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REDUCE – A Python Module for Reducing Inconsistency in Pairwise Comparison Matrices

Kuraś Paweł, Strzałka Dominik, Kowal Bartosz, Mazurek Jiří

Advances in Science and Technology. Research Journal

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2023

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Vol. 17, no 4

227--234

EN

This paper introduces REDUCE, a Python module designed to minimize inconsistency in multiplicative pairwise comparisons (PC), a fundamental technique in Multi-Criteria Decision Making (MCDM). Pairwise comparisons are extensively used in various fields, including engineering science and numerical simulation methods, to compare different options based on a set of criteria. However, human errors in perception and judgment often lead to inconsistencies in pairwise comparison matrices (PCM). REDUCE addresses this issue by implementing several algorithms that identify and correct inaccurate data in PCMs, thereby reducing the inconsistency ratio. These algorithms do not require expert intervention, making REDUCE a valuable tool for both scientific research and small to medium enterprises that may not have access to costly commercial software or dedicated decision-making experts. The main functionality of the module is incorporating iterative algorithms for inconsistency reduction. The REDUCE library, written in Python and utilizing auxiliary libraries such as NumPy, SciPy, and SymPy, offers 21 functions categorized into data input helpers, consistency ratio (CR) reduction algorithms, PCM indexes, and support functions. Performance testing indicates that the library can efficiently handle matrices of varying sizes, particularly those ranging from 3x3 to 10x10, and its use significantly accelerates the process compared to spreadsheets, especially when dealing with large quantities of matrices. The library has already been used in several research papers and application tools, and its availability as a free resource opens up opportunities for small and medium-sized enterprises to leverage multi-criteria decision-making methods. Currently, there are no publicly available libraries for this solution. The authors believe that the proposed module may contribute to do better decision-making process in pairwise comparisons, not only for the circle of scientists but also for small and medium enterprises that usually cannot afford expensive commercial software and do not employ full-time experts in decision-making as they rely on the experience of their employees and free online resources. It should also contributes to the transition to Industry 4.0 and advances research in fields such as fuzzy logic, preference programming, and constructive consistent approximations.

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Some notes on the properties of inconsistency indices in pairwise comparisons

Mazurek J.

Operations Research and Decisions

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2018

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Vol. 28, No. 1

27--42

EN

Pairwise comparisons are an important tool of modern (multiple criteria) decision making. Since human judgments are often inconsistent, many studies have focused on the means of expressing and measuring this inconsistency, and several inconsistency indices have been proposed as an alternative to Saaty’s inconsistency index, CI, and consistency ratio, CR, for reciprocal pairwise comparison matrices. The aims of this paper are threefold: firstly, a row inconsistency index (RIC) is proposed and the properties of this index are examined. Secondly, a comparison of selected inconsistency indices for a corner pairwise comparison matrix is provided. Last, but not least, another axiom about the upper bound on the value of an inconsistency index is postulated, and a set of selected inconsistency indices is examined with respect to this axiom. Numerical examples complete the paper.

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Recent Advances on Inconsistency Indices for Pairwise Comparisons : A Commentary

Brunelli M.

Fundamenta Informaticae

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2016

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Vol. 144, nr 3/4

321--332

EN

This paper recalls the definition of consistency for pairwise comparison matrices and briefly presents the concept of inconsistency index in connection to other aspects of the theory of pairwise comparisons. By commenting on a recent contribution by Koczkodaj and Szwarc, it will be shown that the discussion on inconsistency indices is far from being over, and the ground is still fertile for debates.