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Dombi t-norm (DTN) and t-conorm (TCN) are among the most effective triangular norms in fuzzy systems for aggregation purposes. The environment of interval-valued intuitionistic fuzzy (IVIF) set gives us precision in expressing uncertain information by using a membership grade (MG) and non-membership grade (NMG) in the form of closed subintervals of 0, 1. The goal of this paper is to introduce DTN-based aggregation operators (AOs) for IVIF numbers (IVIFNs) and study their performance in the evaluation of the worth of energy recourses to be opted in Pakistan to deal with the energy crises situation. We first introduced some DTN and TCN-based operations for IVIFNs and developed two new AOs known as IVIF Dombi weighted averaging (IVIFDWA) and IVIF Dombi weighted geometric (IVIFDWG) operators. The validity and fitness of the proposed operators are tested. A case study is presented where the energy resources of Pakistan are discussed and the problem of the selection of sustainable energy resources in the context of Pakistan is investigated. The sensitivity analysis of the proposed IVIFDWA and IVIFDWG operators is studied and a comparative analysis of the current work with previous studies is established.

Multi-attribute decision-making (MADM) is commonly used to investigate fuzzy information effectively. However, selecting the best alternative information is not always symmetric because the alternatives do not have complete information, so asymmetric information is often involved. Expressing the information under uncertainty using closed subintervals of [0, 1] is beneficial and effective instead of using crisp numbers from [0, 1]. The goal of this paper is to enhance the notion of Dombi aggregation operators (DAOs) by introducing the DAOs in the interval-valued T-spherical fuzzy (IVTSF) environment where the uncertain and ambiguous information is described with the help of membership grade (MG), abstinence grade (AG), non-membership grade (NMG), and refusal grade (RG) using closed sub-intervals of [0, 1]. One of the key benefits of the proposed work is that in the environment of information loss is reduced to a negligible limit. We proposed concepts of IVTSF Dombi weighted averaging (IVTSFDWA) and IVTSF Dombi weighted geometric (IVTSFDWG) operators. The diversity of the IVTSF DAOs is proved and the influences of the parameters, associated with DAOs, on the ranking results are observed in a MADM problem where it is discussed how a decision can be made when there is asymmetric information about alternatives.