Analytic hierarchy process-fuzzy sorting: An analytic hierarchy process–based method for fuzzy classification in sorting problems

Abstract

Analytic Hierarchy Process (AHP) is a well-founded and popular method in the Multi-Criteria Decision Analysis (MCDA) field. AHPSort, a recently introduced sorting variant, uses crisp class-assignment of alternatives. This can sometimes be misleading, especially for alternatives near the border of two classes. This paper aims at making the class assignment process in AHPSort more flexible by using fuzzy sets theory, which facilitates soft transitions between classes and provides additional information about the membership of alternatives in each class that can be used to fine-tune actions beyond the crisp sorting process. This essentially complements the ordinal information of its crisp variant with cardinal information as to the degree of membership of an alternative to each class. The applicability of the proposed approach is illustrated in a case study that regards the classification of London boroughs according to their safety levels.

Keywords:

• Multi-criteria decision analysis
• AHP
• AHPSort
• fuzzy sets
• sorting method
• fuzzy linguistic approach

Endnotes

Acknowledgments

We would like to thank four anonymous reviewers for comments and suggestions that greatly helped us in improving this manuscript. This article was produced while Prof Luis Martinez was a visiting Isambard Brunel Kingdom Brunel Research Fellow at the University of Portsmouth.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 At the time of writing this article, the latest available data concern the period April, 2016 – April, 2017.

2 We only delineate changes in membership of Class 1 (“High”) and Class 2 (“Mod”), as no borough presented a change whatsoever as to its membership in Class 3 (“Low”).

Additional information

Funding

This study was funded by Spanish National research project TIN2015-66524-P.