Expected value of generalized trapezoidal bipolar fuzzy number to solve a multi-item marketing planning inventory model with allowable shortages

Autor: Sourav Kumar Giri, Totan Garai, Sahidul Islam
Jazyk: angličtina
Rok vydání: 2024
Předmět:
Zdroj: Franklin Open, Vol 8, Iss , Pp 100164- (2024)
Druh dokumentu: article
ISSN: 2773-1863
DOI: 10.1016/j.fraope.2024.100164
Popis: Decision makers often grapple with the complexity of multi-faceted real-life problems, where uncertainty arises from both positive and negative states of mind. This duality reflects the decision maker’s optimistic and pessimistic perspectives during the decision-making process. To address this, our paper introduces innovative concepts and frameworks for generalized bipolar trapezoidal fuzzy numbers. We propose novel arithmetic operations on these fuzzy numbers, computing the negative α-cut and positive β-cut methods. Furthermore, we uniquely compute the convex combination of expected values from both the positive and negative membership parts. These theoretical advancements are applied to a practical case study: a multi-item marketing planning inventory model with allowable shortages. Our proposed method’s efficacy is highlighted through detailed numerical illustrations, sensitivity analyses and comparative studies complemented by compelling graphical presentations
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