The Influence of the Form of the 9-Point Scale in the Ahp Method on the Consistency of Judgments

Abstract

Quality of decisions depends largely on the ability to correctly define and assess the problem. In the case of complex issues, it is recommended to use decision support methods, e.g. multicriteria methods. The objective of this paper is to report the studies related to the influence of the graphic form of the 9-point, fundamental Saaty's comparison scale used in the AHP method on the consistency of judgments, that is, to measure the fraction of judgments with CR>0,10. Since the AHP is one of the most frequently used decision support methods in management, in terms of modeling decision problems, there is a need to explore one of its most frequently discussed problemsinconsistency of results. It will improve the quality of decisions made with the use of this tool. The empirical study was conducted among 540 respondents, using the AHP method. Due to errors in filling in the questionnaire, only 424 questionnaires were included in further analysis. Individual model was prepared and analyzed for each respondent. All results were then entered into a spreadsheet and subjected to statistical analysis. It examines four most commonly used graphic forms of scale (specifically: numerical, two-stage tabular verbal, tabular verbal horizontal and vertical). Chi-square test and F-test showed no significant difference between them in relation to the existence of inconsistent results (CR > 0.1). It allows suggest that the form of graphic scale does not affect the consistency of answers. However, additional analysis showed that it affects errors in questionnaires.

The Dilemmas Selection of Anti-Crisis Economic Strategy in Forestry and the Wood-Based Sector in the Perspective of a Long-Term Pandemic Threat – the Case of Poland

“…Similar proportionality was also used in the conducted research, choosing between: equal significance (measure 1), small advantage (measure 2), strong advantage (measure 5), very strong advantage (measure 7), and absolute advantage (measure 9). Appropriate measures: 2, 4, 6, 8 -showed intermediate values [44]. On the other hand, marks about opposite relations were marked as inverts of integers.…”

“…Then, the hierarchical model is subjected to analysis, consisting in comparing all pairs of elements created within individual groups, using the fairly commonly used so-called a bipolar, nine-point scale, proposed by Thomas L. Saaty, a professor at the University of Pittsburgh [42,43]. Various aspects of the practical application of the aforementioned nine-point fundamental scale of comparisons, the principles of creating sets of pairs of elements within a hierarchical structure, and practical issues related to the construction of the questionnaire, including the way of presenting and formulating questions, are quite widely discussed in the literature [44,45,46]. For the purposes of this study, generally accepted principles have been applied, adapting the procedure to the specifics of the industry market under investigation.…”

“…The concept of hierarchical analysis modified for research purposes was used. The research scenario was built based on the methodological assumptions of AHP (Analytic Hierarchy Process) multi-criteria hierarchical analysis, however, "imposing" them on the specific structure of a selected segment of the sector under investigation [44,53]. The best possible decision was sought: institutional or market, allowing selection of the optimal anti-crisis strategy for all participants of the industry market (scope).…”

“…As a result, the relative preference scale was determined for individual data included in the study. In the process of comparing elements, the aforementioned 9-degree scale of relative preference of Saaty was used [44]. The following elements of the scale were distinguished: 5 basic stages (to which particular attention was paid) and, additionally, 4 intermediate stages (in the work the scale was simplified, bypassing these stages in the study).…”

“…At this stage, an algorithm adapted to the spreadsheet can be used, based on the mathematical assumptions of the AHP method, by normalizing the data and prioritizing decision options (for this purpose, of course, you can use utility or dedicated software (it can be both a spreadsheet, e.g. MS Excel, and professional tools, such as the R program, and "Super Decisions" or "Expert Choice" applications) [41,44].…”