Distance and similarity measures for bipolar fuzzy soft sets with application to pharmaceutical logistics and supply chain management

Abstract

Pharmaceutical logistics are primarily concerned with handling transportation and supply chain management of numerous complex goods most of which need particular requirements for their logistical care. To find the high level of specialization, suppliers of pharmaceutical logistics must be selected under a mathematical model that can treat vague and uncertain real-life circumstances. The notion of bipolarity is a key factor to address such uncertainties. A bipolar fuzzy soft set (BFSS) is a strong mathematical tool to cope with uncertainty and unreliability in various real-life problems including logistics and supply chain management. In this paper, we introduce new similarity measures (SMs) based on certain properties of bipolar fuzzy soft sets (BFSSs). The proposed SMs are the extensions of Frobenius inner product, cosine similarity measure, and weighted similarity measure for BFSSs. The proposed SMs are also illustrated with respective numerical examples. An innovative multi-attribute decision-making algorithm (MADM) and its flow chart are being developed for pharmaceutical logistics and supply chain management in COVID-19. Furthermore, the application of the suggested MADM method is presented for the selection of the best pharmaceutical logistic company and a comparative analysis of the suggested SMs with some of the existing SMs is also demonstrated.