# Cell Phone Evaluation Base on Entropy and TOPSIS

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2 2.0 EVALUATION CRITERIA OF MOBILE PHONES There are different types of mobile phones brands in the mobile phone market with various sizes, shapes, colors, functions. The most famous brands popular among users are Nokia, Apple, Samsung, Blackberry, SonyEricsson, HTC and others. Different brands come with its unique specifications. The main specifications that describe a mobile phone are; body, display, sound, memory, data, camera, features and battery as shown below in table 1. Twelfth (12) of these specifications would be utilized in our analysis as shown in Table METHODOLOGIES Multiple criteria decision making method (MCDM) is a decision making analysis method which has been developed since 1970s. A decision-making problem is the process of finding the best option from all of the feasible alternatives. In almost all such problems the multiplicity of criteria for judging the alternatives is pervasive. That is, for many such problems, the decision maker wants to solve a multiple criteria decision making (MCDM) problem. A MCDM problem can be concisely expressed in matrix format as: [ ] [ ] Where A 1, A 2, A 3..., A m are possible alternatives among which decision makers have to choose, C 1, C 2, C 3,..., C n are criteria with which alternatives performance are measured, x ij is the performance value of alternatives A i with respect to criterion C j, w j is the weight of criterion C j. In the following sub-sections, 2 MCDM related methods, Entropy Method and Techniques for order preference by similarity to ideal solution (TOPSIS), which are integrated in this research, are discussed. 3.1 Entropy Method for Weight Determination In this research, we applied the concept of entropy to determine the criteria weight. Entropy is a term in information theory, also known as the average amount of information (Ding and Shi, 2005). The criteria weights are calculated by the Entropy Method. According to the degree of index dispersion, the weight of all indicators is calculated by information entropy. Entropy method is highly reliable and can be easily adopted in information measurement (Zou et al., 2005). The calculation steps are as follows: Suppose we have a decision matrix B with m alternatives and n indicators: (1) In matrix B, feature weight p ij is of the ith alternatives to the jth factor: (2) The output entropy e j of the jth factor becomes (3) Variation coefficient of the jth factor: g j can be defined by the following equation: Note that the larger g j is the higher the weight should be. (4) Calculate the weight of entropy α j : (5) Calculate the adjusted weight β j 10

3 3.2 Technique for Order Preference by Similarity to Ideal Solution Method (Topsis) Technique for order preference by similarity to ideal solution TOPSIS was initially developed by Hwang and Yoon (1981), subsequently discussed by many (Chu, 2004; Peng, 2000). TOPSIS finds the best alternatives by minimizing the distance to the ideal solution and maximizing the distance to the nadir or negative-ideal solution (Jahanshahloo et al., 2006). All alternative solutions can be ranked according to their closeness to the ideal solution. Because its first introduction, a number of extensions and variations of TOPSIS have been developed over the years. General TOPSIS process with six steps is listed below: Step 1 Calculate the normalized decision matrix A. The normalized value a ij is calculated as; ( ) Step 2 Calculate the weighted normalized decision matrix ( ) where w j is the weight of the ith criterion and. Step 3 Calculate the ideal solution V * and the negative ideal solution V { } { } { } { } Step 4 Calculate the separation measures, using the m-dimensional Euclidean distance ( ) ( ) Step 5 Calculate the relative closeness to the ideal solution where The larger is, the closer the alternative is to the ideal solution. Step 6 The larger TOPSIS value, the better the alternative. 4.0 APPLICATION OF ENTROPY AND TOPSIS IN MOBILE PHONE EVALUATION Suppose a mobile phone user wants to buy a mobile phone from the mobile phone outlet, decision matrix is shown in Table 2. Based on the proposed methodology, 2 steps are applied for weight and selection of mobile phone. 11

4 4.1 Application of Entropy to Determine Weight In step 1, for the weight using entropy analysis, the procedure is as follows; the decision matrix shown in Table 2. Equation 1 resulted in the data normalization as shown in Table 3 whiles Equation 2, 3, 4 and 5 were applied to obtain the result shown in Table Application of Topsis In step 2, According to TOPSIS algorithm s activities, the results are shown in Tables 5. From the result obtained we can learned that it is feasible to use entropy analysis and TOPSIS to select the best mobile phone from the mobile phone market. 4.3 Analysis of the Decision Result Mobile phone consumers order of ranking mobile phone specification are; price 13.4%, camera and operating system (OS) 11.97%, battery 8.97%, screen size 7.71%, RAM, speed, and CPU 7.07%, Bluetooth 6.59% and weight, memory, and dimensions 6.06% this was obtained through random selection of mobile phone consumers. Mobile phone consumer way of ranking mobile phone specification is subjective; entropy analysis can be applied to smooth this subjectivity and the result is show in Table 3. During the TOPSIS analysis these assumption were made for mobile phone specification for dimension the bigger the better, for weight the lighter the better and price the cheaper the better whiles the rest of the mobile phone specifications the higher (speed, Bluetooth, CPU, operating System (OS), and camera), bigger (RAM, memory and screen size) and longer (battery) the better. TOPSIS analysis selected the best mobile phone with the best mobile phone specification. 5 CONCLUSIONS Buying a mobile phone is a MCDM problem that is affected by several specifications. Entropy and TOPSIS analysis can aid customer in making the right decision. Results from Entropy and TOPSIS analysis are objective and accurate, eliminating subjective weighting of specification. Using this tool, a customer can purchase the best mobile phone whiles manufactures of mobiles phones can produce mobile with unique technological features aimed at particular users. The main limitation of this paper is our inability to convert some specification into figures and not including the market demand of the mobile phone. REFERENCES 1. Chu, T., (2004), Facility Location Selection Using Fuzzy TOPSIS Under Group Decision, International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems, Vol. 10, No. 6, pp Dai L. and Wang J., (2011), Evaluation of the Profitability of Power Listed Companies Based on Entropy Improved TOPSIS Method, ScienceDirect, Vol. 15, pp Ding S., and Shi Z., (2005), Studies on Incident Pattern Recognition Based on Information Entropy, Journal of Information Science, Vol. 31, No. 6, pp Hwang C.L., and Yoon K., (1981) Multiple Attribute Decision Making: Methods and Applications Springer-Verlag: New York. 5. Jahanshahloo G.R., Hosseinzadeh L. F., and Izadikhah M., (2006), Extension of the TOPSIS Method for Decision-Making, Applied Mathematics and Computation, Vol. 181, No. 2, pp Kou et al., (2011), A Dynamic Assessment Method for Urban Eco-environmental Quality Evaluation, Journal of Multi-Criteria Decision Analysis, Vol. 18, pp Peng, Y., (2000), Management Decision Analysis, Peking: Science Publication. 8. Shahanaghi, K. and Yazdian, S. A., (2009), Vendor Selection Using a New Fuzzy Group TOPSIS Approach, Journal of Unsertain System, Vol. 3, No. 3, pp Zou Z, Sun J, and Ren G., (2005), Study and Application on the Entropy Method for Determination of Weight of Evaluating Indicators in Fuzzy Synthetic Evaluation for Water Quality Assessment, ACTA Scientiae Circumstantiae, Vol. 25, No. 4, pp

5 TABLES Table 1, Mobile Phones Specification Specification Body Display Sound Memory Data Camera Features Battery Descriptions Dimensions, Weight Screen Size, Type, Multitouch, Phone Protection Alert Type, Loudspeaker, 3.5mm Jack Card slot, Internal storage GPRS, EDGE, Speed, WLAN, Bluetooth, NFC, USB Primary, Features, Video, Secondary OS, Chipset, CPU, GPU, Sensors, Messaging, Brower, Radio, GPS, Java, Colors Stand-by, Talk time, Music play, battery capacity Table 2, Specifications of 10 different mobile phones available in the mobile phone market Dimensions Weight Screen Size Memory RAM Speed Blue Camera OS(Honey CPU Battery Price (\$) (mm) (g) (inc) (GB) (GB) (mbps) Tooth (mp) comb) (GHz) (mah) MP MP MP MP MP MP MP MP MP MP

6 Table 3, Data after Normalization Dimensions Weight Screen Size Memory RAM Speed Blue Camera OS(Honey CPU Battery Price (mm) (g) (inc) (GB) (GB) (mbps) Tooth (mp) comb) (GHz) (mah) (\$) MP MP MP MP MP MP MP MP MP MP Table 4, Entropy value, the variation coefficient and the entropy of the specifications Dimensions Weight Screen Memory RAM Speed Blue Camera OS(Honey CPU Battery Price (mm) (g) Size (inc) (GB) (GB) (mbps) Tooth (mp) comb) (GHz) (mah) (\$) E j d j w j λ j λj wj β j

7 Table 5, Separation measure S i +, S i -, relative closeness (Y i ) and ranking + - S i S i Y i Ranking MP MP MP MP MP MP MP MP MP MP

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