Extended FTOPSIS with Distance and Set Theoretic-Based Similarity Measure

Abstract

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.

An improvised similarity measure for generalized fuzzy numbers

“…The data of 11 sets of fuzzy numbers in [23] are used to compare the similarity values of the proposed similarity measure with the existing similarity measures. These sets are commonly used by many [24][25][26] as a comparison and benchmarking tool. The similarity values obtained is as in Table 1.…”

Achievement Goals Analysis in the Learning of Calculus Based on Fuzzy Number Conjoint Method

“…To overcome the limitations of previous studies, Osman et al (2019) proposed the use of FCM based on fuzzy numbers. Fuzzy numbers depict the physical world more realistically and can produce attribute weights at different levels of confidence (Dom, Hasan, Shahidin, & Apandi, 2019;Sulaiman et al, 2017;Ramli & Mohamad, 2009). Nonetheless, Osman et al (2019) used Patra and Mondal (2015)'s similarity measure based on area, height, and distance, which cannot differentiate the degree of similarity for some different pairs of fuzzy numbers.…”

Higher Order Runge-Kutta Method for Solving Fuzzy Differential Equations

“…The study of FDEs is one of the new branches of mathematics, which has expanded very quickly in recent years. Its theories and applications have been discussed throughout time by many researchers, which among others are Zadeh (1965), Bede et al (2007), Zimmerman (2010), Jayakumar et al (2012) and Sulaiman et al (2018).…”