Analysis of the benefit generated by using fuzzy numbers in a TOPSIS model developed for machine tool selection problems

Selection of the appropriate machine tools for a manufacturing company is a very important but at the same time a complex and difficult problem because of the availability of wide-ranging alternatives and similarities among machine tools. In the literature, various machine tool selection procedures are developed. The developed procedures mainly use Multi Criteria Decision Making (MCDM) methods. In the literature, fuzzy MCDM models, in which fuzzy numbers are used instead of crisp values, are proposed to deal with the vagueness and imprecision inherent in the machine tool selection problem. Although, the available studies in the literature developed various fuzzy models, they do not propose any approaches to measure the benefit generated by incorporating fuzziness in their selection models. This paper aims to fill this gap by trying to quantify the level of benefit provided by employing the fuzzy numbers in the MCDM models. Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is used as the MCDM approach to rank the machine tools in this paper. In the paper, by increasing the fuzziness level steadily in the fuzzy numbers, the obtained machine tool rankings are compared with the ranking obtained with the crisp values. The statistical significance of the differences between the ranks is calculated using Spearman's rank-correlation coefficient. It can be observed from the results that as the vagueness and imprecison increases, fuzzy numbers instead of crisp numbers should be used. On the other hand, in sitiuations where there is a low level of fuzziness or the average value of the fuzzy number can be guessed, using crisp numbers will be more than adequate.