Multi-criteria decision analysis without consistency in pairwise comparisons

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Highlights

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    A novel MCDM approach is proposed to treat complex inconsistent problems.

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    The AHP is combined with the SSB representation of preferences into a new model.

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    A real industrial case is solved to demonstrate the effectiveness of the approach.

Abstract

Life itself is colorful and brings situations where making the right decision is a matter of compromise given the various criteria, often conflicting with each other. To handle such situations, a plethora of mathematical methods supporting decision-making has been developed. A little attention has been paid to cases where either criteria or expert preferences are not transitive by nature. Usually, standard decision-making methods handle such a case as an input error (input inconsistency). Being designed for consistent cases, standard methods may conclude in wrong results. We present a novel framework aimed at dealing with inconsistent preferences, without forcing experts to reconsider their initial judgments thus distorting their spontaneous assessments. A simulation analysis has been led to check the methodological validity of our proposal. Specifically, by setting different consistency ranges, thousands of experiments on simulated matrices confirm that our framework represents a valid alternative to the traditional practice. The applicability of the proposed approach has been eventually demonstrated through a real-world case study focused on supply chain management of a relevant industrial problem.

Section snippets

Introduction and State of Art

Multi-criteria decision-making methods enable decision-makers to establish which solution (or which set of alternatives) represents the best trade-off according to differently weighted evaluation criteria referring to such practical aspects as, for instance, safety & security, cost, productivity, and so on. Among the plethora of existing methods, literature agrees on considering the analytic hierarchy process (AHP) as one of the most popular. See, for example, (Vaidya and Kumar, 2006, de FSM

Motivation and Existent Methodologies

First we elaborate the motivation to deal with inconsistent preferences, see SubSection 2.1. In SubSection 2.2 basic notation and definitions are summarized together with a concise introduction of the AHP method. An aggregated preference matrix is defined in SubSection 2.3, and the theory of SSB representation is introduced in SubSection 2.4.

New Approach to Cope with Inconsistency

By applying the tools introduced in Section 2, we will obtain a new method that may well handle the possible inconsistency of experts’ judgements (note, however, that from the perspective of the SSB representation, the AHP-inconsistency is, actually, not an inconsistency), see SubSection 3.1. In SubSection 3.2 a relationship of this method to the AHP in the consistent case is discussed; its resistance to the so-called order reversal is elaborated in Section 3.3. These observations are

Applications

Now we apply the above introduced method to various decision making problems. First, we will solve several illustrative examples. Then, a simulation analysis is provided to compare the AHP and the proposed method statistically. Finally, we show a real-world study to demonstrate our method in detail.

Conclusion

A novel approach for solving complex real-world decision-making problems has been proposed, that is based on the preliminary collection of judgements of pairwise comparisons from selected stakeholders. Being elicited by human decision-makers, such judgments are often inconsistent. If minimal consistency requirements are not met in the AHP, experts are requested to revise - and possibly distort - their original judgments. We solve this issue by using the SSB representation of preferences. In

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This research has been financially supported by grant GAČR No. 19-06569S.

Silvia Carpitella PhD in Technological Innovation Engineering and PhD in Mathematics. Her main research interests refer to decision support systems, treatment of uncertainty affecting human evaluations, mathematical modelling, process management and optimisation.

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    Silvia Carpitella PhD in Technological Innovation Engineering and PhD in Mathematics. Her main research interests refer to decision support systems, treatment of uncertainty affecting human evaluations, mathematical modelling, process management and optimisation.

    Masahiro Inuiguchi Professor at the Department of Systems Innovation, Graduate School of Engineering Science, Osaka University. Among his professional interests are fuzzy and interval linear programming, interval AHP, possibility theory, and rough sets.

    Václav Kratochvíl Research assistant at the Department of Decision-Making Theory in the Institute of Information Theory and Automation, the Czech Academy of Sciences. Among his professional interests are Bayesian networks, polyhedral geometry, and Data-mining.

    Miroslav Pištěk Research fellow in the field of Decision-Making Theory. Among his professional interests are utility theory, intransitive preferences, and analysis of Nash Equilibria.

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