Group geometric consistency index of analytic hierarchy process (AHP)

2012 ◽  
Vol 6 (26) ◽  
Author(s):  
Cheng-Tan Tung
Keyword(s):  
Analytic Hierarchy Process ◽  
Consistency Index ◽  
Analytic Hierarchy ◽  
Geometric Consistency ◽  
Hierarchy Process

The Myth of the Importance of Consistency in Analytical Hierarchical Processes

2021 ◽  
Vol 11 (1) ◽  
pp. 1-13
Author(s):  
Johnny J. Dahdah A. ◽  
Gilberto J. Hernández G. ◽  
María J. García G. ◽  
José G.Hernández R.
Keyword(s):  
Analytic Hierarchy Process ◽  
Mathematical Models ◽  
Consistency Index ◽  
Analytic Hierarchy ◽  
Hours Of Work ◽  
Great Relevance ◽  
The Analytic Hierarchy Process ◽  
Hierarchy Process

In this work, rather than relating different areas of knowledge, the authors make use of logic, which is intrinsic to mathematical models. They discuss one of the fallacies that hides behind the analytic hierarchy process (AHP). In particular, the analysis of the consistency index, sometimes referred as the Saaty consistency or simply the consistency, will be discussed. The AHP is based on three fundamental axioms: reciprocity, homogeneity, and synthesis. However, it gives a great relevance to consistency, which is managed like a fourth axiom. On each of these four axioms, some comments will be made. However, this work will focus mainly on discussing the importance of the consistency index, to which, undoubtedly, a large number of essays and many hours of work have been devoted. In trying to answer the question, the calculation of consistency is really important. The aim of the paper is to raise a discussion of one of the fallacies that hides behind the analytic hierarchy process and present a simple and direct way to handle Saaty consistency.

scholarly journals The Triads Geometric Consistency Index in AHP-Pairwise Comparison Matrices

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 926 ◽  
Author(s):  
Juan Aguarón ◽  
María Teresa Escobar ◽  
José María Moreno-Jiménez ◽  
Alberto Turón
Keyword(s):  
Pairwise Comparison ◽  
Consistency Index ◽  
Analytic Hierarchy ◽  
Priority Vector ◽  
Decision Tools ◽  
Geometric Consistency ◽  
The Matrix ◽  
Stability Intervals ◽  
Definition Of ◽  
Hierarchy Process

The paper presents the Triads Geometric Consistency Index ( T - G C I ), a measure for evaluating the inconsistency of the pairwise comparison matrices employed in the Analytic Hierarchy Process (AHP). Based on the Saaty’s definition of consistency for AHP, the new measure works directly with triads of the initial judgements, without having to previously calculate the priority vector, and therefore is valid for any prioritisation procedure used in AHP. The T - G C I is an intuitive indicator defined as the average of the log quadratic deviations from the unit of the intensities of all the cycles of length three. Its value coincides with that of the Geometric Consistency Index ( G C I ) and this allows the utilisation of the inconsistency thresholds as well as the properties of the G C I when using the T - G C I . In addition, the decision tools developed for the G C I can be used when working with triads ( T - G C I ), especially the procedure for improving the inconsistency and the consistency stability intervals of the judgements used in group decision making. The paper further includes a study of the computational complexity of both measures ( T - G C I and G C I ) which allows selecting the most appropriate expression, depending on the size of the matrix. Finally, it is proved that the generalisation of the proposed measure to cycles of any length coincides with the T - G C I . It is not therefore necessary to consider cycles of length greater than three, as they are more complex to obtain and the calculation of their associated measure is more difficult.

scholarly journals Effects of Cropping System (Organic and Conventional) on the Fiber Quality Index, Spinning Consistency Index and Multiplicative Analytic Hierarchy Process of Cotton (Gossypium hirsutum L.)

2015 ◽  
Vol 43 (2) ◽  
pp. 388-391
Author(s):  
Dimitrios J. BILALIS ◽  
Sotiria PATSIALI ◽  
Ioanna KAKABOUKI ◽  
Ilias S. TRAVLOS ◽  
Anestis KARKANIS
Keyword(s):  
Gossypium Hirsutum ◽  
Analytic Hierarchy Process ◽  
Cotton Fiber ◽  
Quality Index ◽  
Cropping Systems ◽  
Fiber Quality ◽  
Cropping System ◽  
Consistency Index ◽  
Analytic Hierarchy ◽  
Hierarchy Process

Markets for organically produced high quality cotton (Gossypium hirsutum L.) are projected to increase. Field experiments were conducted in Palamas, Karditsa in Central Greece, to compare the effects of two cropping systems on fiber quality of three cotton cultivars. The experiments, conducted during three years, were laid out in a split plot design with four replicates, two main plots (organic and conventional system) and three sub-plots (cotton cultivars). Findings suggest that fiber quality index (FQI), spinning consistency index (SCI) and multiplicative analytic hierarchy process (MAHP) are three indices that could be integrated in a useful protocol for the evaluation of different cropping systems for cotton cultivation. In particular, our results indicate that in general there was not any superiority of conventional compared to the organic cropping system regarding fiber quality as shown by the above mentioned indices. Regarding the length of the cotton fiber, this was positively correlated with micronair and the uniformity index of the cotton fiber. The organic system resulted to higher values of SCI than the ones of the conventional (1547.9 and 1522.3, respectively). The present 3-years study shows that organic cultivation of cotton can ensure high fiber quality and this was clearly confirmed by means of the several important indices.

Sign in / Sign up

Export Citation Format

Share Document