A Brief Summary of Subjective Weighting Methods in MCDM

By Data Scientist, Chonghua Yin@CLIMsystems

Subjective weight determination is based on expert opinion, and in order to get the subjective judgments, analyst normally presents the decision makers a set of questions in the process. The methods for weighting the criteria involve decision-makers directly expressing how they feel about the relative importance of the criteria, usually represented in terms of either an interval scale (e.g. criteria are rated on a 0-100 scale) or a ratio scale measurement (e.g. “criterion A is three times as important as criterion B”) from which criterion weights are derived (directly).

The most popular weighting methods that have been used in multi-criteria decision-making studies are listed as below (Zardari et al., 2015; Odu, 2019):

• Fixed Point Allocation

In this method the decision maker is required to distribute a fixed number of points amongst the criteria. A higher point score indicates that the criterion has greater importance, while a lower point score is for a criterion with less importance. Fixed point scoring involving constrained point allocation, where percentages were often used, and the percentage points assigned by the decision makers should added to 100%. Fixed point allocation is the most direct means of obtaining weighting information from the decision maker. It requires the least amount of operations to transform information supplied by the decision maker into a weights vector. However, once the decision makers change their mind to a criterion, they have to adjust the weights of other criteria, or start the whole procedure from scratch.

• Point Allocation

Point allocation method looks like the fixed-point allocation. The key difference is that this method does not require the decision-makers only using a fixed total number of points to be divided. The more points a criterion receives, the greater its relative importance (Golaszewski et al., 2012). For example, they could give 10 points to the less important criterion, while giving the second less important criterion 20 points. Following this way, the most important indicator will get the highest points (e.g., 100 points). Then, these points for all criteria are normalized to sum to 1.0 as weights. This is extremely easy weighting method. However, the weights obtained from the use of point allocation method are not very precise. This method could be difficult if the number of criteria increases to 6 or more.

• Direct Rating

The decision makers directly give a score to each criterion to represent its importance. The score ranges could be like 1~5, 1~7, or 1~9 depending on the number of criteria to be assessed. A higher score indicates that the criterion has greater importance, while a lower score is for a criterion with less importance (Arbel, 1989).

• Ranking

The ranking method requires the decision makers to order the criteria according to their impotence, directly. For example, the most important criterion gets the 1rst place, the second most important one gets the 2nd place, and so on. Then these rank (place) numbers are transformed into the weights of all criteria with one of the three methods (1) rank sum, (2) rank reciprocal and (3) rank exponent method (Raszkowska, 2013).

• Ratio Weighting

The ratio weighting method is just like the ranking method, which requires the decision makers to first rank the relevant criteria according to their importance. Then they assign a weight of 10 to the least important criterion and all others are judged as multiples of 10. The weights are not necessary in the order of 20, 30, 40 etc. and could be something like 30, 70, 80, etc. The resulting raw weights are then normalized to sum to one.

• Swing Weighting

For each criterion, the effects of a ‘swing’ in performance from the worst to the best possible performance is evaluated. The criterion judged to be the most important in terms of the swing gets 100 points. The second-most important criterion is identified and is assigned points relative to the 100 points for the most important criterion. The exercise is repeated for the remaining criteria. Weights for the criteria are calculated from ratios of the points (Parnell and Trainor, 2009).

• Graphical Weighting

Graphical scales where importance is indicated by marking a continuous scale from low to high. A measurement was made to determine the weight. Graphical methods are easy and quick to apply in MCDM, especially when many decision makers do not have sufficient time for some of the more complex and involved approaches (Hajkowicz et al., 2000).

•  Simple Multi-attribute Rating Technique (SMART)

The SMART technique is a compensatory method of MCDM originally developed by Edward in 1971 (Patel et al., 2017). The least-important criterion is identified and is given a value of 10 points. The other criteria are rated relative to this criterion by also assigning points (of higher value) to them. Weights for the criteria are calculated from ratios of the points.

• Simple Multi-Attribute Rating Technique Exploiting Ranks (SMARTER)

The K criteria are ranked in order of their importance. The most-important criterion gets a value of 1, the second-most important criterion gets a value of 2, and so on down to a value of K for the least-important criterion. Weights for the criteria are calculated using the rank sum method (Edwards and Barron, 1994). The SMARTER method is a special case of the Ranking method.

•  SIMOS Weighting Method

The SIMOS weighting method is proposed by Simos (1990). The information provided by the decision maker is utilized by the Simos method for the determination of the weights, according to the following algorithm: (1) ranking of the subsets of criteria from the least important to the most important, considering also the white cards, (2) assignment of a position to each criterion/card and to each white card, (3) calculation of the non-normalized weights, and (4) determination of the normalized weights.

• Revised SIMOS Weighting Method

The SIMOS method was later extended by Figuera and Roy (2002) in order to address certain robustness issues of the original method. The main innovation of this procedure is relating a “playing card” to each criterion. The revised Simos method is widely used in decision making problems for estimating the criteria weights.

• Pairwise Comparison

Pairwise comparison is a well-developed method of ordering criteria, which involves the comparison of each criterion against every other criterion in pairs. Such comparisons force the decision makers to consider all elements of a decision problem to let them understand a whole decision-making context. Calculating weights using the pairwise comparison method has three main steps (1) to develop a matrix comparing the criteria, (2) compute the criterion weights, (3) to compute a consistency ratio. A typical weighting method based on pairwise comparison is the analytic hierarchy process (AHP; Saaty, 2008a).

• DELPHI

The Delphi technique has been widely employed to identify and explore indicators and criteria for unknown and uncertain consensuses, and it has been widely used in the logistics field. In general, three rounds of Delphi surveys are designated to achieve consensus weights (1) participants are chosen, (2) a list of possible alternatives is compiled and distributed to participants, (3) an amended list of alternatives is distributed. The Delphi method is considered as one of the best-known consensus-reaching methodologies (Sekhar et al., 2015).

•  Nominal Group Technique (NGT)

The nominal group technique (NGT) is a group process involving problem identification, solution generation, and decision making (Delbecq and VandeVen, 1971). It can be used in groups of many sizes, who want to make their decision quickly, as by a vote, but want everyone's opinions taken into account (as opposed to traditional voting, where only the largest group is considered) (Dunnette et al., 1963).The method of tallying is the difference. First, every member of the group gives their view of the solution, with a short explanation. Then, duplicate solutions are eliminated from the list of all solutions, and the members proceed to rank the solutions, 1st, 2nd, 3rd, 4th, and so on. The ranks are finally applied to determine the criteria weights (Abdullah and Islam, 2011).

A simple summary

The subjective weighting methods are often time consuming especially when there is no agreement between decision makers of the problem under consideration (Odu, 2019). However, they explain the elicitation process more clearly and more commonly used in practice than objective weighting methods as the objective weight procedure is not very clear and they neglect the subjective judgment information of the decision maker (Aalianvari et al., 2012; Zardari et al., 2015). For objective methods, a numerical decision matrix has to be constructed before carrying out further decision making. However, subjective methods come into play without the restriction. Some subjective methods could be applied as not only qualitative tools, but also quantitative measurements.

References

https://www.decision-deck.org/project/_static/slides15ddw6.pdf

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