solution methods)
Dear Sfetcho
You are correct. LP was the inventor of MCDM, back in 1939 when Kantorovich invented it. It was developed to maximize Russian resources of any kind, againsts the nazi invaders
Kuhn Tucker conditions are also fundamentals and the base for non limear programming
Lagrange multiplier coincides with LP shadow prices in nnly one point, whcih is the intersection of the non linear objective function Z with of the vertices of the polygon.
Dear Nolberto Munier,
Thanks a lot for pointing out the contribution of Kantorovich in the LP modeling part (model creation) and usage in economics applications - similar to the work done by Leontief in LP models' constraints when the only missing part was the objective function in an LP model. Thus, a very important next step is the major break-trough provided by Dantzig with the development of an LP solution tool - the famous Simplex method for efficiently optimizing linear objective function subject to linear constraints.
When it comes to MCDM, you can try utilizing the ANN prediction and obtain the weights needed.
Dear Sfetcho
I am very glad that you recognized the work of George Dantzig, the great mathematician that in 1948 developed the Simplex algorithm (Since1993, it is an Excel add-in), and that allowed the use of LP created by Leonid Kantorovich (Nobel Prize 1956)
The Simplex was nominated as one of the most important and useful algorithm of the 20th Century, and paved the road for using LP in thousands of companies (at present about 70,000 in USA).
LP is UNMATCHED in modelling and solving MCDM problems, because it works with inequations instead of equations (or spaces, instead of lines), and is based on solid economics principles.
The best alternatives are selected following the economic concept of Cost of Opportunity. In addition, the result for each criterion is Pareto efficient.
It does not need weights for criteria, because internally, it computes and UPDATES in each iteration the importance of each criterion as a function of the alternative that it has to evaluate. This is science!
And yes, DM rational, not intuitionistic or invented weights can be incorporated in LP.
By the way, normally any normalization procedure can be used since they do not affect the results. All rankings coincide
Unfortunately, LP also has the drawback of being mono objective, and accepting only quantitative criteria, when most problems have multiple objectives, and multiple objectives
That was solved by SIMUS, taking advantage of the power of PL by repeatedly using the Simplex, and allowing to have hundreds of objectives and solving all of them simultaneously. However, it does not guarantee an optimal solution - as no MCDM method does - except LP. Instead, it produces a compromised or balanced solution.
Of course, the very important economic contribution of Wassily Leontief (Nobel Prize 1973) in his famous I/O matrix, extensively used today, also is LP
The interesting aspect is that all of these LP and SIMUS characteristics can be mathematically explained. There are no assumptions here!
Finally, and not the least, both LP and SIMUS are free.
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