Area, Perimeter and Shape of Fuzzy Geographical Entities

Abstract

This paper focuses on crisp and fuzzy operators to compute the area and perimeter of fuzzy geographical entities. The limitations of the crisp area and perimeter operators developed by Rosenfeld (1984) are discussed, as well as the advantages of the fuzzy area operator developed by Fonte and Lodwick (2004). A new fuzzy perimeter operator generating a fuzzy number is proposed. The advantage of using operators generating fuzzy numbers is then illustrated by computing the shape of a FGE, through its compactness, using the extension principle and the fuzzy area and perimeter.