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In this paper, we introduce a new class of fuzzy measures, referred to as q-measures, based on a modification of the definition of the well-known Sugeno λ-measure. Our proposed definition of the q-measures not only includes the λ-measure as a special case, but also preserves all desirable properties and avoids some of the limitations of the conventional λ-measure. The q-measure approach provides a more flexible and powerful method for constructing various fuzzy measures. We provide an iterative algorithm for constructing an interesting sequence of q-measures and analytically prove its convergence as a distinguishing characteristic of the proposed formulation.