A Fuzzy Delphi Consensus Methodology Based on a Fuzzy Ranking

Antonio Francisco Roldán López De Hierro,Rafael Montoya-Juárez,Concepción Roldán,Miguel Sánchez,Daniel Puente-Fernández

doi:10.3390/math9182323

Antonio Francisco Roldán López De Hierro, Rafael Montoya-Juárez + Show 3 more

Open Access

https://doi.org/10.3390/math9182323

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Journal: Mathematics	Publication Date: Sep 19, 2021
Citations: 5	License type: CC BY 4.0

Affiliation: University of Granada

Abstract

Delphi multi-round survey is a procedure that has been widely and successfully used to aggregate experts’ opinions about some previously established statements or questions. Such opinions are usually expressed as real numbers and some commentaries. The evolution of the consensus can be shown by an increase in the agreement percentages, and a decrease in the number of comments made. A consensus is reached when this percentage exceeds a certain previously set threshold. If this threshold has not been reached, the moderator modifies the questionnaire according to the comments he/she has collected, and the following round begins. In this paper, a new fuzzy Delphi method is introduced. On the one hand, the experts’ subjective judgments are collected as fuzzy numbers, enriching the approach. On the other hand, such opinions are collected through a computerized application that is able to interpret the experts’ opinions as fuzzy numbers. Finally, we employ a recently introduced fuzzy ranking methodology, satisfying many properties according to human intuition, in order to determine whether the expert’s fuzzy opinion is favorable enough (comparing with a fixed fuzzy number that indicates Agree or Strongly Agree). A cross-cultural validation was performed to illustrate the applicability of the proposed method. The proposed approach is simple for two reasons: it does not need a defuzzification step of the experts’ answers, and it can consider a wide range of fuzzy numbers not only triangular or trapezoidal fuzzy numbers.

Highlights

The Delphi method was developed during the 1950–1960s to forecast the impact of technology on warfare by Dalkey and Helmer [1] and Rieger [2]
To face the above-mentioned problems, the main aim of this paper is to develop a simple theoretical and methodological approach that leads to diverse applications in many fields and can be employed without a defuzzification step, considering a wide range of fuzzy numbers to collect the experts’ judgments
On the other hand, such opinions are collected through a computerized application that is able to interpret the experts’ opinions as fuzzy numbers

Summary

Introduction

The Delphi method was developed during the 1950–1960s to forecast the impact of technology on warfare by Dalkey and Helmer [1] and Rieger [2]. Iterative surveys (often more than two, up to three or four rounds) are usually used The experts give their opinions about each item in a numeric way or by using labels and make some commentaries to improve the statement of the item from their respective point of views An anonymous group of experts is invited to participate through the process of mail or online questionnaires and to give their independent opinions (the questionnaire survey is conducted anonymously and does not require meeting them in person) about the items of the questionnaire.

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