Prioritization of thermal energy techniques by employing picture fuzzy soft power average and geometric aggregation operators

Abstract Energy storage is a way of storing energy to reduce imbalances between demand and energy production. The ability to store electricity and use it later is one of the keys to reaching large quantities of renewable energy on the grid. There are several methods to store energy such as mechanical, electrical, chemical, electrochemical, and thermal energy. Regarding their operation, storage, and cost, the choice of these energy storage techniques appears to be interesting. This issue becomes very serious when there involves uncertainty. To consider this kind of uncertain information, a picture fuzzy soft set is found to be a more appropriate parameterization tool to deal with imprecise data. Based on the advanced structure of picture fuzzy soft set, here in this article, firstly, we have developed the notions of basic operational laws for picture fuzzy soft numbers. Then based on these developed operational laws, we have established the notions of picture fuzzy soft power average $$\left({\mathrm{PFS}}_{\mathrm{ft}}\mathrm{PA}\right)$$ PFS ft PA , weighted picture fuzzy soft power average $$\left({\mathrm{WPFS}}_{\mathrm{ft}}\mathrm{PA}\right)$$ WPFS ft PA and ordered weighted picture fuzzy soft power average $$\left({\mathrm{OWPFS}}_{\mathrm{ft}}\mathrm{PA}\right)$$ OWPFS ft PA aggregation operators. Moreover, we have introduced the notions for picture fuzzy soft power geometric $$\left({\mathrm{PFS}}_{\mathrm{ft}}\mathrm{PG}\right)$$ PFS ft PG , weighted picture fuzzy soft power geometric $$\left({\mathrm{WPFS}}_{\mathrm{ft}}\mathrm{PG}\right)$$ WPFS ft PG and ordered weighted picture fuzzy soft power geometric $$\left({\mathrm{OWPFS}}_{\mathrm{ft}}\mathrm{PG}\right)$$ OWPFS ft PG aggregation operators. Furthermore, we have established the application of picture fuzzy soft power aggregation operators for the selection of thermal energy storage techniques. For this, we have developed a decision-making approach along with an explanatory example to show the effective use of the developed theory. Furthermore, a comparative analysis of the introduced work shows the advancement of developed notions.