Dual hesitant fuzzy set in multi-objective transportation problems in time sequence frame work

Decision makers may have different information in different situations when making decisions about the same attributes, depending on the circumstances. A time-sequential framework is necessary for navigating these kinds of circumstances. We established the notion of a Time-sequential dual hesitant fuzzy set (TS-DHFS) to illustrate the significance of time sequence in decision-making with the aid of a dual hesitant fuzzy set (DHFS), one of the important tools to handle the uncertainty embedded in the real world. The proposed set describes the hesitant situations more accurately by inducing a time sequence framework. We defined the fundamental operations, two score function for ranking and a series distance measures for the proposed set. For the pragmatic application of our proposed set, we devised the mathematical model in three different types of Time-sequential dual hesitant fuzzy multi-objective transportation problems (TS-DHF-MOTPs). The proposed three models are classified based on the nature of the parameters such as transportation cost (TC), transportation time (TT), availability, and demand. The goal of the proposed transportation systems is TC and TT simultaneously in a single framework. We established an approach utilizing one of the ranking functions that have been proposed, followed by the fuzzy programming (FP) and weighted sum technique (WST), to optimize the constructed models. Additionally, numerical computations are also carried out to emphasize the efficiency and benefits of MOTP under the TS-DHF environment.