# Finding Business Failure Reasons through a Fuzzy Model of Diagnosis

By Scherger, Valeria; Vigier, Hernán P. et al. | Fuzzy Economic Review, May 2014 | Go to article overview

# Finding Business Failure Reasons through a Fuzzy Model of Diagnosis

Scherger, Valeria, Vigier, Hernán P., Barberà-Mariné, M. Glòria, Fuzzy Economic Review

(ProQuest: ... denotes formulae omitted.)

1. INTRODUCTION

In literature there are very few models which use fuzzy relations to diagnose problems in firms [1] to [5]. In this work is proposed to apply the Vigier and Terceño diagnosis model [1] to analyse the causes that generate problems or diseases in firms. This model based on fuzzy binary relations between causes and symptoms has advantages over other prediction models, understanding the process of business failure and has the capacity to diagnose problems and simulate (or complement) the analyst's task. One of the main results of this model is to forecast firms' health and find out the failure reasons. It provides a different point of view from the traditional models ([6], [7], [8], [9], [10], [11], etc.), incorporating elements of subjectivity and uncertainty formalized by fuzzy logic, and gives solutions (or introduces improvements) concerning most of the methodological problems discussed in the literature1. Due to characteristics of the proposed problem, which uses a large number of qualitative variables or expert analysts' opinions, it is very difficult to find a comprehensive solution using a classical method of resolution.

The application of the model is based on the construction of incidence matrices of symptoms and causes and the estimation of an economic-financial knowledge matrix to detect the reasons of failure.

2. THE DIAGNOSIS MODEL

The model presented by [1] is based on the estimation of an economic-financial knowledge matrix (R) that starts in the estimation of the symptoms-causes matrices. The construction of the matrix R is determined by a group of symptoms S = {Si} , where i = 1,2,...,n, of causes C = {Cj} , where j = 1,2,...,n, p., and of firms E = {Eh} , where h=1,2,3,...,m, in which is possible to identify symptoms and causes.

... (1)

being,

Q = [qhit] = [qiht] : transposed membership matrix of the firms' symptoms

P = [phj] : membership matrix of the firms' causes

a : fuzzy relations operator

That is,

... (2)

where

...

The matrix R is used for predicting the incidence level of each one of the causes defined in the model2

The model recommends that, to perform a study as homogeneous as possible, the set of selected companies (E) be from a region and a specific productive sector and also be composed of healthy and unhealthy companies to detect differences in indicators of both groups. Finally, the set of the years or periods T = {Tk} , where k=1,2,3,...,t, for which the estimate is made must be defined.

As mentioned above, each matrix element rij is obtained through the operation between the transposed membership matrix of symptoms and the membership matrix of causes that satisfy the smaller ratio. As the model proposes the determination of possible diseases from the estimate of R, each rij shows the level of incidence between the symptom Si and the cause Cj .

To overcome potential inconsistency problems, the model provides the use of a filtering method based on the decomposition and operation of each of the rij , that is, (qi1ap1j ) ; (qi2ap2j ) ;....; (qihaphj ) ;....; (qimapmj ) . The inconsistency occurs when there are high intensity levels for many companies, and low ones for a few, therefore the alpha indicator may incorrectly select the lowest intensity. The methodology consists of the removal of those companies that can cause inconsistent levels of incidence3. Furthermore, the model develops the distinctive features in the aggregation of matrices and the verification of trends that may distort the results of the model. These techniques allow obtaining a matrix with temporary validity and capacity to predict (R ).

The matrix R is used to make predictions regarding the health of the companies, being necessary the determination of significant levels of incidence between symptoms and causes to assign a degree of occurrence of a specific disease. …

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