The role of fuzzy logic in GIS modelling Philippe Puig DEUG de Science Licence de Géologie appliquée Maitrise de Géologie appliquée D.E.A. de Géologie appliquée Graduate Diploma in Education (Secondary) Graduate Diploma in Geographic Information Faculty of Engineering, Health, Science and the Environment Charles Darwin University PhD thesis 2011 Philippe Puig – PhD thesis Thesis declaration I hereby declare that the work herein, now submitted as a thesis for the degree of Doctor of Philosophy of the Charles Darwin University, is the result of my own investigations, and all references to ideas and work of other researchers have been specifically acknowledged. I hereby certify that the work embodied in this thesis has not already been accepted in substance for any degree, and is not being currently submitted in candidature for any other degree . Philippe Puig Date: 7 April, 2011 ii Philippe Puig – PhD thesis ACKNOWLEDGMENTS This research was carried out in Darwin, in the Northern Territory of Australia, between 2001 and 2010, while working full time on a variety of GIS projects in the Top End of the Northern Territory. During that relatively long period of time both my professional and my research environments changed. Within that context, first and foremost, I am deeply indebted to my wife Patricia and my two sons, Julien and Guillaume, who provided a stability and support in my private life without which I would not have been able to complete this work. Without the guidance and friendly encouragement of my two supervisors, Dr Diane Pearson and Dr Stefan Maier, this thesis would not have been written. I thank them for their unflinching support, their expert advice and their confidence in my capabilities. In addition to those I named before, many more persons and organisations contributed to my research. Out of fear of unfairly forgetting some, I decided to express my deepest gratitude to all relatives, friends, colleagues, professionals and researchers who played a role in my endeavour. iii Philippe Puig – PhD thesis GLOSSARY AAGIS Anindilyakwa Aquaculture GIS AHP Analytic Hierarchy Process AI Artificial Intelligence BOM Bureau Of Meteorology CI Consistency Index COG Centre Of Gravity CR Consistency Ratio DAC Darwin Aquaculture Centre DEM Digital Elevation Model DOF Degree Of Fulfillment EDA Exploratory Data Analysis FCM Fuzzy C-Means FIS Fuzzy Inference System FKC Fuzzy K-Clustering GIS Geographic Information System GAM Generalised Additive Model GLM Generalised Linear Model GK Gustafson Kessel (algorithm) KBS Knowledge Based System KE Knowledge Engineering MAUP Modifiable Areal Unit Problem MCDA Multi Criteria Decision Analysis MF Membership Function MOM Mean Of Maxima NRM Natural Resource Management NT Northern Territory sciFLT Scilab Fuzzy Logic Toolbox SMI Semantic Import Approach TFN Trapezoidal Fuzzy Number TRF Timor Reef Fishery TS Takagi Sugeno iv Philippe Puig – PhD thesis UBC University of British Columbia XLFIS Excel Fuzzy Inference System v Philippe Puig – PhD thesis Table of contents 1. Introduction Scope of this thesis 2 1.1 Background 2 1.2 Geography and linguistic uncertainty 6 1.3 Statistical uncertainty and quantitative geography 8 1.4 Outline of this thesis 12 2. Some fundamental concepts of fuzzy logic Overview 15 2.1 Models and modelling methods 15 2.2 Fuzzy sets and membership functions 18 2.3 Fuzziness, statistics and uncertainty 28 2.4 GIS, raster and direct application of membership functions 29 2.5 Acquisition of membership functions 34 2.6 Manual design of membership functions 43 2.7 Structure and functions of a fuzzy rule-based model 52 2.8 Implementation of a fuzzy rule-based model 62 Summary 67 3. GIS fuzzy multicriteria decision analysis Overview 70 3.1 Background 72 3.2 Method and data 73 3.3 Results 83 3.4 Discussion 87 Summary 90 4. Data driven fuzzy rule-based modelling Overview 93 4.1 Application of fuzzy rule-based modelling to classification 94 4.2 Multivariate predictive modelling on the basis of variables 106 of unknown influence on the outcome 4.3 What drives elephant seals’ foraging patterns? 122 Summary 130 vi Philippe Puig – PhD thesis 5. Knowledge driven fuzzy rule-based modelling Overview 133 5.1 Knowledge versus data driven fuzzy rule-based modelling 134 5.2 The need to capture human knowledge 138 5.3 Modelling fishing power from fishers’ knowledge 142 5.4 Implementation and applications of a functional fuzzy 155 rule-based expert system Summary 164 6 Conclusion Overview 168 6.1 Material presented in this thesis 168 6.2 What the case studies presented in this thesis tell us 170 6.3 Future directions of research in GIS applications of fuzzy 172 logic 6.4 What is the role of fuzzy logic in GIS modelling? 176 Summary 177 References 179 vii Philippe Puig – PhD thesis Appendices Appendix 1 Excel Fuzzy Inference System XLFIS A-1 A1.1 Introduction to XLFIS A-1 A1.2 MODEL worksheet A-6 A1.3 IO and S_IO worksheets A-6 A1.4 V worksheets A-8 Appendix 2 Anindilyakwa Aquaculture GIS A-13 A2.1 Prawn farming suitability criteria A-13 A2.2 Some strategies to generate fuzzy maps A-16 A2.3 AAGIS source data A-18 A2.4 Calculation of AHP weightings A-20 Appendix 3 Data driven fuzzy-rule based modelling A-22 A3.1 Fisher’s iris dataset A-22 A3.2 Output membership values calculated by Fuzme for 5 clusters A-26 A3.3 Fuzzy rule-based modelling with Scilab A-30 A3.4 Elephant seals dataset A-33 Appendix 4 Knowledge driven modelling A-35 A4.1 Deriving membership functions from questionnaires A-35 A4.2 Introduction to sciFLT, a fuzzy logic toolbox for Scilab A-37 A4.3 Cheung’s comments on calculations of vulnerability to fishing A-47 pressure of Pristipomoides multidens viii Philippe Puig – PhD thesis Tables Table 2.1 ………………………………………………………… 22 Comparison of membership values of all integer values of X in Figure 2.1 and 2.2. Table 2.2 ………………………………………………………… 50 Membership function coordinates derived from panel E in Figure 2.11. Table 2.3 ………………………………………………………… 51 Fuzzy patch properties derived from panel E in Figure 2.11. Table3.1 ………………………………………………………… 75 Source data sets of AAGIS. Table 3.2 ………………………………………………………… 75 Criteria used to assess the suitability of prawn farming sites Table 3.3 ………………………………………………………… 77 Relative importance of criteria assessed by pair wise comparisons. Table 3.4 ………………………………………………………… 77 Values of relative importance used in suitability criteria pair wise comparisons. Table 3.5 ………………………………………………………… 79 Values of relative importance of criteria C1 to C5. Table 3.6 ………………………………………………………… 79 Weightings of criteria C1 to C5. Table 3.7 ………………………………………………………… 80 Evaluation of weightings’ consistency. Table 3.8 ………………………………………………………… 80 Weightings of suitability criteria considered in AAGIS. Table 3.9 ………………………………………………………… 81 Classes of suitability expressed in linguistic terms. Table 3.10 ………………………………………………………… 82 Membership functions representing linguistic terms of suitability. Table 4.1 ………………………………………………………… 94 Flower metrics used to classify iris flowers. ix Philippe Puig – PhD thesis Table 4.2 ………………………………………………………… 99 Values of flower metrics of the iris varieties considered. Table 4.3 ………………………………………………………… 100 Input membership functions of fuzzy flower metrics. Table 4.4 ………………………………………………………… 101 Output membership functions of Boolean iris varieties. Table 4.5 ………………………………………………………… 104 Evaluation of the fuzzy classifier performance. Table 4.6 ………………………………………………………… 111 Nakanishi’s dataset used in the simplified identification method. Table 4.7 ………………………………………………………… 112 Effect of number of clusters on class size disparity. Table 4.8 ………………………………………………………… 115 Vertex coordinates of output trapezoidal membership functions. Table 4.9 ………………………………………………………… 118 Membership function coordinates of variables derived from a detailed visual examination of plots in Appendix 3. Table 5.1 ………………………………………………………… 147 Recalibrating estimates to compensate for informant’s bias. Table 5.2 ………………………………………………………… 148 Rescaled informants’ estimates. Table 5.3 ………………………………………………………… 149 Membership functions for medium values of fishing power. Table 5.4 ………………………………………………………… 151 Membership functions of a fuzzy rule-based model of fishing power. Table 5.5 ………………………………………………………… 152 List of rules of the fuzzy model of fishing power. Table 5.6 ………………………………………………………… 160 Rules from Cheung’s expert system retained in the model of fish vulnerability to fishing pressure in the TRF. Table 5.7 ………………………………………………………… 161 Vulnerability to fishing pressure. Table A1.1 ………………………………………………………… A – 6 Example of an IO worksheet of XLFIS. x Philippe Puig – PhD thesis Table A1.2 ………………………………………………………… A - 7 Example of S_IO worksheet of XLFIS. Table A1.3 ……………………………………………………… A - 9 Functional blocks of the input data membership calculation sheet. Table A2.1 ……………………………………………………… A - 20 Calculations of AHP weightings Table A3.1 ………………………………………………………… A - 23 Fisher’s iris dataset (1 of 3). Table A3.2 ………………………………………………………… A - 24 Fisher’s iris dataset (2 of 3). Table A3.3 ………………………………………………………… A - 25 Fisher’s iris dataset (3 of 3). Table A3.4 ………………………………………………………… A - 33 Variables of the fuzzy model for elephant seals foraging patterns (1 of 2) Table A3.5 ………………………………………………………… A - 34 Variables of the fuzzy model for elephant seals foraging patterns (2 of 2). Table A4.1 ………………………………………………………… A - 35 Example of binary transcription of informant’s records to a scratchpad. Table A4.2 ………………………………………………………… A - 36 Tally of informants’ scores. Table A4.3 ………………………………………………………… A - 36 Display of membership function