342 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) ISSN (Print) 2313-4410, ISSN (Online) 2313-4402 ยฉ Global Society of Scientific Research and Researchers http://asrjetsjournal.org/ Sustainable Way of Choosing Effective Electronic Devices Using Fuzzy TOPSIS Method Mahmud Hasana*, Saddam Hossainb, Mir Kaosar Ahamedc, Md. Sharif Uddind a,bMathematics and Natural Sciences Department (MNS), BRAC University, ,Dhaka-1212 cDepartment of General Educational Development Daffodil International University, Dhaka 1207 dMathematics Department, Jahangirnagar University, Dhaka 1342 aEmail: mahmudmathju@gmail.com bEmail: saddam.hossain@bracu.ac.bd cEmail: kaosar.ged@diu.edu.bd dEmail: msharifju@yahoo.com Abstract Choosing sustainable electronic device is a growing concern among the peoples of Bangladesh. A perfect choice can reduce the Cost as well as sufferings. In this paper, we have considered four smart phone manufacturing company corresponding four major features such as Android version, Battery power, RAM and Cost which is characterized by weighted value under fuzzy consideration to find a sustainable device. This selection is illustrated by modified TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method for normalizing the given data. TOPSIS is one of the numerical methods of the multi-criteria decisions making (MCDM), which is a broadly applicable method with a simple mathematical model. Furthermore, the numerical analysis suggests that, modified TOPSIS method could be very effective to find a sustainable device which can also be cost effective for the peoples of Bangladesh. Keywords: Sustainable Device; TOPSIS Method; MCDM; Android Version; Cost Effective. 1. Introduction The user-oriented design is the most important issue in todayโ€™s Smartphone market in Bangladesh. In recent years, usability of effective design has become expected, particularly different features of Smartphone. Usability considers soaring user happiness in juxtaposition with user performance [5]. ------------------------------------------------------------------------ * Corresponding author. http://asrjetsjournal.org/ American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 35, No 1, pp 342-351 343 To the peoples of Bangladesh usability includes three main concepts: effectiveness, efficiency, and user happiness. User assessment of the usability dealings affects purchasing of the creation [6].It could be said that the last quarter of the 20th century and the beginning of new millennium have flourished in different studies and researches aiming to expand the decision-making systems in situations in which dealings within the system and the environment are becoming ever more convoluted and more active and when the reaction time to actual or understood dysfunctions becomes a substantial aspect of achievement [2]. Since manufactures have provided different types of Smart phones in the market, the daily usage of Smart phones have created a decision making problem for buyers/users nowadays which are varies in features. Though there is argument that the price of Smart phones determines the quality of Smart phones but that is not true since our lifestyle are getting sophisticated and consumers are ready to pay any amount of money to purchase high quality Smart phones. So how can a Smart phones user buy the best Smart phones from the market? This paper aims to answer the stated question perspective of Bangladesh by modified TOPSIS method. Considering overall user of Smartphone we have modified TOPSIS method [14] to make best option. In the proposed method ,we considered four smart phone manufacturing company Samsung, Symphony, Walton, Micromax corresponding four major features such as Android version, Battery power, RAM and Cost to identify perfect device. The objective of this study is to design a methodology for evaluation of best devices for the customers. Most of the people of Bangladesh are interested to emphasize on price for buying any kinds of Smartphone. The methodology will serve tool for decision making in purchasing Smartphone; we modified the method for the Smartphone users of Bangladesh not only cost effective but also effective viability and well features. Basically we make small data analysis to choose best feature of Smartphone from 100 students at BRAC University. This analysis helps to give weighted value for specific features. This Section dealing with effective purchasing will become a part of the whole decision making chain where the return on investment and the expected usability of the device must also be considered. This study, how- ever, addresses solely the issues of the choice of a suitable device, not the issue of their deployment. We have applied proposed method [15] for best device selection by proper modification. 2. Statistics smart phone users in bangladesh According to latest reports, there are 106,000,000 active mobile phone subscribers in Bangladesh, and roughly 95% of them are prepaid connection users. However, there is no official statistic for Smartphone owners. The proliferation of local, low cost smart phones has changed the handset user dynamics over the last few years. Whereas Nokia had 80% market share even a few years ago, nowadays most new handset sale is going to Symphony, a local brand that gets handsets made and branded in China; closely followed by Samsung, Maximus, Micromax, Walton (another local brand) and a few other minor players. Apple and Nokia are here, but their contribution is very low. As a rough estimate, we can assume that there are around 1 million Smartphone users in Bangladesh. The forecast illustrates the number of total mobile data subscriptions in Bangladesh from 2010 to 2015. The number of mobile data subscriptions is projected to amount to 102 millions, in 2015 [4]. Hence, from the statistics shows American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 35, No 1, pp 342-351 344 the proper choice of electronic device especially Smartphone is major important for the Smartphone user. An overall mobile market in Bangladesh shown in below: As per latest research from the Smartphone sub-segment saw a strong 20% growth highlighting a rapid decline in feature phone demand (-10%) during the quarter. The smart phones as a share of total mobile phones is estimated to rise from 28% to almost 50% by the end of 2017[14] Table 1: Bangladesh Smartphone Shipment share in 2016 [14] Symphony mobile 45% Samsung 15% Huawei 9% Walton 9% Lava 8% Others 14% Total 100% Table 2: Smartphone import growth in Bangladesh [14] Year Number of Smartphone ( in $ millions) 2012 21 2013 118 2014 262 2015 316 2016 379 2017 421 2018 491 3. Data Analysis for weighted value The study was the question to 100 students of BRAC university about the best feature of a modern Smartphone which is their priority to among the features Price, Cost, Android version, Ram,Screen size, Design, Camera. The overall data analysis is shows that most of the students priority is minimum cost and from the priority we choose the weighted value under fuzzy consideration. We characterized fuzzy value for four features Cost, Android version, Battery power and Ram that is w= [.1, .4, .2, .1]. Normally in Topsis method weighted value is characterized randomly, But in our proposed method weighted value given after analysis of small data. American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 35, No 1, pp 342-351 345 Figure 1: Data analysis of Smartphone 4. TOPSIS Method TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) is one of the numerical methods of the multi-criteria decision making. This is a broadly applicable method with a simple mathematical model. Furthermore, relying on computer support, it is very suitable practical method. The method is applied in the last three decades (on the history of TOPSIS see [9,8]), and there are many papers on its applications (see [13,10,11]). Technique for order performance by similarity to ideal solution (TOPSIS), TOPSIS method is a technique for order preference by similarity to ideal solution that maximizes the benefit criteria/attributes and minimizes the cost criteria/attributes, whereas the negative ideal solution maximizes the cost criteria/attributes and minimizes the benefit criteria/attributes. A MADM problem can be concisely expressed in a matrix format, in which columns indicate attributes considered in a given problem; and in which rows list the competing alternatives. Specifically, a MADM problem with m alternatives (๐ด๐ด1, ๐ด๐ด2,โ€ฆ, ๐ด๐ด๐‘š๐‘š) that are evaluated by n attributes (๐ถ๐ถ1 , ๐ถ๐ถ2, ..โ€ฆ, ๐ถ๐ถ๐‘›๐‘›) can be viewed as a geometric system with m points in n- dimensional space. An element ๐‘‹๐‘‹๐‘–๐‘–๐‘–๐‘– of the matrix indicates the performance rating of the ๐‘–๐‘–๐‘ก๐‘กโ„Ž alternative, ๐ด๐ด๐‘–๐‘– , with respect to the ๐‘—๐‘—๐‘ก๐‘กโ„Ž attribute, ๐ถ๐ถ๐‘–๐‘–, as shown: ๏ฟฝ ๐‘ฅ๐‘ฅ11 ๐‘ฅ๐‘ฅ12 ๐‘ฅ๐‘ฅ13 ๐‘ฅ๐‘ฅ21 ๐‘ฅ๐‘ฅ22 ๐‘ฅ๐‘ฅ23 โ‹ฏ ๐‘ฅ๐‘ฅ1๐‘›๐‘› โ‹ฎ โ‹ฑ โ‹ฎ ๐‘ฅ๐‘ฅ๐‘š๐‘š1 ๐‘ฅ๐‘ฅ๐‘š๐‘š2 ๐‘ฅ๐‘ฅ๐‘š๐‘š3 โ‹ฏ ๐‘ฅ๐‘ฅ๐‘š๐‘š๐‘›๐‘› ๏ฟฝ Let W = (๐‘ค๐‘ค1,๐‘ค๐‘ค2,๐‘ค๐‘ค3, โ€ฆ โ€ฆ๐‘ค๐‘ค๐‘›๐‘›) be the relative weight vector about the criteria, satisfying. Then the procedure of TOPSIS can be expressed in a series of steps. 4.1. Objective of proposed TOPSIS method 1. To find a sustainable Smartphone which can be cost effective? American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 35, No 1, pp 342-351 346 2. Improve quality and flexibility to meet end-customers' value and reduce lead time at different stages of the supply chain in the markets of Bangladesh. 3. Another important objective is Smartphone selection process is to reduce purchase risk, and develop closeness and long-term relationships between buyers and suppliers in Bangladesh. 4.2. Assumptions We have considered four smart phone manufacturing company Samsung, Walton, Micromax, Symphony corresponding four major features such as Android version, Battery power, RAM and Cost. And our objective to find a sustainable device which is can be considered as a best option for the customer. Also we take fuzzy consideration for the weighted value according to the data in Figure 1where weighted value โ€˜๐‘ค๐‘ค๐‘–๐‘–๐‘–๐‘–โ€™belongs to between 0 and 1. โ€ข m = Four alternatives ( Smart phone models) โ€ข n = 4 Four attributes/criteria โ€ข ๐‘ฅ๐‘ฅ๐‘–๐‘–๐‘–๐‘– = score of option i with respect to criterion j โ€ข {๐‘ฅ๐‘ฅ๐‘–๐‘–๐‘–๐‘–} 4ร—4 score matrix. โ€ข J = set of benefit attributes: Cost, Android version, Ram, Battery power (more is better) โ€ข J' = set of negative attributes: cost (less is better) Also it must be noted that weighted value ๐‘ค๐‘ค๐‘–๐‘–๐‘–๐‘– โˆˆ [0,1] 5. Steps of topsis method Step 1: Construct normalized decision matrix. This step transforms various attribute dimensions into non-dimensional attributes, which allows comparisons across criteria. Normalize scores or data as follows: ๐‘Ÿ๐‘Ÿ ๐‘–๐‘–๐‘–๐‘– ๐‘ฅ๐‘ฅ๐‘–๐‘–๐‘–๐‘– โˆ‘๐‘ฅ๐‘ฅ๐‘–๐‘–๐‘–๐‘– 2 for ๐‘–๐‘– = 1, โ€ฆ ,๐‘š๐‘š; and ๐‘—๐‘— = 1, โ€ฆ ,๐‘›๐‘› (1) Step 2: Construct the weighted normalized decision matrix. Assume we have a set of Weights for each criteria wj for j = 1,โ€ฆn. Multiply each column of the Normalized decision matrix by its associated weight. An element of the new matrix is: vij = wj rij (2) Step 3: Determine the positive ideal and negative ideal solutions. Positive Ideal solution. A* = {v1 * , โ€ฆ, vn *}, (3) where vj * ={ max (vij) if j โˆˆ J ; min (vij) if j โˆˆ J' (4) Negative ideal solution. A' = { v1' , โ€ฆ,v n' }, (5) American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 35, No 1, pp 342-351 347 where v' = { min (vij) if j โˆˆ J ; max (vij) if j โˆˆ J' } (6) Step 4: Calculate the separation measures for each alternative: The separation from the positive ideal alternative is: Si * = [ ฮฃ (vj *โ€“ vij)2 ] ยฝ i = 1, โ€ฆ,n. (7) The separation from the negative ideal alternative is: S'i = [ ฮฃ (vj' โ€“ vij)2 ] ยฝ j = 1, โ€ฆ,m (8) Step 5: Calculate the relative closeness to the ideal solution Ci * = S'i / (Si * +S'i ) 0 < Ci * < 1. (9) Step 6: Rank the preference order. 6. Numerical Illustration Initially give classical range of four smart phone manufacturing company Samsung, Walton, Micromax, Symphony corresponding four major features. The weighted value ๐‘ค๐‘ค๐‘–๐‘–๐‘–๐‘– is under fuzzy consideration whose values is between 0 and 1 given below. Table 3 Weight 0.1 0.4 0.2 0.1 Android version Cost Battery power Ram Symphony 7 9 9 8 Samsung 8 7 8 7 Micromax 9 6 8 9 Walton 6 7 8 6 Steps of TOPSIS Step 1(a): Calculate ๏ฟฝโˆ‘๐‘ฅ๐‘ฅ๐‘–๐‘–๐‘–๐‘–2 for each column American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 35, No 1, pp 342-351 348 Table 4 Android version Cost Battery power Ram Symphony 49 81 81 64 Samsung 64 49 64 49 Micromax 81 36 64 81 Walton 36 49 64 36 ๏ฟฝ๐‘ฅ๐‘ฅ๐‘–๐‘–๐‘–๐‘–2 230 215 273 230 ๏ฟฝ๏ฟฝ๐‘ฅ๐‘ฅ๐‘–๐‘–๐‘–๐‘–2 15.17 14.66 16.52 15.17 Step 1 (b): According to (1) normalized matrix ๐‘Ÿ๐‘Ÿ๐‘–๐‘–๐‘–๐‘– Table 5 Symphony 0.46 0.61 0.54 0.53 Samsung 0.53 0.48 0.48 0.46 Micromax 0.59 0.41 0.48 0.59 Walton 0.40 0.48 0.48 0.40 Step 2 (b): From (2) weighted normalized matrix v ij Table 6 Symphony 0.046 0.244 0.162 0.106 Samsung 0.053 0.192 0.144 0.092 Micromax 0.059 0.164 0.144 0.118 Walton 0.040 0.192 0.144 0.080 Step 3 (a): Determine ideal solution A*. A* = {0.059, 0.244, 0.162, 0.080} using (3) and (4) Step 3 (a): Find negative ideal solution A'. A' = {0.040, 0.164, 0.144, 0.118} using (5) and (6) Step 4 (a): using (7) Determine separation from ideal solution A* = {0.059, 0.244, 0.162, 0.080} American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 35, No 1, pp 342-351 349 Table 7 Symphony (.046-.059) 2 (.244-.244) 2 (0) 2 (.026) 2 Samsung (.053-.059) 2 (.192-.244) 2 (-.018) 2 (.012) 2 Micromax (.053-.059) 2 (.164-.244) 2 (-.018) 2 (.038) 2 Walton (.053-.059) 2 (.192-.244) 2 (-.018) 2 (.0) 2 Step 4 (a): Separation from ideal solution S i *: ฮฃ(v j *โ€“v ij )2 S i * = [ ฮฃ (v j *โ€“ v ij )2 ] Symphony 0.000845 0.029 Samsung 0.003208 0.057 Micromax 0.008186 0.090 Walton 0.003389 0.058 Step 4 (b): Using (8) find separation from negative ideal solution, A' = {0.040, 0.164, 0.144, 0.118} Table 8 Symphony (.046-.040) 2 (.244-.164) 2 (.18) 2 (-.012) 2 Samsung (.053-.040) 2 (.192-.164) 2 (0) 2 (-.026) 2 Micromax (.053-.040) 2 (.164-.164) 2 (0) 2 (0) 2 Walton (.053-.040) 2 (.192-.164) 2 (0) 2 (-.038) 2 Step 4 (b): Determine separation from negative ideal solution Siโ€ฒ : Table 9 ฮฃ(v j 'โ€“v ij )2 S i ' = [ ฮฃ (v j 'โ€“ v ij )2 ] ยฝ Symphony 0.006904 0.083 Samsung 0.001629 0.040 Micromax 0.000361 0.019 Walton 0.002228 0.047 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2017) Volume 35, No 1, pp 342-351 350 Step 5: Calculate the relative closeness to the ideal solution using (9) Table 10 S' i /(S i *+S' i ) C i * Symphony 0.083/0.112 0.74 Samsung 0.040/0.097 0.41 Micromax 0.019/0.109 0.17 Walton 0.047/0.105 0.45 7. Result Discussion Topsis method is an excellent effective method for decision making especially, it is a best technique for the customers to choose any product within specific criteria. And that opportunity is reflected by the proposed method which we see from steps 5 that our best option for a smart phone is Symphony. Though it depends on customers to classify best criteria which he prefer and it will numerically allocated by fuzzy set. According our data analysis Symphony is the most effective Smartphone for the customers of Bangladesh. The overall ranking for decision making given below. Symphony (0.74) Walton (0.45) Samsung (0.41) Micromax (0.17) 8. Conclusion The study discussed that how to select the effective Smartphone when decision makers set the target value of each criterion. The study proposed a method and a procedure to extend the TOPSIS method to solve the problem. The main advantages of using modified TOPSIS method is giving highest weighted value to a feature after proper analysis of customer satisfaction which done in our paper. The computation processes are straightforward. The concept permits the pursuit of best alternatives criterion depicted in a simple mathematical and data analysis for desired features of peoples. Acquired results from numerical example determine that this model could be used for decision making optimization in electronic device selection. References [1] Vladimir Rogalewicz, I vana Juล™iฤ kovรก, Multiple-criteria decision making: application to medical devices, Proceedings IWBBIO 2014. Granada 7-9 April, 2014, [2] Zoran MARKOVIฤ† Modification of TOPSIS method for solving of multicriteria tasks, Yugoslav Journal of Operations Research Volume 20 (2010), Number 1, 117-143. 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