The primary goal of research in multiple criteria decision analysis is to develop tools to help people make more reasonable decisions. In many cases, the development of such tools requires the combination of knowledge derived from such areas as applied mathematics, cognitive psychology, and organizational behavior. Verbal Decision Analysis (VDA) is an example of such a combination. It is based on valid mathematical principles, takes into account peculiarities of human information processing system, and fits the decision process into existing organizational environments. The basic underpinnings of Verbal Decision Analysis are demonstrated by early VDA methods, such as ZAPROS and ORCLASS. New trends in their later modifications are discussed. Published applications of VDA methods are presented to support the findings.
A large number of decision making situations require taking into consideration multiple, often conflicting, influencing factors or criteria. A number of different multiple criteria decision aids (MCDA) have been developed to support this class of decision problems. In the majority of multiple criteria tasks, the “objectively” best alternative may often not be defined. As a result, in spite of crucial differences in approaches, many methods dealing with multiple criteria environments are based on subjective information about relative importance of objectives and criteria to the decision maker.
The subjective nature of information in the majority of multiple criteria models makes it a challenge to obtain consistent and accurate results in such tasks. As a result, elicitation of the decision makers’ preferences should take into account peculiarities of human behavior in the decision processes. This is the central goal of Verbal Decision Analysis or VDA [
The Verbal Decision Analysis is a framework for designing methods of MCDA by using preferential information from the decision makers in the ordinal form, a type of judgment known to be much more stable and consistent. VDA is based on the same principles as multiattribute utility theory (MAUT) [
Traditional methods of VDA were oriented on problems with a rather large number of alternatives but a relatively small number of criteria. They were designed to elicit a sound preference relationship that could be applied to future sets of real alternatives, while many other methods, for example, outranking methods [
New developments in the area of VDA illustrate some changes in the goals and ways of verbal analysis. The paper reviews the main principles of Verbal Decision Analysis, describes classical methods associated with this framework, and then analyzes new trends in the development and application of new methods.
Term “Verbal Decision Analysis” was introduced in 1997 by Larichev and Moshkovich [
In the area of MCDA, the decision maker is usually the central person in the decision process and tries to maximize utility (under uncertainty) or value function that depends on the criteria and/or attributes. Verbal Decision Analysis acknowledges that known constraints of human information processing system as well as the psychological validity of input data in decision analysis should be taken account while designing decision aiding methods. VDA is oriented on the construction and application of such methods.
This requirement means that if the decision maker takes into account qualitative characteristics of the alternatives (e.g., “car in a good condition”) or uses generalized notions while conducting analysis (e.g., “good credit,” “high risk,” etc.), the decision aids should use them for alternatives’ evaluations. Here comes the notion of “verbal scales.”
Larichev [
In aggregate, there are four major admissible groups of preferential information elicitation: rank ordering of criteria importance, qualitative comparison of attribute values against one, two, or three criteria, qualitative evaluation of probabilities, direct classification of an alternative.
The requirement means that all or part of the elicited information should provide auxiliary preferences which may be used to check for consistency of preferences as well as for verification of the underlying axioms. For example, many MAUT methods assume preferential independence of criteria and/or transitivity of preferences.
The last requirement assumes that the information elicited from the decision maker will be used in an easily understandable way to provide the solution, and as such the result may be easily explained to the decision maker.
Within this framework, the majority of the VDA methods are based on the rules of dominance (Pareto Principle) as a result of ordinal scales and transitivity of preferences. If we try to compare VDA to the existing major groups of approaches to multiple criteria decision analysis [
Like outranking methods [
On another hand, VDA is based on the same principles as multiattribute utility theory (MAUT) but is oriented on using the verbal form of preference elicitation and on evaluation of alternative decisions without resorting to numbers. As MAUT, classical methods of VDA work in the criterion space to provide universal ordering rules for any set of real alternatives.
As VDA, the Analytical Hierarchical Process (AHP) [
VDA among other approaches to MCDA.
Comparison of approaches based on the resulting order and applicability of derived rules
Comparison of approaches based on the use of heuristics and quantitative versus qualitative form of preference elicitation
In 1997, three methods were introduced as a VDA toolkit for three major types of decision problems. Method ZAPROS based on [
All methods assume that discrete alternatives are evaluated against a set of
In this case, we can form a set of all possible vectors in the space of
There is also a subset
Method ZAPROS is intended for problems in which there is a need to rank order a rather large number of alternatives and the set of the alternatives may change while decision rules stay in place. An example of such a problem will be the distribution of limited resources among research projects submitted to a government agency [
Method ZAPROS elicits the decision maker’s preferences through pairwise comparisons of hypothetical alternatives from the set
“
Elicited information is checked for consistency through transitivity of preferences and comparing the same criterion values at two reference points (for criterion independency check). As a result of the complete set of these comparisons, the so-called Joint Ordinal Scale (JOS) in the criterion space is formed. It rank orders different criterion values and is not connected to a specific set of alternatives.
JOS allows partial pairwise comparison of real alternatives (see Figure
Comparison of alternatives
Comparison on the basis of dominance
Comparison on the basis of JOS
Method ORCLASS is used when there is a need to define appropriate class for each real alternative out of
As ZAPROS, ORCLASS aims at constructing the classification rule in the criterion space and then applying it to any submitted alternative(s). The decision maker is presented with hypothetical alternatives (vectors from
Partial order among vectors from
Based on the dominance principle, possible classes for other alternatives from
The process stops when all vectors from
The classification process allows for consistency check. If the decision maker assigns class outside of the ones possible for this vector (based on previous classifications), there is a contradiction which may be explained to the decision maker and resolved through some reclassification.
Different heuristics are used to find vectors from
For easier classification of real alternatives once the classification is built, the notion of class boundaries is introduced. Lower border for each class is presented by least preferable vectors from the class on the basis of dominance, while upper border is formed by the most preferable vectors of the class. These two borders accurately represent each class and may be used to define if another vector belongs or does not belong to the class.
Method PACOM, called in Russian publications as PARK and in earlier version as ASTRIDA [
Let us assume that we have two real alternatives:
Compensation procedures in PACOM.
Real alternatives
Comparison of hypothetical vectors
Next comparison if
Information about comparison of basic alternatives may be used to compare real alternatives. It is proposed to form hypothetical alternatives for comparison in an iterative goal-seeking mode, quickly establishing the principal possibility for comparison of two real alternatives.
If alternatives
When all pairs of real alternatives from the initial list are analyzed using the proposed procedures, the general analysis of the results is carried out. As the aim of the analysis is to select the best alternative if two alternatives are compared, the least preferable one is excluded from the list and is not used in further analysis (as it cannot be a candidate for the final choice). The more preferable alternative is then compared with the next alternative, and so on. If there is only one alternative left in the initial list, the problem is solved. If there are incomparable alternatives left in the list, it is concluded that likely there is no satisfactory alternative among those in the initial list to make the real choice. The decision maker is proposed to analyze the list of adjusted alternatives that has been formed in the process of the analysis (evaluating the possibility to obtain a real alternative with such characteristics).
In this part, we described the “classical methods” of VDA. All presented methods are theoretically sound: all approaches assume additive value function though they do not seek it explicitly, elicit preference information in a qualitative form, provide opportunities to check this information for consistency, and apply only easily explainable rules of dominance and transitivity to reach the solution. Proposed methods do not guarantee complete rank ordering of alternatives or selection of the best one. Those working within the VDA framework believe that if it is not possible to select the best alternative based on the qualitative analysis, the solution should not be forced by assigning arbitrary numbers to different evaluations. The VDA approach recommends in this case that the
During the last decades, quite a number of new approaches within the field appeared, and modifications of the “classical methods” occurred. Figure
Verbal Decision Analysis methods.
ZAPROS III [
Comparison of alternatives
In ZAPROS III or STEP-ZAPROS, it is possible to ask the decision maker the questions as follows:
“
The main difference between ZAPROS III and STEP-ZAPROS is in the completeness of the process. In ZAPROS III, all the above mentioned hypothetical alternatives should be compared. After that the JSVQ is formed and applied to comparison of real alternatives. As the number of comparisons is large, this approach is mostly appropriate for a relatively small number of criteria and small number of possible criterion values.
STEP-ZAPROS uses additional comparisons only after the JOS is used to compare real alternatives. The method proposes an iterative procedure of identifying a minimal set of comparisons necessary to compare a small number of real alternatives left incomparable on the basis of JOS.
UniCombos [ the approach assumes that we need to rank order only a small number of real alternatives; a decision maker can consistently compare alternatives’ values against more than two criteria (in general, they try to limit it to three); the ability of the decision maker to compare complex combinations of alternatives’ values is helped by special ways of visualization of those values.
As STEP-ZAPROS, UniCombos assumes three steps in the process. The first step, as in all VDA methods, is connected with comparison of alternatives’ values on one criterion, resulting in ordinal scales and the dominance rule for pairwise comparison. If the rank ordering is not achieved, the second step is to compare all alternatives’ values against two criteria (the so-called “dyads”). It is the same as constructing JSQV in ZAPROS III, but the comparisons are limited to combinations, present among the real alternatives and necessary to compare real alternatives.
As an interactive system, the UniCombos checks the comparability of the real alternatives after each additional piece of preferential information is obtained. It will stop as soon as all alternatives are compared and/or the best alternative is found. Once all possible pairs of alternatives’ values are compared, but there are still incomparable alternatives in the set, the system will present the decision maker with the so-called “tryads” of alternatives’ values—values different against three criteria (analogous to example in Figure
Main improvements in ORCLASS approach were oriented on making the process of information elicitation more efficient. As the decision maker has to classify many hypothetical alternatives from
DIFCLASS is applicable only in cases with two decision classes where indirect classification of alternatives is quick and always consistent. CYCLE proposes the construction of “chains” of vectors between vectors
Subset of alternatives classification (SAC) [
In the SAC method, the principle of evaluating “informativeness” of vectors from
Method CLARA is also oriented on classification of real alternatives, but selection of alternatives to be presented to the decision maker for classification is based on method CYCLE. Again only real alternatives are taken into account when constructing and analyzing chains.
As PACOM, scale of normalized and ordinal differences (SNOD) [
First, normalized scales are used to “quantify” criterion values. Then, these values are used for pairwise comparison of real alternatives to define the “potentially best alternative.” All alternatives dominated by this one are eliminated from the analysis. All other alternatives are ordered in accordance to the total scoring difference between the “potentially best alternative” and this one.
This order is used in the dialog with the decision maker in assumption that it will lead to the solution quicker than in the traditional way of PACOM. Though use of quantified scales for alternatives evaluation and/or comparison is outside the framework of VDA, this method does not influence the outcome of the decision process, only its efficiency. At no time, any final decisions are made on the basis of the preliminary analysis. If the best alternative is not found quickly, previously discarded alternatives will be returned into the process, and “normalized and ordinal differences” may be revised.
The analysis of new VDA methods shows several trends in their modifications: tendency to concentrate on the comparison/classification of real alternatives as opposed to the idea of working in the criterion space for universal rules; implementation of iterative procedures for preferential information elicitation with the goal of solving just the problem at hand; gradual increase in the complexity of information elicited from the decision maker and minimization of verification processes.
Figure
Trends in VDA methods.
VDA has positive features of using psychologically valid preference input, providing checks for input consistency, and implementing mathematically sound rules. VDA was used in a number of applications starting with earlier applications of ZAPROS in R&D planning [
Tamanini et al. [
The ordinal classification approach was used for R&D planning and journals’ evaluation, as well as for job selection [
MCDA is an applied science. The primary goal of research in MCDA is to develop tools to help people make more reasonable decisions. In many cases, the development of such tools requires combination of knowledge derived from such areas as applied mathematics, cognitive psychology, and organizational behavior. Verbal Decision Analysis is an example of such a combination. It is based on valid mathematical principles, takes into account peculiarities of human information processing system, and places the decision process within the organizational environment of the decision making.
This paper has reviewed the basics of Verbal Decision Analysis. They were demonstrated with early VDA methods, such as ZAPROS and ORCLASS, and their later modifications, such as ZAPROS III, UniCombos, CLARA, and others.
The clear differences between “classical” VDA and more recent modification of the methods analyzed in this paper is the tendency to concentrate on problems with relatively small number of real alternatives and to carry out goal oriented solution process rather than constructing possible decision rules in the criterion space. The observed changes may be a reflection of the goal of MCDA researchers to create methods which are easier to apply in the real world. The majority of real life situations include a relatively small number of unique alternatives. The decision situation will change with their different set and as a result will require reelicitation of relevant preference information. Iterative processes based on real alternatives decrease the time and effort the decision maker has to invest into the process and produces quicker results.
There is an active research in further development of VDA methods, both in Russia, the home of VDA, and in the Americas. A number of published applications to real decision problems were discussed here, demonstrating the maturity of VDA. Next important step in the evolution of VDA will be the production of easily available computer systems. Currently, only proprietary research version of such systems exists in different parts of the world.