Soft set was introduced soft set in 1999 as a model to capture uncertainties. Recently, Smarandache introduced a notion which he calls hyper soft set. In soft set theory a soft is associated with a function which assigns a subset of the universe of discourse to each parameter.
In case of hyper soft sets, also we have a function which associates every parametric value tuple with a subset of the universe of discourse.
As claimed by Smarandache, his notion generalises an earlier notion of Gamma soft sets. That is when number of parameters is 2 we gat Gamma soft sets.
But, as dealt by the authors of Gama soft set, the second component is a fixed set of parameters. This does not seem to be the case of hyper soft sets.
So, my query is why the notion of Smarandache be called as hyper soft set. It would have been termed so if we are getting soft set when the number of parameters is reduced to 1.
I would like to get inputs from researchers in soft set theory as well as hyper soft set theory.
I read the definition of Gama soft set in [Srinivasa Rao T, Srinivasa Kumar B and Hanumantha Rao S, A Study on Fundamentals of Γ- Soft Set Theory ]. The authors did not stipulate that the second set of parameters is fixed.
Is there another reference defined Gama soft set?
Anyway, even if they imposed this condition, Gama soft set is still a special case of the hypersoft set because it can be taken the hypersoft set with respect to two sets of parameters such that one of them is fixed.
Dear Dr. Al-shami,
See their definitions of union and intersection of Gamma soft sets. They are taking two such sets as (F, A, Gamma) and (G, B, Gamma). So, it is clear that Gamma remains fixed.
The query is to relate soft set as a special case of hyper soft set!!!
Anyway thanks for participating in this discussion.
I would like to have your mail ID for correspondence.
Thank you very much and regards.
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