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Comparing fuzzy numbers is an essential process in deducing the output of many fuzzy decision making methods. One of the comparison methods commonly used is by using similarity measure. The main advantage of the similarity measure over other approaches is its ability to minimize the loss of information in the computational process. Several similarity measures have been applied effectively in fuzzy decision making methods. In this paper, a new similarity measure based on the geometric distance, the center of gravity, Hausdorf distance and the set theoretic similarity formula known as the Dice similarity index are incorporated into the Extended Fuzzy Technique for Order Preference by Similarity to Ideal Solution (FTOPSIS) method particularly in calculating the closeness coefficients. This similarity measure is in favor of others as it is able to discriminate two similar shape fuzzy numbers effectively with two different locations. A validation process is carried out by implementing the proposed procedure of the Extended FTOPSIS with the new similarity measure in solving a supplier selection problem and the ranking outcome is then compared with the Extended FTOPSIS with other existing similarity measure. The result shows that the Extended FTOPSIS with the proposed similarity measure gives a consistent result without reducing any information in the computational process.

The introduction of Sharia-compliant stocks at Bursa Malaysia can be considered as a type of socially responsible investing mechanism, especially for Muslim investors. An increase in the public interest in stock investment has led to the introduction of methods of categorizing and selecting preferred stocks effectively. Fuzzy decision-making methods have also become an important approach due to the nature of ambiguous and imprecise available data in the decision-making process. Nevertheless, some simplifications are inevitable to reduce the complexity of the problem, and consequently, loss of vital information may occur. In this paper, a similarity-based fuzzy grey relational analysis (FGRA) is proposed to rank selected Sharia-compliant stocks. An element of similarity measure is introduced in the original FGRA to reduce the loss of information in the computation when the distance between fuzzy numbers is utilized. The similarity measure can capture more information compared to distance measure since, in the computation, additional geometrical features of fuzzy numbers will be incorporated. An improvised procedure of FGRA is offered and implemented to rank selected Sharia-compliant stocks based on some fundamental analysis criteria. A comparison is then made on the preference obtained by the proposed procedure with the original FGRA.

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