Applying fuzzy MCDM for financial performance evaluation of Iranian companies

AbstractFinancial performance evaluation is very important in a highly competitive business environment. Accordingly, an accurate and appropriate performance evaluation is critical. Financial performance indicators reflect the competitiveness of a company and they must be carefully identified in the evaluation process. Generally, accounting measures are used for performance evaluation. However, these measures are not sufficient for performance evaluation in the today’s competitive economy. Therefore, value based measures have recently been introduced to express the company value. In this study, a hybrid approach is proposed for financial performance evaluation of automotive companies of Tehran stock exchange (TSE). For this purpose, a hierarchical financial performance evaluation model is structured based on the accounting measures and economic value measures. In this approach Fuzzy Analytic Hierarchy Process (FAHP) is applied to determine weights of criteria. Then the companies are ranked by using Fuzzy ...


introduction
In a competitive environment, characterized by the scarcity of resources, performance measurement and management play a crucial role (Amado et al. 2012). Accordingly, an accurate and appropriate performance evaluation is very crucial.
Financial aspect is one of the main aspects of the organization performance. Traditionally it should be attractive. Seeing that profit is the main goal of many companies, financial performance and proper evaluation is very important. As financial performance indicators reflect the competitiveness of a company, they must be carefully identified in the evaluation process .
Most of the economical, industrial, financial or political decision problems are multi attribute. Multiple Criteria Decision Making (MCDM) is an advanced field of operation research. It provides decision makers and analysts with a wide range of methodologies, which are overviewed and well-suited to the complexity of economical decision problems (Zavadskas, Turskis 2011). The application of multi-criteria decision making methods significantly improves the robustness of financial analysis and business decisions in general (balezentis et al. 2012).
In the current research a new multiple criteria model, consisting of Accounting measures and Economic value measures is presented, also a hybrid approach of MCDM methods in fuzzy environment for financial performance evaluation of companies is provided. At first FAHP (Fuzzy Analytic Hierarchy Process) is used to determine the weights of the main criteria and sub criteria. Then fuzzy VIKOR (Fuzzy VlseKriterijumska Optimizacija I Kompromisno Resenje), ARAS-F (Fuzzy Additive Ratio Assessment) and fuzzy COPRAS (Fuzzy Complex Proportional Assessment) are applied simultaneously for ranking the automotive companies traded on Tehran stock exchange in 2002-2011. Final ranking of companies is provided by using mean ranks.

literature review
Several studies on financial performance evaluation are focused on ranking the alternatives according to their financial performance measures, included in their comparison environments. Kung et al. (2011) applied fuzzy MCDM methods for selecting the best company, based on financial report analysis. The approach used FAHP to select weighting indicators and fuzzy TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) for outranking the five major airlines. balezentis et al. (2012) used fuzzy TOPSIS, fuzzy VIKOR and ARAS-F methods for integrated assessment of Lithuanian economy in 2007-2010 periods, based on financial ratios. Ergul and Seyfullahogullari (2012) applied ELECTRE III for ranking of retail companies trading in Istanbul stock exchange (ISE), based on their financial performance in 2008-2010. Lee et al. (2012) performed a comparative study on financial positions of shipping companies in Taiwan and Korea. At first the study applied Entropy to find the relative weights of financial ratios of four companies, and then it used grey relation analysis to rank the companies. Yalcin et al. (2012) constructed a hierarchical structure of the financial performance model for ISE's manufacturing company. The approach used FAHP, VIKOR and TOPSIS. bayrakdaroglu and  proposed to use MCDM for strategic financial performance evaluation of ISE. The research applied FAHP for determining the relative significances of criteria and used VIKOR for best company selection. Ignatius et al. (2012) surveyed financial performance of Iran's Automotive Sector based on PROMETHEE II in the study. Cheng et al. (2012) developed an approach combining fuzzy integral with Order Weight Average (OWA) method for evaluating financial performance in the semiconductor industry of Taiwan in 2008. Cement firms are evaluated by taking into consideration only some of the traditional financial performance measures.
Recent studies on the subject are summarized in Table 1.

Proposed model
A new multi criteria model, consisting of Accounting measures and Economic value measures is developed with help of the financial experts and presented in the current study. A combinative approach of MCDM methods in Fuzzy environment for financial performance evaluation of companies also provided. Yalcin et al. (2012) constructed hierarchal structure for financial evaluation of manufacturing company on the ground of value based financial performance and accounting based financial performance as main criteria and each having four sub criteria. The model proposed by the Authors differs from Yalcin et al. (2012) model. The proposed model is shown in Figure 1

MCDM methods
MCDM is an advanced field of Operation Research that provides decision makers and analysts with a wide range of methodologies, well-suited to the complexity of economical decision problems. Available methodologies and their application for economic decisions are broadly overviewed by Zavadskas and Turskis (2011).
In the presented study four fuzzy MCDM methods were used and applied for evaluation of TSE's companies. At first FAHP was used to determine weights of main criteria and sub criteria. Next the research used fuzzy VIKOR, ARAS-F and fuzzy COPRAS for ranking the companies according to best financial performance.

Fuzzy Analytic Hierarchy Process (FAHP)
Analytic Hierarchy Process (AHP) was introduced by Saaty (1971). In the current research the weights of financial performance criteria are obtained by using extent FAHP method. That is because of the computational easiness and efficiency .
Calculation of FAHP can be described as follows. Assume that be an object set, and be a goal set. Each object is taken and extent analysis for each goal is performed, respectively. Therefore, m extent analysis values for each object can be obtained, with the following signs: 1 2 ,..., ,..., , The further steps of extent FAHP can be given as follows.
Step 1. The value of fuzzy synthetic extent with respect to the i th object is defined as: Table 2 perform the fuzzy addition operation of β extent analysis values for particular matrix such that: and to obtain values such that: Then the inverse of the vector above is computed: Step 2. As ( ) are two triangular fuzzy numbers, the degree of possibility of 2 and can be equivalently expressed as follows: where d is the ordinate of the highest intersection point D between 1 Q µ  and 2 Q µ  (Fig. 2).
To compare 1 Q  and 2 Q  , we need both values of ( ) Step 3. The degree possibility for a convex fuzzy number to be greater than k convex fuzzy 1 Q  (i = 1, 2, … , k) numbers can be defined by: Assume that ( ) ( ) Then the weight vector is given by: are n elements.
Step 4. Via normalization, the normalized weight vectors are: where W is a non-fuzzy number.

Fuzzy MCDM outranking methods
In this study three fuzzy outranking methods are used. Let us assume the fuzzy decision making matrix , where 1,2,..., i m = and 1,2,..., j n = represent the number of alternatives and criteria, respectively. In this study m = 6 and n = 11. The j th criterion of the i th alternative is represented by triangular fuzzy number ( ) . Also each j th criterion is assigned with respective coefficient of significance j w  , that it obtained by FAHP. benefit criteria are members of benefit criteria set B, while cost criteria are members of respective set C.

Fuzzy viKor
based on crisp VIKOR that was introduced by Opricovic (1998), also Opricovic and Tzeng (2004), fuzzy VIKOR was developed later and presented in many studies (Antucheviciene et al. 2011(Antucheviciene et al. , 2012Chou, Cheng 2012;Vinodh et al. 2013). VIKOR is based on measuring the closeness to the ideal alternative according to separate cases of p L metric (balezentis et al. 2012). Computing of fuzzy VIKOR consists of following steps: Step 1. The fuzzy best values j f +  and the fuzzy worst values j f −  are found: max , min , , min , max , .
Step 2. The distances of each alternative from the ideal one are determined: Step 3. The reference point is defined by computing values of S +  , S −  , R +  , and R −  , which, in turn, enable to obtain the final summarizing ratio i Q  : min , max , min , max ; Step 4. Defuzzifying triangular fuzzy numbers i S  , i R  , and i Q  into crisp values. A center of area (COA) defuzzification method is used to determine the best non-fuzzy performance (BNP). The bNP value of the triangular fuzzy number (l i , m i , u i ) can be found by the following equation: Step 5. Ranking the alternatives, sorting by the values S i , R i and Q i , in decreasing order. The results are three ranking lists.
Step 6. Proposing as a compromise solution, for given criteria weights, the alternative (a'), which is the best ranked by the measure Q if the following two conditions are satisfied: C1. "Acceptable advantage": Q(a") -Q(a') ≥ DQ, where a" is the alternative with second position in the ranking list by Q; m is the number of alternatives (Chou, Cheng 2012).
C2. "Acceptable stability in decision making": Alternative a' must also be the best ranked by S or/and R. This compromise solution is stable within a decision making process, which could be: "voting by majority rule" (when v > 0.5 is needed), or "by consensus" v ≈ 0.5, or "with veto" (v < 0.5). Here, v is the weight of the decision making strategy "the majority of criteria" (or "the maximum group utility").
If one of the conditions is not satisfied, then the set of compromise solutions is proposed, which consists of: Alternatives a' and a", if only the condition C2 is not satisfied; Alternatives a', a",…,a (k) , if the condition C1 is not satisfied; a (k) is determined by the relation Q(a (k) ) − Q(a') ≈ DQ, the positions of these alternatives are "in closeness".

ArAs-F
The ARAS-F is based on comparing every alternative with the hypothetic ideal one (Turskis, Zavadskas 2010;Kersuliene, Turskis 2011;balezentis et al. 2012). The calculation steps of ARAS-F are as presented below.
Step 1. In this method the ideal alternative is described in the following way: Step 2. The normalized values ij d  are obtained: Step 3. Each ij d  is weighted by computing elements of the weighted-normalized matrix: where j w  is coefficient of significance and ˆi j d  is the weighted-normalized value of the j th criterion of the i th alternative.
The overall utility i S  of the i th alternative is computed in the following way:  is a fuzzy number, the COA method is applied for defuzzification: Finally, the relative utility of the ith alternative i K is found: The best alternative is found by maximizing value of i K .

Fuzzy CoPrAs
COPRAS method was first put forward by Zavadskas and Kaklauskas (1996). Fuzzified COPRAS was presented by Zavadskas and Antucheviciene (2007). It is used to prioritize the alternatives on the basis of several criteria along with the associated criteria weights. This method works on a stepwise ranking and evaluation procedure of the alternatives in terms of their significance and utility degree. Crisp or modified method for uncertain environment has been successfully applied in for maintenance strategy or performance evaluation, for selection of effective decisions in construction or management (Yazdani et al. 2011;Kanapeckiene et al. 2011;Fouladgar et al. 2012;Tamosaitiene, Gaudutis 2013;Das et al. 2012;Mulliner et al. 2013;Staniunas et al. 2013;Palevicius et al. 2013).
Calculations of fuzzy COPRAS can be described as follows: Step 1. Normalize the values of ij d  by using the following formula: Step 2. Determine the weighted normalized decision matrix: where ij d  is the normalized performance value of i th alternative on j th criteria and j w is the associated weight of the j th criteria.
Step 3. The sums i S + and i S − of weighted normalized values are calculated for both beneficial and non-beneficial criteria, respectively. For benefit criteria, higher value is better and for cost criteria, lower value is better for the attainment of goal. i S + and i S − are calculated using the following equations: Step 4. Determine the relative importance or priorities of the candidate alternative by the following equation: Step 5. Since ( ) 1 2 3 , , , 0,1,..., ,  is a fuzzy number, the COA method is applied for defuzzification: where the relative importance i H of an alternative shows the extent of satisfaction attained by that alternative. Among the alternatives, one with the highest i H value is the best alternative.
Step 6. Calculate the performance index ( ) i PI of each alternative as: Here H max is the maximum value of relative importance. i PI value is utilized to get complete ranking of the alternatives.

Applications of the proposed approach
The aim of this study is to present a fuzzy approach to evaluate the financial performance of the companies in the Iran, traded on TSE, by using both Accounting measures and Economic value measures together and in a fuzzy environment. This approach was applied for evaluation of automotive companies of TSE in 2002-2011, i.e. in a period of ten years. Six companies were selected for this study. For this period of the research, annual financial statements of companies which passed independent external auditing are considered. Data was gathered from the TSE's Database and using Rahavard Novin software.
The overall results were obtained by taking the geometric mean of individual evaluations. Combined pairwise matrix of main criteria with their weights from FAHP is shown in Table 4. With respect to the results, Economic value measures are more important than Accounting measures in financial performance evaluation of TSE's companies. Table 5 shows the weights of the sub criteria were obtained by FAHP. CVA, TVA, REVA have highest weight among sub criteria, respectively, so TSE's companies should Pay special attention to this measures about their financial performance.

ranking the alternatives
The following approach was used for convert crisp numbers of financial measures into fuzzy numbers. As for time series data, when Let us assume are the initial values of each criterion, obtained using Eq. (28). As some of values in each criterion were negative, for preventing of any problem in computation, all the values in each criterion are transformed to positive values by the following equation: Indeed the above equation is the same as in the computation steps of methods.
As it was mentioned, six Iranian automotive companies are analysed. Initial data on their financial performance measurements is presented in Annex 1.
At first fuzzy VIKOR is used to rank the companies. usually in other studies, the value of v is considered 0.5, but in this study different values of v are considered and ranking of Q was obtained from average of different values of Q i . Table 6 shows the results of fuzzy VIKOR with different values of v. As one can see from the Table 6, RENA has the minimum score with respect to the Q values, also conditions of Acceptable advantage and Acceptable stability in decision making are satisfied by this alternative. Accordingly, RENA is chosen as the best company in terms of financial performance among other companies. Table 7 shows the results obtained from ARAS-F and fuzzy COPRAS together. In this proposed model all the criteria are of benefit, while for applying COPRAS a cost criterion is necessary. Hence values of one criterion (OPG) for all alternatives have been reversed for feasibility of using fuzzy COPRAS method for this study. As it shown, RENA is the best company with respect to the financial performance among automotive companies traded on TSE in 2002-2011.
Finally, for composing the final order of priority among all alternatives, average of obtained ranks of the three methods has been considered. Table 8 shows the final ranks of the companies.

Conclusions
Financial ratios provide useful quantitative financial information about performance of a company. In this context, this study displays a fuzzy hybrid approach for the financial performance evaluation of companies.
In the proposed approach, at first FAHP is used to determine the weights of the main-criteria and also sub-criteria. Then fuzzy VIKOR, ARAS-F and fuzzy COPRAS are used for ranking the companies based on financial performance, simultaneously. Finally, by combining the results of these three methods via mean ranks, final ranking of the companies can be presented.
In today's world economy, good financial situations provide company's competitive advantage. Many studies in the literature involving MCDM procedures use only the traditional financial ratios. In this study both of Accounting measures and Economic value measures have been used for financial performance evaluation. Results showed that Economic value measures are more important than Accounting measures for companies' evaluation. Also, to achieve better performance evaluation, companies should pay more attention to CVA, TVA, REVA and other measures in line with calculated their relative significances.
A case study of automotive parts producer companies traded on TSE in 2002-2011 is presented. The proposed approach is applied for measuring financial performance of companies in uncertain environment with respect to multiple criteria.
Further study can include some other Economic value measures like shareholder value added (SVA), equity economic value added (EEVA) and other for performance measures. In addition to the proposed methods in this study, some other MCDM methods can be used in this area.