[375] Is it enough what MCDM methods propose as results, or are only well-intentioned proxies?

Nolberto Munier

MANIFESTO

At present, there are more than 200 MCDM methods. Out of them only a handful are rational, from the human and mathematical points of view, like ELECTREE, PROMETHEE, TOPSIS and VIKOR. By ‘rational,’ I mean methods that support what they claim, based on mathematical principles, or by the DM reasoning and experience, not by at random selection of importance of criteria or by intuitions. The above-mentioned methods comply with these elemental bases. A method must give always the same result, independent of the DM that estimate the inputs, and this does not happen at present. Why?

Because they work with preferences in lieu of rationality. They rely on assumptions instead of mathematics and common sense, they operate with wishes, not with facts, with illusions not with real perspectives and analysis. They follow a descriptive procedure instead of a normative one. This pseudo technical landscape started 70 years ago, and it is time to change this pattern, that is, make decisions based by considering a problem as it is, a whole and not a partitionable object, and without altering data with artificial weights. The best example is the human body, that marvelous set of muscles, bones, and organs, all of them related, and thus, a change or a prescription for a part, may affect many others; the human body is not a set of isolated components; we are an extraordinary precision machinery that can even repair itself and able to produce new lives.

But we have MCDM methods oblivious to this universal structure and using partitions, modifying arbitrarily the values given by experts, and inventing procedures that grant the right to a DM to express his wishes and preferences, as if they had any relationship with reality. We are circling again and again around old structures that could have been useful in the past but with no practical utility in the present. Of course there has been some progress, but these are insignificant changes to improve the innards of some methods and no realizing that we need to modify a body not a part. It is like replacing the upholstery of a car, we improve comfort but not the car performance.

It is supposed that all MCDM methods are mathematically supported, something that is utopian in most and consequently, using different algorithms, and since mathematic is universal, we have to conclude that the discrepancy in results is due to personal opinions. Personal opinions and intuitions are fundamental in personal decisions where individual psychology is fundamental, but we do not need psychology in industrial problems. In here we deal and work with facts, with existing conditions and needs, not with feelings and moods.

We work with formulas, axioms, theorems, using common sense, and what it distills after considering hundreds of combinations of our restrictions in money, resources, manpower, environments limits, and of course some preferences, but manifested at reaching in practice, goals or targets as much as close as to our selection. Not pretending to model the problem according to what we think ‘should be’, because we have to adapt to facts, to realities, not to pretend that reality adapts to us.

Of course, to consider DM opinions, wisdom, knowledge is a must, but when done in time and reasoned, if not, we would be instructed by a machine. Curiously, AHP, heralded as the method closest to the DM estimates, is subject to what a machine mandates, regarding transitivity in estimates, like it or not.

Today we have methods based on the DM intuitions and feelings, that may change in the next hour, or others that tallow the DM the decision to select witch is the best and the worst criteria, or another that encourages to remove criteria, or divide a problem, not for better understanding, which would be reasonable, but for solving each one separately and them adding up results, or most of them that happily make a summation of each criteria results, and get the final solution. It appears that everything is valid, even contradicting mathematical theories like in Systems Theory, or taking decisions for other people, against the Arrows’ Impossibility Theorem, or assuming that subjective criteria can evaluate alternatives, against what Shannon’s’ Theorem says.

Many researchers along decades have pointed out these algorithmic inconsistences, but apparently to no avail. Some methods are institutionalized and taught in schools, discussed in symposiums, even when many researchers know that they are false. What is being done? Nothing. This is called intellectual complacence

Rational methods may naturally have subjectivity, but pondered and ruminated, and examined as in the preference statistical functions in PROMETHEE, as well as its GAIA frame, or as the veto threshold in ELECTREE, or in TOPSIS and VIKOR, where subjectivity is elaborated, based in reasoning, know-how and experience, and propose algorithms that shed light on many decision-making problems. Methods that force the DM to analyze, investigate and think. Others, which I will not name, are based on assumptions that do not resist the most minimum analysis, not even from the common-sense point of view, without any mathematical support, and inducing the DM to just fill a matrix with numbers of their preferences and press the start button

Where is science here?

On what grounds the voting system by DMs, taking sides without the interested parties being informed can be considered legal?

Where is the rational of asking people to make tedious pair-wise comparisons when many people don’t even understand what they are asking?

This is what we are still accepting in our 21st Century?

Wouldn’t it be more logical to select no more of five questions asking people questions like these?

“How do you see this project is going to benefit your community? Positively, Negatively or No effect?”

“ Do you think that this project fills a need in your community?” Yes, No

“ Do you want at add anything as per your experience?” Yes. No

But of course, this system will destroy the carefully built scaffolding that some MCDM methods need. The system asks people to make comparisons on aspects that it needs, but what people say or feel about the project is not important.

In addition, and unfortunately, all of MCDM methods, whatever their conception, either prescriptive of normative, do not consider a fundamental aspect. They forget that in real-life everything is related, and in general the result of an action is not a consequence of an isolated issue or the addition of many situations. Selecting a location site to install a plant, is not a matter or preferences, but a cumulus of many things, like economics and its various potential situations, transportation, government regulations, workers qualifications, social issues and it also numerous aspects, existent infrastructure in each site, water availability, environmental and engineering conditions, legal aspects, etc., and we are asking people to make them?

Real life, at least in selecting projects, is not related to personal preferences or inventions, but on facts. From my point of view, based on different disciplines like sustainability, health, engineering, economics, etc. is that a goal is not reached by considering most constituent elements and adding them up.

As an example.

Poverty as defined by United Nations is provoked by many different aspects like employment, health, water, electricity, education, transportation, etc., and you can have scores for each one but they are useless. A poor guy may look at a distance to a magnificent hospital, but he can’t reach it, because he does not have transportation and not even shoes. It shows a lot of good scores which independently considered aspects that are of no use, because what this guy needs is a combination of factors like transportation and shoes to allow him to reach the hospital, or the school, or a grocery. It can be seen that each one of these issues must participate in a certain degree and at the same time, and this is not obtained b y summations but by intersections

You can improve education but if people living in shanty houses, with flooded and muddy dirt streets, and no transportation because buses do not enter in the area, cannot access the schools, even if they are excellent, or go to a very good hospitals and care, if they do not have electricity, even if the electric grid in the city is good. You can sum the good hospitals, the electrical grid, and fabulous schools, but their total does not represent reality, because each of them needs from the other. Look at sustainability.

The definition of sustainability is when Economics, Health and Environment coincide. Look at the very well-known Venn diagram on sustainability; it shows that to achieve it convergence or overlapping of certain sectors of the three legs form a space. In there you can find sustainability

This false summation scenario considering independent all components of a project and adding them up, is what we have been doing since the 70s. There is no MCDM method that works with intersections. I still do not understand why researchers continue with this philosophy. I can understand students and practitioners, but not seasoned researchers and professors.

The key word here is ‘emerge’. Look at what AI defines emerge in decision making:” In short, when something "emerges" in decision-making, it means it wasn't fully designed in advance—it developed through interaction, learning, and adaptation. This contrasts with deliberate strategies, which are carefully planned and executed as intended from the start”.

In other words, there is not need for preconceived ideas, instead let the problem speaks by itself

In this unbiased and well documented definition look at the bold sentence. That is, things emerge as a set of actions that act jointly. It means that in our decision making we must consider all facts or criteria concurrently, not by a sum as is done nowadays, but on their interrelation. And this is not dome by any MCDM method.

There are thousands of examples:

A person baking a cake combine, milk, sugar, chocolate, eggs, and aims at the final product that emerge as a blend of all ingredients where some affect others. This person looks for a special taste given by this mixture or intersection of textures, granulometry, acidity, etc. to get a final flavor, this person is not expecting when eating a piece of the cake be able to identify the sugar, the eggs or the lemon.

However, this is what we are doing in MCDM: To get a solution that is the sum of the parts not their merge

This can be verified in every aspect of life

In designing a car, we do not optimize each part separately as the engine, the transmission and the aerodynamics, and by adding all of them get the perfect vehicle. The engineers know this and for this reason develop a mock-up of the vehicle and put it in a wind tunnel to learn how the aerodynamics affects the engine output, maximum speed, or the efficiency of the engine

In construction. A tall rise takes into account solar irradiation, wind, slopes, etc. and certainly does not add up the ‘importance’ of each one. Combines them

In medicine: An antibiotic may fight infection but may also affect negatively other organs

In macroeconomy, the best product to export depends of many factors, like international price, weather, demands, etc., and all of them play at the same time mutually influencing each other. A farmer may export maize, wheat and soy, and without mathematics and MCDM, he knows when he must change, exporting more wheat that soy, because the international prices of soy drop.

Look at a flower. It emerges as a beautiful thing due to the combination of soil quality, weather, water, etc.

Look at education: We learn that the multiplication is linked with summation, and that logarithms are linked to a power of a base. They are not isolated issues

Consequently, if we want that our MCDM methods really represent reality, we have to combine by interactions not adding their ‘importance’. This is the reason that they can be considered only approximations or proxies. Linear Programming solved this problem about 1940, when it was created by Kantorovich to maximize the war effort in the WWII. Was made available by Dantzig in 1948, and it is in your Excel as a macro since 1993, and made available for any quantity of objectives by the SIMUS software in 2014.

I ask AI if there is a reason by working with intersections in lieu of summations

Yes, there is, working scientifically, reasoning, thinking, and using “spatial logic, where the criterion that allows maximum intersection with other key criteria often becomes pivotal, not because it is the most important in isolation, but because it enables the coherence of the entire suitability model. It's like a keystone species in an ecosystem: its value is tied to how it supports the rest of the structure” (AI)

And now, just to dispel any doubts regarding my ideas about subjectivity. In my opinion, the software to solve MCDM problems must work with real values like cost, benefits, quantities, environment limits, etc. Of course, subjective criteria appear always in these problems, but we cannot tackle them with invented weights, but with values coming from surveys, crisp values from fuzzy, obtained considering a pair of reasonable values foe each criterion; what is irrational is to alter initial data with arbitrary weights.

What is proposed here is to have an initial decision matrix with actual values, objective and subjective, as reliable as possible. Then, to solve the problem using a MCDM method and then obtaining a result without human interference, and thus reflecting only data inputted. After that, the DM has a solid base, mathematically obtained, although imperfect from other points of view, but also the perfect base for using and taking advantage of the perception, know how and experience of the DM. There are aspects that no machine can detect as for instance the influence of external factors but the DM can and act as function of them and the results.

The DM is able to study the result, makes a sensitivity analysis and if it is positive, he may rest confident of the selection made by the method. If not, he can correct it, and select the second-best solution and so on. A lot of difference with the present-day method

The DM may have for instance, the feeling that the result does not reflect the true importance of a certain criterion. This is his opportunity to introdue4 changes, and even applying a certain weight to a criterion or two, but there is no need to apply a weight to all criteria. However, that change must obey to reasoning, investigation and research.

What can we do to improve MCDM? I would suggest to study a problem rationally, considering as much as possible all its characteristics, and develop a MCDM method able to model reality, and then, study how to create an algorithm that works with intersections not with summations.

Do we have the elements for that task? I believe we do, for instance:

Using ArcGIS for determining the best locations for industries or plants. We do not need to compute any layer’s weight here because ARCGIS does it very exactly considering r he different layers at the same time

Using Linear and Non-Linear Programming

Using Spatial Analysis

Using Spatial Geometry to understand concepts like Rank Reversal

Using Economic principles like Opportunity Costs

Considering endogenous and exogenous variable at the same time

To finish, I have justified every nuance of the new paradigm, given real-life examples, and explaining each step. It is not my intention to recommend any approach or method, my only purpose is to show the necessity to change, to abandon old structures and perhaps mimicking what happens around us.

Nolberto Munier