Application of fuzzy measures in multi-criteria evaluation in GIS

TLDR

Multi‑criteria evaluation (MCE) is perhaps the most fundamental of decision support operations in geographical information systems (GIS). The study reviews Boolean and Weighted Linear Combination MCE approaches in GIS, proposes fuzzy measures to reconcile them, and introduces the Ordered Weighted Average as a new aggregation operator. The authors apply fuzzy measures to unify Boolean and WLC approaches and employ the Ordered Weighted Average operator, illustrated through a case study of industrial allocation in Nakuru, Kenya. The fuzzy‑measure perspective offers a strong theoretical basis for standardizing factors and aggregating them.

Abstract

Multi-criteria evaluation (MCE) is perhaps the most fundamental of decision support operations in geographical information systems (GIS). This paper reviews two main MCE approaches employed in GIS, namely Boolean and Weighted Linear Combination (WLC), and discusses issues and problems associated with both. To resolve the conceptual differences between the two approaches, this paper proposes the application of fuzzy measures, a concept that is broader but that includes fuzzy set membership, and argues that the standardized factors of MCE belong to a general class of fuzzy measures and the more specific instance of fuzzy set membership. This perspective provides a strong theoretical basis for the standardization of factors and their subsequent aggregation. In this context, a new aggregation operator that accommodates and extends the Boolean and WLC approaches is discussed: the Ordered Weighted Average. A case study of industrial allocation in Nakuru, Kenya is employed to illustrate the different approaches.