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Variants of Inner Product Similarity Measures between Expected Interval Generalized Fuzzy Numbers

D. Mohamad, I. Sigam

Abstract


Similarity measures have been used to solve various decision making problems under fuzzy environment. In particular, Ye (2012) proposed a decision making method using expected Dice similarity measure between generalized trapezoidal fuzzy numbers (GTFNs). In this paper, we develop two variants of inner product families of similarity measures, namely the Jaccard and Cosine similarity between the expected intervals of GFTN. Comparisons are made between the three similarity measures using 15 sets of generalized fuzzy numbers. It is found that the Jaccard based similarity measures shows akin result to Dice similarity measure as compared to Cosine similarity measure. This study enriches the study of fuzzy similarity measure and its applications.

Keywords


Similarity measure; expected interval; generalized fuzzy numbers.

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