Time-sequential probabilistic fermatean hesitant approach in multi-objective green solid transportation problems for sustainable enhancement

Abstract

In order to delineate the randomness and imprecision in a single framework of time-sequential information, we proposed the notion of a time-sequential probabilistic fermatean hesitant set (TS-PFHS). Triangular time-sequential probabilistic fermatean hesitant number (Tr-TS-PFHN) is also initiated as a triangular version of TS-PFHS along with its fundamental operations and a ranking function. For the employment of our proposed set, we formulated a solid transportation problem (STP) with multiple objectives with TS-PFHS parameters for a sustainable green environment. Consequently, we proposed an algorithm by utilizing fuzzy programming (FP) and weighted sum technique (WST) to address proposed green transportation model. Additionally, to highlight the significance of the suggested technique, a numerical instance based on the transportation of electric vehicles in India is also investigated. Finally, conclusion along with the future prospects and limitations of the work done are discussed.

Keywords

• Time-sequential probabilistic fermatean hesitant set
• Time sequential information
• Green solid transportation problem
• Sustainability
• Fermatean fuzzy set
• Dual hesitant fuzzy set