References
- Atkinson P, Zhang J, Goodchild MF. 2014. Scale in spatial information and analysis. CRC Press.
- Capó M, Pérez A, Lozano JA. 2018. An efficient K-means clustering algorithm for massive data. ArXiv: 1801.02949. Available from: https://arxiv.org/pdf/1801.02949.pdf.
- Claramunt C. 2005. A spatial form of diversity. In: International conference on spatial information theory. Ellicottville, New York, Sep. 14–18; p. 218–231.
- Crooks GE. 2017. On measures of entropy and information. Available from: http://threeplusone.com/info [last accessed on January 27, 2016].
- Dai J, Xu Q. 2013. Attribute selection based on information gain ratio in fuzzy rough set theory with application to tumor classification. Appl Soft Comput. 13(1):211–221.
- Dubois D, Prade H. 1990. Rough fuzzy sets and fuzzy rough sets. Int J General Syst. 17(2–3):191–209.
- Feng Y, Liu Y, Tong X, Liu M, Deng S. 2011. Modeling dynamic urban growth using cellular automata and particle swarm optimization rules. Landsc Urban Plan. 102(3):188–196.
- Finkelstein MO. 2009. Basic concepts of probability and statistics in the law. New York: Springer.
- Gao P, Li Z, Zhang H. 2018. Thermodynamics-based evaluation of various improved Shannon entropies for configurational information of gray-level images. Entropy. 20(1):19.
- Habibi S, Asadi N. 2011. Causes, results and methods of controlling urban sprawl. Proc Eng. 21:133–141.
- Hamdy O, Zhao S, Salheen MA, Eid YY. 2017. Analyses the driving forces for urban growth by using IDRISI® Selva Models Abouelreesh-Aswan as a case study. IJET. 9(3):226–232.
- Hegazy IR, Kaloop MR. 2015. Monitoring urban growth and land use change detection with GIS and remote sensing techniques in Daqahlia governorate Egypt. Int J Sustain Built Environ. 4(1):117–124.
- Holte RC. 1993. Very simple classification rules perform well on most commonly used datasets. Mach Learn. 11(1):63–90.
- Jang JS. 1993. ANFIS: adaptive-network-based fuzzy inference system. IEEE Trans Syst Man Cybern. 23(3):665–685.
- Jensen R, Tuson A, Shen Q. 2014. Finding rough and fuzzy-rough set reducts with SAT. Inf Sci. 255:100–120.
- Jolliffe IT. 1986. Principal component analysis and factor analysis. In: Principal component analysis. New York: Springer; p. 115–128.
- Lesne A. 2014. Shannon entropy: a rigorous notion at the crossroads between probability, information theory, dynamical systems and statistical physics. Math Struct Comp Sci. 24(3):e240311.
- Li X, Yeh AGO. 2002. Urban simulation using principal components analysis and cellular automata for land-use planning. Photogram Eng Remote Sens. 68(4):341–352.
- MacQueen J. 1967. Some methods for classification and analysis of multivariate observations. In: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, CA, Dec. 27, 1965–Jan. 7, 1966.
- Mosammam HM, Nia JT, Khani H, Teymouri A, Kazemi M. 2017. Monitoring land use change and measuring urban sprawl based on its spatial forms: The case of Qom city. Egypt J Remote Sens Space Sci. 20(1):103–116.
- Pawlak Z. 1982. Rough sets. Int J Comput Inform Sci Program. 11(5):341–356.
- Pijanowski BC, Tayyebi A, Doucette J, Pekin BK, Braun D, Plourde J. 2014. A big data urban growth simulation at a national scale: configuring the GIS and neural network based land transformation model to run in a high performance computing (HPC) environment. Environ Model Software. 51:250–268.
- Qian J, Guo X, Deng Y. 2017. A novel method for combining conflicting evidences based on information entropy. Appl Intell. 46(4):876–888.
- Quinlan JR. 1992. C4.5 programs for machine learning. San Mateo, CA: Morgan Kaufmann.
- Ray A, Majumder SK. 2014. Derivation of some new distributions in statistical mechanics using maximum entropy approach. Yugosl J Oper Res. 24(1):145–155.
- Shannon CE. 1948. A mathematical theory of communication. Bell Syst Techn J. 27(3):379–423.
- Tian L, Ge B, Li Y. 2017. Impacts of state-led and bottom-up urbanization on land use change in the peri-urban areas of Shanghai: Planned growth or uncontrolled sprawl? Cities. 60:476–486.
- United Nations. 2016. The world’s cities in 2016. Available from: https://www.un.org/en/development/desa/population/publications/pdf/urbanization/the_worlds_cities_in_2016_data_booklet.pdf.
- Wang C, Zhao H. 2018. Spatial heterogeneity analysis: Introducing a new form of spatial entropy. Entropy. 20(6):398.
- Weilenmann B, Seidl I, Schulz T. 2017. The socio-economic determinants of urban sprawl between 1980 and 2010 in Switzerland. Landsc Urban Plan. 157:468–482.
- Yao Y. 1997. Combination of rough and fuzzy sets based on α-level sets. In: Rough sets and data mining. Boston, MA: Springer; p. 301–321.
- Yeh AGO, Li X. 2001. Measurement and monitoring of urban sprawl in a rapidly growing region using entropy. Photogram Eng Remote Sens. 67:83–90.
- Zadeh LA. 1965. Fuzzy sets. Inform Control. 8(3):338–353.
- Zeng A, Li T, Liu D, Zhang J, Chen H. 2015. A fuzzy rough set approach for incremental feature selection on hybrid information systems. Fuzzy Sets Syst. 258:39–60.
- Zhang TY, Suen CY. 1984. A fast parallel algorithm for thinning digital patterns. Commun ACM. 27(3):236–239.
- Zheng A, Jiang B, Li Y, Zhang X, Ding C. 2017. Elastic K-means using posterior probability. PloS One. 12(12):e0188252.