I am not sure if this is the right site to post this. But I seek some valuable suggestions, and I believe I can get them here.
At present, I am in the final semester of my BSMS Mathematics course. I have been working on neutrosophic fuzzy soft sets (NFSS) (the term "neutrosophy" roughly translates to "knowledge obtained from neutral thoughts!") since last semester. Specifically, I constructed a flood alarm model based on NFSS as a non-structural flood mitigation method. I found Euclidean and Hamming similarity measures intuitive enough to be efficacious tools in this regard. In my last semester's dissertation, I demonstrated the said model with the help of a fabricated numerical example. Naturally, the speculative nature of my theory raises concerns about its dependability. (By "fabricated numerical example," I meant an example where the data or the neutrosophic grade values used to draw the final conclusion are all made up!)
I, however, have seen papers where the authors illustrate the application of their proposed approach with the help of a fictitious numerical example. My question here is, in order to write a paper (with the intention of publishing!), whether it actually suffices to demonstrate how my approach works with a made-up example or if I need to procure a real set of meteorological data concerning a particular region. If the latter is necessary, it would be tough for me because I have no prior experience dealing with a practical data set!
Next, I proposed two similarity measures between two NFSSs in my dissertation. One of which is defined with the help of the normalised Euclidean metric and the other is based on the normalised Hamming metric. We know that similarity measures lie within the range $[0,1].$ There are a few ways that I could think of to define the similarity measures. For example, each of the following expressions would work for me: $1-d$, $\frac1{1+d}$, and $e^{-\alpha d}$ $(\alpha>0)$, $d$ being a metric. For simplicity, I chose the first expression to define the aforementioned similarity measures in my dissertation. But I am confused about which one would be the most appropriate for my model. If I go for writing a paper, then should I define the said similarity measures in all the above-mentioned forms and compare their results?
I do have a supervisor. However, her area of interest mainly concerns fuzzy topology and related things. I wasn't interested in dealing with fuzzy topology, so I took up neutrosophic sets and their applications. Moreover, she told me in the beginning that she wouldn't be able to assist me in the future because she doesn't have enough experience with neutrosophic logic and applied math. She is also the H.O.D. of our department, so she remains mostly busy. She has given me complete freedom to do the necessary research and wants me to write a paper by the end of this semester. I am sort of on my own now and don't really have a clear idea of how to proceed further with my model. So, any suggestion would be highly appreciated...
