Soft Comput (2017) 21:3537–3550 DOI 10.1007/s00500-017-2621-8 FOCUS Fuzzy transforms prediction in spatial analysis and its application to demographic balance data Ferdinando Di Martino 1 · Salvatore Sessa 1,2 Published online: 11 May 2017 © Springer-Verlag Berlin Heidelberg 2017 Abstract We present a new prediction algorithm based on fuzzy transforms for forecasting problems in spatial analysis. Our algorithm allows to predict the spatial distribution of assigned parameters of the problem under exam. Here, we test our method by exploring the demographical balance data measured every month in the period 01/01/2003–31/10/2014 in the municipalities of “Cilento and Vallo di Diano” National Park located in the district of Salerno (Italy). We use this method for predicting the value of the parameters “birthrate” and “deathrate” in November 2014. We apply this process in all the municipalities in the area of study; moreover, we present a fuzzification process for establishing the thematic map of the errors calculated between the real data and the predicted data. The thematic maps are constructed in a GIS environment. Keywords Fuzzy transform · Forecasting · GIS · Time series Communicated by F. Di Martino, V. Novákc. B Salvatore Sessa sessa@unina.it Ferdinando Di Martino fdimarti@unina.it 1 Dipartimento di Architettura, Università degli Studi di Napoli Federico II, Via Toledo 402, 80134 Naples, Italy 2 Centro Interdipartimentale di Ricerca in Urbanistica Alberto Calza Bini, Università degli Studi di Napoli Federico II, Via Toledo 402, 80134 Naples, Italy 1 Introduction In many spatial analysis problems, the decision maker needs to use support tools that allow to predict the evolution of a phenomenon by assessing its spatial distribution in a period of time on the area of study and displaying it on a thematic map. Prediction models are statistical and applied for estimat- ing the future trend of a variable starting from a set of numer- ical data. These models are used in many practical problems including, e.g., real-time signal processing problems, cur- rency forecasting, transport planning, land use forecasting, weather forecasting, etc. Many forecasting methods exist in literature, as multivariate autoregressive models, nonlin- ear models, simulation methods, fuzzy interpolation, causal methods, linear regression: Some comparisons have been shown in Abraham and Ledolter (1983), Armstrong (2001), Farnum and Stanton (1989), Makridakis et al. (1998), Palit and Popovic (1999). Other methods involve soft computing for supporting uncertainty in the data, as fuzzy rules extrac- tion algorithms (Cai et al. 2015; Chang and Liu 2008; Chen et al. 2013; Chen and Hwang 2000; Chen and Wang 1999; Chissom 1993; Jilani et al. 2008; Lee et al. 2006; Liu 2007; Palit and Popovic 1999; Shahrabi et al. 2013; Singh and Borah 2013; Singh 2009; Song and Chissom 1993, 1994; Sullivan and Woodall 1996; Thawonmas and Abe 1999; Tsaur et al. 2005; Wang and Mendel 1992), multi-level neural networks (Aliev et al. 2006; Chen et al. 2006, 2004; Inoue et al. 2001; Lendasse et al. 2007; Li and Kozma 2003; Li et al. 2003; Su and Li 2003; Tamura et al. 2008) and genetic algorithms (EL-Naggar and AL-Rumaih 2005; Li et al. 2006; Liao and Tsao 2004, 2006). In Di Martino et al. (2011), a new fuzzy forecasting method based on fuzzy transforms (for short, F-transforms) (Perfilieva 2006) is presented. In this method, an optimal fuzzy partition of the input variable domains is given, but 123