TOPSIS with similarity measure for MADM applied to network selection
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TOPSIS with similarity measure for MADM applied to network selection Iman Mohamad Sharaf1
Received: 9 October 2017 / Revised: 30 November 2017 / Accepted: 16 December 2017 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2017
Abstract In this article, a new method is introduced to handle fuzzy multi-attribute decisionmaking problems. The method preserves fuzziness in the preference technique to avoid the drawbacks of defuzzification. The study modifies the technique of order preference by similarity to an ideal solution (TOPSIS) for interval-valued fuzzy numbers. The traditional TOPSIS uses the relative degree of closeness to rank the alternatives. Instead, a similarity measure based on map distance is used for preference. The degree of similarity between each attribute of an alternative and the ideal solution is computed, and a similarity matrix is formed. Then, the total degree of similarity for all the attributes of an alternative is used for ranking. The alternative corresponding to the one norm of the similarity matrix is the best alternative. Thus, the comparison is done on a fuzzy basis to avoid the loss of information due to converting the elements of the weighted normalized decision matrix to crisp values by defuzzification. An illustrative example is given to demonstrate the approach. A practical example in network selection to optimize vertical hand offs is solved where both user preferences and network parameters are treated as interval-valued fuzzy numbers. Keywords Fuzzy multi-criteria decision-making · TOPSIS · Similarity measure · Network selection Mathematics Subject Classification 90B50 · 90C70 · 90C90
1 Introduction The purpose of multi-attribute decision-making (MADM) is to choose the best candidate from a set of alternatives using experts’ evaluations of the multiple attributes of the alternatives Communicated by Marcos Eduardo Valle.
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Iman Mohamad Sharaf [email protected] Department of Basic Sciences, Higher Technological Institute, PO Box 228, Ahmad Hamdy Street, First District, Tenth of Ramadan City, Egypt
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I. M. Sharaf
(Chen and Lee 2010). In the process of decision-making, ambiguity and uncertainty are often confronted when evaluating the criteria weights and the alternatives of the problem. Some of the evaluation criteria are subjective and qualitative in nature which hinders expressing the preference using exact numerical values. Until recently, MADM using type-1 fuzzy sets (T1FSs) attracted many researchers and many studies were introduced. However, T1FSs have a crisp membership function value in the interval [0,1]. Using a crisp membership function can decrease the flexibility and precision of decision-making in an uncertain environment, as it is hard to estimate the exact membership function of fuzzy sets in many situations (Ghorabaee 2016). Currently, MADM methods use more sophisticated fuzzy sets, e.g., interval type-2 fuzzy sets (Chen and Kuo 2017; Qin 2017; Cheng et al. 2016; Mendel 2016; Chen and Hong 2014; Chen and Wang 2013) and intuiti
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