I have been seeing and following a lot of work on these topics, it even seems that there are more results on them than on the corresponding classical topics, particularly on general topology.
What could be the cause of such results?
Soft sets and soft topology are new area of research which are very rich in applications. The application of soft sets are richer than that of fuzzy sets and probability theory in decision making.
David Adebisi Afariogun That's a strong assertion, given the obvious difference in time of existence of compared subjects, considering the relatively recent definition of soft sets (Molodtsov 1999), and the long tradition in applications of both Fuzzy set theory and Probability theory, particularly the last one in the field of decision making.
Dear Colleagues,
If U and E are fixed sets, A is a subset of E, and F is a function
of A to the power set of U , then F should be called a soft set
over U and E , instead of the pair (F, A).
Thus, since set-valued functions can be identified
vith relations, a soft set over U and E is actually a relation
on E to X. That is, a subset of the product set of E and U.
Therefore, several defininitions and theorems on soft sets,
consuming a lot of pages, are superfluous. Moreover, notations
and terminology can be simplified.
Arpad Szaz Then, (one) factor is the simplicity of that approach, or, probably better, greater level of abstraction when dealing with similar situations in the real (ideal or material) world.
No, soft sets and soft topologies are not very popular in mainstream mathematical or computational research today. They are niche topics, mainly explored in specific theoretical studies and some applied fields like decision-making.
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