A Q-fuzzy set is a mapping from [0,1] X Q × → where X is the universe of discourse and Q is a non-empty set. Some works has been emanated for this Q-fuzzy set. In all the above work the set 'Q' is treated as a non-empty set without any algebraic structure. This article presents an algebraic structure for Q-fuzzy set over a semiring named as 1 Q-fuzzy set and provide some properties and results.

This paper expose a study on interval-valued Q-fuzzy ideals generated by an interval-valued Q-fuzzy subset on ordered semi-groups. Some characterizations of such generated interval-valued Q-fuzzy ideals are also discussed.

Molodtsov introduced the concept of soft sets, which can be seen as a new Mathematical tool for dealing with uncertainty. In this paper, we initiate the study of soft intersection ideals of semirings by using the soft set theory. The notions of soft intersection semirings, soft intersection left(right, two-sided) ideals of semiring and soft intersection quasi and bi-ideals of semirings are introduced and several related properties are investigated.

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The authors in [9] introduced Q1 -fuzzy set which is a natural generalization Q-fuzzy sets studied by [5, 7, 12, 13] and studied some results related to level subsets of Q1 -fuzzy set. In this study composition of two Q1 -fuzzy sets, Q1 -fuzzy points, Q1 -fuzzy quasi (prime, semiprime, irreducible, strongly irreducible) ideals are defined and revealed some related properties of these mentioned ideals. Further Q1 -fuzzy left (right) ideals generated by fuzzy points are exhibited and some quasi-ideals in terms of idempotent Q1 -fuzzy points are found.