The q-rung orthopair fuzzy soft set is an advanced leeway of orthopair fuzzy sets, such as intuitionistic fuzzy soft set (IFSS) and Pythagorean fuzzy soft set (PFSS). The very lax requirement gives the evaluators excessive freedom to express their beliefs about membership degrees and non-membership degrees, making q-rung orthopair fuzzy soft set (q-ROFSS) have a broad scope of application in practical life. Considering the interaction, this paper will develop some novel operational laws for q-rung orthopair fuzzy soft numbers (q-ROFSNs). Some aggregation operators (AOs) such as q-rung orthopair fuzzy soft interactive weighted average (q-ROFSIWA) and q-rung orthopair fuzzy soft interactive weighted geometric (q-ROFSIWG) operators have been introduced. Also, we will prove some desirable properties such as idempotency, boundedness, and homogeneity for q-ROFSIWA and q-ROFSIWG operators. Multi-criteria decision-making (MCDM) plays a vital role to deals with the complications in manufacturing design for material selection. But, the prevailing MCDM methods habitually deliver incompatible outcomes. Based on the projected interactive aggregation operators, a robust MCDM method is planned for material selection in manufacturing design to accommodate this drawback. Furthermore, a comprehensive comparative analysis has been presented to confirm the pragmatism and validity of the proposed technique with some already available methods. The obtained outcomes through comparative studies show that our developed method is more efficient than existing approaches.

This article investigates heat and mass transport enrichment in natural convection fractionalized nanofluid flow inside a channel with isothermal and ramped wall conditions under the effects of chemical reactions, radiation, heat absorption, and the Soret effect. To obtain the fractional model, the Caputo time-fractional derivative definition is used, and analytical results are obtained by the Laplace transform. In two base fluids, water and glycerin, the impacts of two nanoparticles, single-wall carbon nanotubes (SWCNTs) and multiple-wall carbon nanotubes (MWCNTs), are investigated. The comparison of six distinct fluids, including water, water–SWCNT, water–MWCNT, glycerin, glycerin–SWCNT and glycerin–WMCNT, is explored graphically. Physical parameters’ effects on isothermal and ramped conditions are graphically depicted and explained in depth. For isothermal wall conditions, the variation in concentration, temperature and velocity is exponential, while for ramped wall conditions, the variation is steady. Finally, the results of skin frictions, Nusselt numbers and Sherwood numbers and for both ramped wall and isothermal wall conditions are evaluated in tabular form for various values of volume fraction. Moreover, it is observed that the temperature, velocity, Nusselt numbers and skin frictions increase by increasing the volume fraction of CNTs.

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