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

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