Transportation is among the more vital economic activities for a business and our daily life actions. At present, transport is one of the key branches playing a crucial role in the development of the economy. Transportation decision-making looks for ways to solve current and anticipated transportation problems while avoiding future problems. An interval-valued complex fuzzy set (IVCFS) is an extended form of fuzzy, interval-valued fuzzy and complex fuzzy sets, and it is used to evaluate complex and inaccurate information in real-world applications. In this research, we aim to examine the novel concept of IVCF soft relations (IVCFSRs) by utilizing the Cartesian product (CP) of two IVCF soft sets (IVCFSSs), which are determined with the help of two different concepts, referred to as IVCF relation and soft sets. Moreover, we investigated various types of relations and also explained them with the help of some appropriate examples. The IVCFSRs have a comprehensive structure discussing due dealing with the degree of interval-valued membership with multidimensional variables. Moreover, IVCFSR-based modeling techniques are included, and they use the score function to select the suitable transportation strategy to improve the value of the analyzed data. Finally, to demonstrate the effectiveness of the suggested work, comparative analysis with existing methods is performed.

The utilization of energy (EU) encompasses technologies aimed at discovering more effective methods for using electricity across various sectors, including residential, commercial, industrial, and transportation. Energy is an integral aspect of modern society and a driving force behind many processes in the universe. This paper aims to introduce a new concept, the Complex q-rung Orthopair Fuzzy Soft Relation (CqROFSRs), achieved through the Cartesian product of two Complex q-rung Orthopair Fuzzy Soft Sets (CqROFSSs). The proposed model has the capability to effectively capture and model graded imprecision and vagueness, which are commonly encountered in human interpretations. It provides a parameterized mathematical framework for ranking-based fuzzy modeling of two-dimensional paradoxical data. The theory integrates the CqROFS with the parametric structure of soft sets to achieve this purpose. Moreover, the utilization of complex numbers imbues these structures with the ability to effectively address phase-related and multidimensional challenges, thus conferring them with unparalleled power in managing ambiguity. Furthermore, we delved into various types of relationships, providing corresponding examples, which led to the establishment of accurate outcomes. The CqROFSRs framework is inclusive, encompassing both membership and non-membership degrees with regard to time duration. Additionally, the use of CqROFSRs techniques in selecting the optimal EU area for a daily living has been demonstrated, empowering individuals to make informed decisions and obtain verified results through the score function. To clarify the distinction, a comprehensive comparative analysis was conducted between the proposed concept and previous concepts.