Using Fuzzy Set Theory to Help Resolve Governmental Hospitals’ Health Care Decision Conflicts

While cost allocation decisions attract considerable attention in the management accounting literature, many studies are contradicting and inconclusive. They often seek to develop product or service weights in order to make operating decisions with the sole objective of maximizing the firm’s profitability. But before developing these weights, the studies must first rank these products – which is a complex endeavor that is often driven by many hierarchical financial and nonfinancial goals and objectives. Ranking is also difficult due to using such complex concepts as time, uncertainty, cost, and interdependencies between accounting systems and manufacturing systems and among the products of the product mix. These concepts are inherently fuzzy and coextensively applied often with a confluence of variables operating simultaneously. This paper applies an advanced mathematical model to account for a hospital cost allocation decisions in treating spinal cord injuries (SCI). The model combines the powers of fuzzy set theory (Zadeh, 1965) and the analytic hierarchy process (Saaty, 1978). The precise ratings required in the conventional analytic hierarchy process but practically hard to obtain are replaced by naturally semantic variables by using the fuzzy set concept. de Korvin and Kleyle’s (1999) fuzzy-analytic-hierarchical process (FAHP) then develop these ambiguous variables. FAHP can help to optimize decisions involving ambiguous variables and the web of prioritized strategies and goals of cost leadership, product differentiation, financial objectives of earnings, cash flows, and market share and nonfinancial goals such as tradition and owners’ convictions and philosophies. We use data from seven Michigan SCI facilities in applying the FAHP model to rank and otherwise develop more optimal strategies and goals and compare our results to the decisions of hospital management.