5.1. Comparative Analysis 1’s Problem Statement
We use the problem outlined by Mitra Basu et al. [
8] to validate our approach. He came up with the following problem formulation. Consider a situation where there are three friends and they all have a friend in common. They all want to get a dress for their mutual friend. Let
be the collection of four dresses. Let
be the parameter set. According to our algorithm, let the experts be
and the opinion be
.
Step 1: Construct the ISES.
The ISES data have been tabulated and are presented in the following
Table 3.
Now, we write the AISES and DISES using
Table 3.
Step 2: We can find distance measures on all the alternatives.
Step 4: .
Step 5: Find
.
Similarly, we can find
Step 6: Calculate
.
Similarly, we can find
Step 7: Compute min
The minimum of is .
Step 8: As per the expert opinion, the three friends will jointly buy the dress .
From the above-mentioned steps and also
Table 4, we strongly claim that, in the existing literature, two alternatives were identified as the best alternatives, whereas in our proposed framework, only one has been identified. From this perspective, we have emphasised that our strategy is more effective than the existing strategy by a diagrammatic representation in
Figure 2.
5.2. Comparative Analysis 2’s Problem Statement
Make the assumption that a family wishes to purchase a car from the market, letting
and be the parameter set. According to our algorithm, let the experts be and the opinion be .
Step 1: Construct the ISES.
The ISES data have been tabulated and are presented in the following
Table 5.
Now, we write the AISES and DISES using
Table 5.
Step 2: We can find distance measures on all the alternatives.
Step 4: .
Step 5: Find .
Similarly, we can find
Step 6: Calculate
.
Similarly, we can find
Step 7: Compute min
The minimum of is and .
Step 8: As per the expert opinion, the family may choose any car from
and
is shown in
Table 6.
Our work is compared with [
11]. In that paper, soft rough sets were transformed into fuzzy sets (low, middle and high confidence) and weighting vectors were also used. The range of the alternative was also modified if the weighting vectors varied. In other words, the alternative was not unique. However, our method of decision-making is unique and accurate which is clearly depicted in
Figure 3.
Even though our strategy yields a large number of possibilities, it is much simpler than the prior one. Consequently, our approach is more effective than the earlier approach.