| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 397253 | International Journal of Approximate Reasoning | 2016 | 9 Pages |
•Every hesitant fuzzy set can be considered a soft set on a common universe.•Every soft set on a denumerable universe can be considered a fuzzy set.•Interval type-2 fuzzy sets, interval-valued fuzzy sets can be considered as soft sets.•We prove coincidence of notions of hesitant fuzzy soft set, fuzzy soft set, soft set.
We prove that every hesitant fuzzy set on a set E can be considered either a soft set over the universe [0,1][0,1] or a soft set over the universe E . Concerning converse relationships, for denumerable universes we prove that any soft set can be considered even a fuzzy set. Relatedly, we demonstrate that every hesitant fuzzy soft set can be identified with a soft set, thus a formal coincidence of both notions is brought to light. Coupled with known relationships, our results prove that interval type-2 fuzzy sets and interval-valued fuzzy sets can be considered as soft sets over the universe [0,1][0,1]. Altogether we contribute to a more complete understanding of the relationships among various theories that capture vagueness and imprecision.
