A Formalization of the Theory of Expertons. Theoretical Foundations, Properties and Development of Software for Its Calculation

By Comalat, J. C. Ferrer; Mustarós, S. Linares et al. | Fuzzy Economic Review, May 2016 | Go to article overview

A Formalization of the Theory of Expertons. Theoretical Foundations, Properties and Development of Software for Its Calculation


Comalat, J. C. Ferrer, Mustarós, S. Linares, Coll, D. Corominas, Fuzzy Economic Review


JEL Classification: C02, C65

1.INTRODUCTION

Many economic situations that require some decision-making are unlikely to be treated with total objectivity and can be controversial. Sometimes, the poor quality of objective data means that many forecasts cannot be made satisfactorily by using only historical data from statistical series and so the compilation of expert information is more appropriate.

Aggregating the opinions of a group of experts has been studied from different perspectives by Rantilla and Budescu (1999) to determine how a decision-maker might aggregate different types of entry data to generate an adequate global response. Given that the data provided by experts are based on a subjective opinion, however, it is normal to think that these data may contain some level of uncertainty. Treatment of this uncertainty from a probabilistic standpoint is a valid first option. Gerardi, McLean and Postlewaite (2009) tried to eliminate errors caused by such uncertainty using a Bayesian model.

Treating uncertainty using fuzzy models is another valid option. With the birth of fuzzy logic, a new approach to information-gathering techniques also begins, in which the aggregation of information supplied by various experts, from the perspective of fuzzy logic work, leads to the emergence of new data fusion techniques. Exploring new techniques of data aggregation obtained from the fuzzy treatment of data brings us to the concept of experton (Kaufmann,1987, 1988), which allow all of the data expressed by a group of experts regarding their opinion of a certain vague characteristic to be drawn together.

In the economic field, experton theory was developed by Kaufmann and Gil Aluja (1987, 1990, 1993). Its practical applications have been numerous, especially in the social sciences and particularly in the area of economics. Thus, Couturier and Fioleau (1996) applied the experton concept to financial diagnosis. García and Lazzari (1996) introduced the experton to develop evaluation instruments, while Cassú, Ferrer and Bonet (2001) applied the concept to the study of growth prospects in economic sectors. Lopez and Mendaña (2003) and Merigó, Gil Lafuente and Barcellos (2010) used it in decision-making problems. Gil-Lafuente and Bassa (2010) applied the experton to determine customer needs. Merigó, Casanovas and Yang (2014) used the concept in a multi-decision problem. Sirbiladze, Khutsishvili and Ghvaberidze (2014) introduce it for an investment problem. Jaile, Ferrer and Linares (2015) apply the concept of experton to construct a neural network that allows predictions of future values of an economic variable. And Chavez, González-Santoyo, Flores B. and Flores J. J. (2015) use it for a human resource management problem.

However, more attention has generally been paid to the practical construction of an experton following the initial construction proposed by Kaufmann and Gil Aluja and less to the mathematical formalization of the concept and its relationship with Φ-fuzzy sets and probalilistic fuzzy sets.

This work aims to substantiate the concept by formalizing it and in doing so justify various properties of expertons and build software to calculate expertons that can be used in any field study.

The concept of the experton which is built based on the aggregation of the opinion of various experts on a specific question is very closely linked to the concept of the fuzzy set, and as we will show, is defined as a certain type of probablistic fuzzy set, a concept introduced by Hirota (1977). We will therefore be using the concept of Φ-fuzzy sets introduced by Sambuc (1975) and Sánchez and Sambuc (1976) and the concept of Hirota's probabilistic fuzzy set (Hirota 1977, 1981, Hirota and Pedrycz 1983).

This work has been divided as follows: there will be a first section on concepts, which will show that the concept of the experton is closely linked to the concept of fuzzy sets, since it will be defined as a certain type of probabilistic fuzzy set. …

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