An integrated probabilistic bipolar fermatean hesitant fuzzy transportation configuration for sustainable management of floral waste with risk assessment

This paper proposes the probabilistic bipolar fermatean hesitant fuzzy set (PBFHFS) and its triangular version as generalizations of bipolar fuzzy set (BFS) for delineating randomness and imprecision in a single framework. To enhance pragmatic applicability, the devised set has been examined based on its fundamental operations, basic properties, and defuzzification mechanism. Offerings made to temples are considered sacred, so they cannot be disposed of in landfills. Waste from temples is usually disposed of in nearby lakes, ponds, and rivers. Thus, management of the temple floral waste (TFW) is essential to enhance the sustainability of the environment. In this regard, a green 4-dimensional transportation system under PBFHF settings is developed for the effective and sustainable managements of floral waste that is dumped from places of worship. For the most cost-effective and environmentally friendly results, this transportation system optimises a number of metrics, transportation expenditure (TE), carbon emission (CE), transportation time (TT), and labour cost (LC). Three sub-models are further developed from the proposed model under PBFHF conditions by incorporating the theory of carbon policy and risk assessments. The suggested transportation system is addressed by employing a fuzzy methodology, fuzzy programming (FP) as well as two non-fuzzy approaches, weighted sum technique (WST) and goal programming technique (GP). At last, there is a numerical computation along with comparison analysis, management insights, a conclusion with limitations, and a scope for further study.