Addressing Cost-Efficiency Problems Based on Linear Ordering of Piecewise Quadratic Fuzzy Quotients

Abstract

Ordering of quotients is a critical aspect of cost-efficiency problems, which hold significant interest and importance for suppliers of goods and services as well as consumers. Comparisons (ordering) are straightforward when dealing with ordinary numbers, yet in many instances, the data are imprecise, vague, or subject to seasonal variations. Consequently, such data may be unknown or derive from expert opinions. Unlike ordinary numbers, fuzzy data render quotients only partially ordered. This study examines the linear ordering of quotients with fuzzy data, expressed in terms of confidence intervals, $\alpha$-cuts, or piecewise quadratic fuzzy numbers (PQFNs), within the context of cost-efficiency problems. Moreover, the challenges associated with quotient ordering in cost-efficiency problems are introduced.