Ranking Tehran’s Stock Exchange Top Fifty Stocks Using Fundamental Indexes and Fuzzy TOPSIS

Investment through the purchase of securities, constitute an important part of countries economic exchange. Therefore, making decisions about investing in a particular stock has become one of the most controversial areas of economic and financial research and various institutions have began to rank companies stock and determine priorities of stock purchase to investment. The current research, with the determination of important required indexes for companies ranking based on their shares value on the Tehran stock exchange, can greatly help to the accurate ranking of fifty premier listed companies. Initial ranking indicators are extracted and then a decision-making group (exchange experts) with the use of the Delphi method and also non-parametric statistic methods, determines the final indexes. Then, by using Fuzzy ANP, weight criteria are obtained with taking into account their interaction with each other. Finally, using fuzzy TOPSIS and information extraction about the premier fifty listed companies of Tehran stock exchange in 2014 are ranked with the software "Rahavard Novin”. Sensitivity analysis to criteria weight and relevant analysis presentation was conducted at the end of the study procedures. Keywords-performance evaluation; stock efficiency; companies ranking; ANP Fuzzy; TOPSIS.


INTRODUCTION
Much research in ranking and evaluating companies has been conducted, especially on stock exchange companies.In [1], authors applied time series analysis and multi-criteria decision to anticipate the financial performance of companies.The aim of this study was to estimate the financial performance of companies in Turkey between 2012 and 2015.For this purpose, two time series analysis and multi-criteria decision approach analysis were used.In [2], authors checked to evaluate the efficacy data on the value of stock options in the Taiwan market.In [3], authors began to combine soft computing and fundamental analysis to select stocks.The results show that the proposed method could pay to stock selection, well.In [4], using CBR select stocks was investigated.The study results show that the proposed model could select the stock's choice based on the determined indexes very well.In [5], the performance of banks was evaluated with fuzzy hierarchical analysis and fuzzy TOPSIS.In [6], authors surveyed the TOPSIS approach as a ranking approach.
In this paper, the 2014 Tehran Stock Exchange market is considered and its statistical population is the heads of 87 Tehran Stock Exchange agencies.Also for the financial information extraction of the companies, the "Rahavard Novin" software is used.Two fuzzy network analysis and Fuzzy TOPSIS technique are used to analyze the results and rank companies.Two matrix (middle number and near fuzzy number) of each matrix are derived and then an adaption of each matrix based on the computing hours is computed.

II. BASICS OF USED ANALYSIS METHODS
The steps of computing fuzzy matrix pairwise comparison compatibility rate are:

A. Step 1
In the first phase divide triangular matrix to two matrixes.

B. Step 2
Each vector weight vector with using saati method is computed as below: The biggest Eigen vector for each matrix is calculated with below relations:

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Step 4 Consistency index is calculated with using below relations.
To calculate the consistency rate (CR), the CI index is divided to random index (RI).If the result value is less than 0.1, matrix diagnosed consistent and usable.To produce random matrixes, first the middle value of triangular fuzzy number produced randomly in [1/9, 9] interval mutually.Then, low bound of each triangular number in [produced middle value, 1/9] interval and upper bound value in [1/9, produced middle value] interval is produced randomly and at last, their random index value was obtained by dividing resultant random matrix to two middle bound matrix and geometric mean of up and low bounds matrix.We compare computed consistency rate for two matrix based on below relations with threshold 0.1: If both indexes were lower than 0.1, fuzzy matrix is consistence.While both were more than 0.1, decision-making will be asked to reconsider the priorities presented and while only CR m (CR g ) was more than 0.1, decision-making of reconsidering in middle values (bounds) make fuzzy inference.

III. STEPS OF OBTAINING COMPONENT WEIGHTS WITH FUZZY NETWORK ANALYSIS
Based on super-matrix, steps of component weights computing include: The first step is to bring together experts comments, the paired comparisons of geometric mean respondents is taken.Second: the Eigen vector comparison: to calculate Eigen vector comparison each pairwise comparisons tables aggregated, according to equation logarithmic least squares method is used.
While, there was not one level ii W matrix , it is necessary to substitute identity matrix with the same degree of that matrix.
In the other word, below formula is used.
TOPSIS method is a common approach in decision making multi-criteria (MADM) to the development phase space.This method requires a decision-making matrix which rows of this matrix is options and columns of the matrix are the criteria [7,8,9].With a systematic approach, we can develop a TOPSIS decision making method to fuzzy space.To increase the accuracy of calculations, we can assume that the degree of importance of decision criteria and qualitative variables rates as linguistic variables were collected.In fuzzy space, linguistic variables can be defined in the form of fuzzy numbers.Many decision-making techniques in fuzzy space rather profit paired comparisons to reach a decision matrix.Always a multi-criteria decision-making problem in fuzzy space can be shown in matrix form as below.Note that each of the linguistic variables X ij and W j can be in the form of triangular fuzzy numbers is defined as follows: For the TOPSIS technique, it is necessary to normalize obtained data in decision-making matrix using Euclidean norms.This normalization method has high complexity.But if we want to use this technique in a fuzzy space, we can use simpler norms such as linear to data homogenization.Thus, normalized fuzzy decision matrix is obtained as follows

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If we define B and C respectively as set of same direction criteria with cost and profit, we have: By using this normalizing method, we can now homogenize all fuzzy data based on obtained triangular numbers in a range between zero and one.Now, based on row vector of criteria weights (W) and normalized decision matrix R can be obtained the decision weighted matrix.
Each of the weighted normalized decision matrix elements are fuzzy triangular numbers which their numbers are homogenized between zero and one.Based on this matrix, positive and negative ideal options can be defined: ) ,..., , ( ) ,..., , ( After calculating positive and negative ideal options, the distance of each options of these two ideal choices will be achieved At last, the closeness coefficient is calculated to determine the priorities of options.This coefficient can be obtained based on the values * , i i d d  of each alternative as follows: Now, we can sort all options based on higher value of CC i .

IV. DATA ANALYSIS RESULTS
In this step, the most important financial ratios were identified as primary indexes.These indexes are mentioned in 12 criteria-groups in below and were offered to experts by questionnaire to each experts mention their opinions about importance of this criterion in the ranking process of Tehran Stock Exchange company's shares (Table I).Answers of 51 completed questionnaires regarding the importance of criteria of ranking Tehran Stock Exchange company shares is shown as table and graph with Delphi method by descriptive approach.In this questionnaire, the importance of intended indexes in the direction of the research purposes has been questioned.In this part, with considering Figure 1, we calculate each fifty premier company ranking indexes weight and active company of Tehran Stock Exchange with ANP fuzzy approach for group decision making.Then, pairwise comparison of 6 final criteria is defined, rather than goal and other criteria (control criteria) including 7 tables in second questionnaire were offered to persons who complete the first questionnaire and decision-making group members compared criteria pairwise comparison in Verbal terms forms "same preferences, small preferred, the strong preference, preferred very strong "which respectively represent fuzzy numbers are 1,3,5,7,9.It should be noted that the decision group members were asked to fill out entries above the main diagonal of pair-wise comparison tables, because in considered fuzzy ANP approach, pairwise comparison matrices elements are reversed in comparison to the main diameter.Summarizing shows the pairwise comparison of indexes for 22 W matrix (Table II  Fuzzy weight for each factor of prioritizing top and active companies in stock exchange is as shown in Table IX.The fuzzy weight of each prioritizing indicator of active and top companies in stock exchange is shown in Table X.In the next phase, ranking of companies using TOPSIS fuzzy approach is determined with respect to the decision criteria specified above and the above weights (Tables XII-XII).Company stock ranking is a method to convert raw data into relevant information for decision-making.Ranking can be performed based on different parameters such as the criteria and fundamental analysis elements.The aim of this study is to provide a fuzzy multi-criteria decision making model to rank the stocks of companies of Tehran Stock Exchange.At first by using stock exchange experts as a decision-making group and then by using non-parametric statistical analysis to establish ranking criteria.Then, the ANP multi-fuzzy technique is used to determine their weight.Then, the fuzzy TOPSIS technique is used and the fifty top stocks in the Stock Exchange were ranked.After performing the ranking for sensitivity analysis of criteria weight, their weights are shifted mutually with each; hence, the rank of companies will be compared in fifty-one situations, by selecting two criteria of six criteria.A consistency is shown.The company that was placed in the second rank in main ranking occupied the first rank in all 51 situations and the company occupied the second rank in all 51 situations was placed in the first rank in main ranking.It is noteworthy that the decision maker can present a ranking by giving the desired amount of six indicators of the company.One can even begin to analyze the sensitivity of rate changes by criteria weight shift.The first ranking company has a higher special value per share and D/E allocation ratio in comparison to other companies..In the same manner, comparing financial ratios with other companies will uncover confirm acceptability and accuracy of ratings.Moreover, the results of interviews with the authorities on the final indicators of the research represent that the criteria are the most basic possible indicators for ranking stocks so that some experts believe that 80 percent of ranking result depends on three first factors that have more weights.In addition, the results of surveying experts about shares' obtained ranks in the ranking express that the results are very much close to reality; especially, companies with higher ranks can meet the demands of shareholders largely.

VI. SUGGESTIONS FOR FUTURE STUDIES
Further studies can define subscales for each scale through more investigations; they can also solve the model according to mutual impacts of subscales of each group on each other as well as on other scales and subscales.As there are many problems in estimating the beta value in Tehran Stock Exchange, one can extract beta coefficient from other models like Dimson instead of using Rahavard Novin Software in order to obtain better results.

First matrix is formed of middle numbers of
matrix contains Geometric mean of the upper and lower triangular numbers,

Fig. 1 .
Fig. 1.Company ranking indexes weight and active company of Tehran Stock Exchange with ANP fuzzy

TABLE I .
THE IDENTIFIED PRIMARY CRITERIA FOR RANKING COMPANY STOCKS

TABLE II .
COMMON PAIRED COMPARISONS AVERAGE FUZZY IN RANKING INDICATORS OF ACTIVE COMPANIES AND TOP STOCKS (MATRIX)

TABLE III .
COMMON PAIRED COMPARISONS AVERAGE FUZZY IN RANKING INDICATORS IN RELATION TO BETA COEFFICIENT INDEX COMMON PAIRED COMPARISONS AVERAGE FUZZY IN RANKING INDICATORS IN RELATION TO EARNINGS PER SHARE (EPS)