# 138

Dear Pedro Villanueva, Sergio Bona, Rubén Lostado-Lorza and Fernando Veiga

I read your paper:

Morphological Design of a Bicycle Propulsion Component

Using the Hierarchical Analysis Process (AHP)

My comments:

1- I have to recognize the originality of the subject in your paper, as well as the presentation of diagrams and figures; really a remarkable well-presented piece of work.

As I see the problem, you have three different alternatives to recover mechanical energy in a bike for its further utilization, and subject to eleven criteria, and you plan to select the best alternative by using a MCDM method like AHP as well as QFD deployment, i.e. a methodology used to determine a measure of customer satisfaction or preferences, a useful tool indeed.

I am confused here, since both procedures aim at the same thing, the only difference is that in AHP you use a pair-wise comparison procedure and finding a superiority of one criterion over another, while QFD acts independently. Both methods follow the same line of work, that is, they are descriptive for they obey to the wishes of persons. Hence, both are irrational, since they conform to personal intuitions and feelings, where no rationality is involved.

The remaining number of MCDM methods follow a normative approach, considering norms and established procedures and generally do not take into account personal wishes, although consider values based on expertise, know-how, research, educated assumptions, etc.

That is, they act rationally

In your paper you realize a good albeit short analysis of several methods, and although that it is evident that you favour AHP, you also make very honest negative comments about it, which are undoubtedly true.

However, there are contradictions, since some paragraphs affirm that AHP is useful for complex scenarios, and some lines below you say that it is not very good and that, and give one example, that is absolutely true, but that few authors mention, and it is the weakness of the method in complex problems due to its lineal hierarchy, something that I have said unaccountable times in RG.

There is another common mistake AHP users do, and it is not the fault of the method, but the users. Saaty, clearly explained in writing that AHP works only with independent criteria. Most people, and you can see it in published papers, even authorized by reviewers, that this fact is ignored or blatantly neglected at purpose and for their convenience.

I would like to briefly comment on some paragraphs when you describe other methods:

a) Page 3 - “MAUT (Multiattribute Utility Theory) allows for decision-makers to consider preferences through

a utility function [10], reflecting the value or utility each alternative has for the decisionmaker.

It provides a strong axiomatic foundation for rational decision-making”

See the underlined sentence. If the value of the utility depends on the wish and need of the DM, how can you say that it has a axiomatic strong foundation. Can you tell mi which axiom are you referring to? Utility is a valuable concept, but it is not axiomatic, unless it is built using criteria marginal values as in Linear Programming dual problem (shadow prices)

b) Page 3 “various reasons. ELECTRE offers advantages such as avoiding the transitivity of achievements”

I am not sure about that, because I wonder why there should be transitivity in achievements. Who says that?

Why there should be transitivity? The world is not transitive; independently that if A > B and B >C axiomatically A>C, but that is algebra, and we are talking on real-world. I guess that this was something that AHP introduced in its procedure simply to conform the Eigen Value analysis, that demands transitivity. Our methods must be based on reality, not the other way around. For instance, why in AHP the results obtained by a forced transitivity, can be applied to the real world? On what grounds?

c) Page 3- ELECTRE has theoretical weakness?

I doubt it. Of course it is not perfect, no MCDM method is, but at least it requires reasoning, experience, consultation, thinking and research. Of course there are subjective thresholds like veto, but that are based on analysis n of on intuition

d) Page 3 “PROMETHEE has some theoretical limitations”

Could you tell us which are they? It is a very rational method, based on outranking and its only drawback is using subjective weights. Same as ELECTRE, there are thresholds that must be established by the experts, but again, as a consequence of analysis, not at random.

In addition, GAIA diagram that shows relationships between criteria and alternatives is an excellent tool, that no other MCDM method has.

e) Page 3 “VIKOR is a useful tool in a multi-objective environment [11], providing scientifically and reasonably sound results for decision-makers.”

In disagree, because the underlined sentence is a misconception, since how does the DM know that he results are sound, if there is not a yardstick to compare to? And this applies to all MCDM methods.

f) In page 3 you say “ AHP is a valuable tool in decision-making by providing a hierarchical

structure and systematic methodology to address complex problems”.

The bold are your words and thus, you consider them true and transmit a reader that idea. However, I guess that you know that this statement is false.

You use the following criteria: sound quality, simplicity of emergency stop, affordability, resistance to falls, innovation, and minimizing mechanical losses.

In my opinion, you must use more criteria, like cost, weight, reliability, efficiency, etc., however, you know that a bicycle is a mechanical system formed by many parts, and as that must be considered holistically, according to System Engineering. Consequently, if you alter even a tooth of a gear for instance, it may affect the whole system, therefore, you in cannot consider them pairs but as a whole, something that of course, for AHP is an impossible task, but not for other MCDM methods.

You mention that AHP can handle ‘complex problems’, but all depends at what you call complex problems. If you believe it, please think if AHP can handle this not even very complex actions required in many scenarios:

- Modelling inclusivity and exclusivity in alternatives, as in road projects

- Precedence between alternatives, as in road and construction projects

- Alternatives that must comply with a minimum number of criteria, as in determination of best undertakings in urban development

- Criteria with negative values, as in problems dealing with incineration of domestic garbage

- Criteria with zeros and non-zero values, as in problems where an alternative may have not values for a certain criterion. For instance, if a criterion is ‘CO2 contamination’, it is obvious that wind turbines do not produce any, as well as other alternatives for electric power generation, while other alternatives do

- Establishing maximums and minimums for a same criterion and simultaneously, for instance minimum and maximum water consumption in a housing development

- Reducing number of alternatives and keeping the maximum information content

- Working with say 180 alternatives and 94 criteria, and making several different tests changing values

- Integrate new projects in a scenario where already exists projects under construction, for instance in hydro dams

For some people complexity is generated by the number of lineal hierarchies and number of criteria and sub-criteria levels. In my opinion, that is only cumbersome, especially due to the load work

g) Needless to say, that your idea is intriguing, original and valuable, however, I wonder if it can be practically applied to the real-life considering the advances of ebikes, and the question if a rider is willing to deal with more weight, more complications and higher cost. The key question here is, in my opinion, the spring mechanism, that you wisely compare with an old clock. If the release energy is in a very short period of time, I do not see its advantage. If, as in the case of an old clock it can be realise gradually, the question is the duration of that constant release.

To finish my comments, I wonder why and how you are using AHP and QFD. The first gives you a measure, from the point of view of the expert, that may change with another expertM, about the importance of each criterion. The second gives you practically the same information, but from the point of view of the market, which represent a universe of people, and as that by far more reliable.

How are you going to reconcile both?

I hope my comments can be of help

Nolberto Munier