Abstract
This research article aims at establishing the foundations of generalized hybrid frameworks for dealing with uncertainties in knowledge-based systems. First, by combining the notions of picture fuzzy soft set, spherical fuzzy soft set, and T-spherical fuzzy soft set with a rough set, we introduce the novel models of Picture Fuzzy Soft Rough Sets (P\(_{\mathrm{c}}\)FSRSs), Spherical Fuzzy Soft Rough Sets (S\(_{\mathrm{p}}\)FSRSs), and T-Spherical Fuzzy Soft Rough Sets (T\(_{\mathrm{s}}\)FSRSs) for the parameterized fuzzy modelling of inconsistent data. Moreover, we explore some basic operational laws and fundamental properties of the developed models. We introduce a family of promising aggregation operators, namely, picture fuzzy soft rough ordered weighted averaging operator (P\(_{\mathrm{c}}\)FSROWAO), picture fuzzy soft rough ordered weighted geometric operator (P\(_{\mathrm{c}}\)FSROWGO), spherical fuzzy soft rough ordered weighted averaging operator (S\(_{\mathrm{p}}\)FSROWAO), spherical fuzzy soft rough ordered weighted geometric operator (S\(_{\mathrm{p}}\)FSROWGO), T-spherical fuzzy soft rough ordered weighted averaging operator (T\(_{\mathrm{s}}\)FSROWAO), and T-spherical fuzzy soft rough ordered weighted geometric operator (T\(_{\mathrm{s}}\)FSROWGO). We inspect some dominant peculiarities of these proposed operators inclusive of idempotence, boundedness and monotonicity. Further, we design a proficient approach using the proposed operators to untangle the complexity behind multi-attribute group decision making in real-world problems. We validate the effectiveness of the proposed technique by investigating its high potential in two real-world case studies. Finally, we demonstrate a comparative analysis of the proposed methodology with existing decision-making techniques to substantiate the accountability of the developed strategy.
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Akram, M., Martino, A. Multi-attribute group decision making based on T-spherical fuzzy soft rough average aggregation operators. Granul. Comput. 8, 171–207 (2023). https://doi.org/10.1007/s41066-022-00319-0
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DOI: https://doi.org/10.1007/s41066-022-00319-0