The Linear Fuzzy Space: Theory and Applications

Abstract

AbstractThe basic properties of dynamic systems include imprecisions and uncertainties in both spatial and temporal data which require adequate representations and further manipulations. Existing literature covers various approaches that address the representations and manipulations of such data, with fuzzy theory being one of the most widely and most frequently used. The linear fuzzy space is an original fuzzy-based approach that provides an effective and compact model of imprecise data. In this chapter we present the main theoretical results of the linear fuzzy space and analyze its capacity to facilitate the modelling of spatial and spatio-temporal systems through representative examples of its applications in selected real-world problems. The chapter consists of five sections. The first section is an introduction which states the problem and briefly presents relevant research. The second section contains a brief, yet comprehensive, overview of linear fuzzy space theory. The third section presents an analysis of fuzzy linear space theory concerning the modelling of spatial and/or temporal systems. The fourth section presents two examples which show its applications in image analysis and time series modelling. The fifth section concludes the chapter and recommends some directions for future research.KeywordsFuzzy setLinear fuzzy space. planar spatial objectsFuzzy pointFuzzy metricSpatial modellingTemporal modelling2D image segmentationGDASCAQI index