Complex decision making tasks of different natures, e.g. economics, safety engineering, ecology and biology, are based on vague, sparse, partially inconsistent and subjective knowledge. Moreover, decision making economists / engineers are usually not willing to invest too much time into study of complex formal theories. They require such decisions which can be (re)checked by human like common sense reasoning. One important problem related to realistic decision making tasks are incomplete data sets required by the chosen decision making algorithm. This paper presents a relatively simple algorithm how some missing III (input information items) can be generated using mainly decision tree topologies and integrated into incomplete data sets. The algorithm is based on an easy to understand heuristics, e.g. a longer decision tree sub-path is less probable. This heuristic can solve decision problems under total ignorance, i.e. the decision tree topology is the only information available. But in a practice, isolated information items e.g. some vaguely known probabilities (e.g. fuzzy probabilities) are usually available. It means that a realistic problem is analysed under partial ignorance. The proposed algorithm reconciles topology related heuristics and additional fuzzy sets using fuzzy linear programming. The case study, represented by a tree with six lotteries and one fuzzy probability, is presented in details.

Department of Economics Faculty of Business and Management Brno University of Technology Brno Czech Republic

Department of Informatics Faculty of Business and Management Brno University of Technology Brno Czech Republic

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Dondi R, El-Mabrouk N, Swenson K. Gene tree correction for reconciliation and species tree inference: Complexity and algorithms. J Discrete Algorithms. 2013; 25: 51–65 10.1016/j.jda.2013.06.001 PubMed DOI PMC

Vats S, Vats G, Vaish R, Kumar V. Selection of optimal electronic toll collection system for India: A subjective-fuzzy decision making approach. Appl Soft Comput. 2014; 21: 444–452. 10.1016/j.asoc.2014.04.006 DOI

Daniel K, Hirshleifer D, Teoh S. Investor Psychology in Capital Markets: Evidence and Policy Implications. J Monet Econ. 2011; 48: 139–209. 10.1016/S0304-3932(01)00091-5 DOI

Hodouin D. Methods for automatic control, observation, and optimization in mineral processing plants. J Process Control. 2011; 21: 211–225. 10.1016/j.jprocont.2010.10.016 DOI

Maroney J, McGarry C, Ó hÓgartaigh C. Familiarity, home bias and investors' reactions to 20-F reconciliation gains and losses and perceptions of the quality of accounting principles. Br Account Rev. 2008; 40: 103–122. 10.1016/j.bar.2008.01.001 DOI

Vasebi A, Poulin É, Hodouin D. Dynamic data reconciliation in mineral and metallurgical plants. Annu Rev Control. 2012; 36: 235–243. 10.1016/j.arcontrol.2012.09.005 DOI

Stiglic G, Kocbek S, Pernek I, Kokol P. Comprehensive decision tree models in bioinformatics. PLoS ONE. 2012; 7: s.e33812 10.1371/journal.pone.0033812 PubMed DOI PMC

Thipwiwatpotjana P, Lodwick W. Pessimistic, optimistic, and minimax regret approaches for linear programs under uncertainty. Fuzzy Optim Decis Mak. 2014; 13: 151–171. 10.1007/s10700-013-9171-z DOI

Yuan WJ, Xia CY. Role of Investment Heterogeneity in the Cooperation on Spatial Public Goods Game. PLoS One. 2014;9: e91012 10.1371/journal.pone.0091012 PubMed DOI PMC

Kuzilek J, Kremen V, Soucek F, Lhotska L. Independent Component Analysis and Decision Trees for ECG Holter Recording De-Noising. PLoS ONE. 2014; 9: e98450 10.1371/journal.pone.0098450 PubMed DOI PMC

Qin G, Luo L, Lv L, Xiao Y, Tu J, Tao L, et al. Decision tree analysis of traditional risk factors of carotid atherosclerosis and a cutpoint-based prevention strategy. PLoS ONE. 2014; 9: e111769 10.1371/journal.pone.0111769 PubMed DOI PMC

Dubois D. On various ways of tackling incomplete information in statistics. Int J Approx Reason. 2014; 55: 1570–1574.

Fargier H, Amor N, Guezguez W. On the Complexity of Decision Making in Possibilistic Decision Trees; 2012. Available: arXiv:1202.3718. Accessed 17 January 2015.

Dubois D, Fargier H, Guyonnet D. Data Reconciliation under Fuzzy Constraints in Material Flow Analysis Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology. Atlantis Press, 2013.

Lee Y, Li M, Yen T, Huang T. Analysis of fuzzy Decision Making Trial and Evaluation Laboratory on technology acceptance model. Expert Syst Appl. 2011; 38: 14407–14416. 10.1016/j.eswa.2011.04.088 DOI

Pedrycz W, Al-Hmouz R, Morfeq A, Balamash A. Building granular fuzzy decision support systems. Knowl Based Syst. 2014; 58: 3–10. 10.1016/j.knosys.2013.07.022 DOI

Zeinalkhani M, Eftekhari M. Fuzzy partitioning of continuous attributes through discretization methods to construct fuzzy decision tree classifiers. Info Sci. 2014; 278: 715–735. 10.1016/j.ins.2014.03.087 DOI

Jegadeesh N, Kim J, Krische S, Lee C. Analyzing the analysts: When do recommendations add value?. J Finance. 2004; 59: 1083–1124. 10.1111/j.1540-6261.2004.00657.x DOI

Bradshaw M. How Do Analysts Use Their Earnings Forecasts in Generating Stock Recommendations?. SSRN Working Paper Series. 2004. 10.2139/ssrn.256438 DOI

Xia CY, Wang L, Sun S, Wang J. An SIR model with infection delay and propagation vector in complex networks. Nonlinear Dynamics. 2012; 69: 927–934. 10.1007/s11071-011-0313-y DOI

Xia CY, Sun SW, Liu ZX, Chen ZQ, Yuan ZZ. Epidemics of sirs model with nonuniform transmission on scale-free networks. Int J Mod Phys B. 2009; 23: 2203–2213. 10.1142/S021797920905211X DOI

Dehmer M, Kraus V. On extremal properties of graph entropies. Match-Commun Math Cmput Chem. 2012; 68: 889–912.

Dehmer M, Grabner M. The Discrimination Power of Molecular Identification Numbers Revisited. Match-Commun Math Cmput Chem. 2013;69: 785–794.

Kraus V, Dehmer M, Schutte M. On Sphere-Regular Graphs and the Extremality of Information-Theoretic Network Measures. Match-Commun Math Cmput Chem. 2013;70: 885–900.

Kyburg H. Jr. Bayesian and non-bayesian evidential updating. Artif Intell. 1987; 31: 271–293.

Kim M, Cheeti A, Yoo C, Choo M, Paick J, Oh S. Non-invasive clinical parameters for the prediction of urodynamic bladder outlet obstruction: analysis using causal bayesian networks. PLoS ONE. 2014; 9: e113131 10.1371/journal.pone.0113131 PubMed DOI PMC

Wang P. The limitation of Bayesianism. Artif Intel. 2004; 158: 97–106. 10.1016/j.artint.2003.09.003 DOI

Sais F, Thomopoulos R. Ontology-aware prediction from rules: A reconciliation-based approach. Knowl Based Syst. 2014; 67: 117–130. 10.1016/j.knosys.2014.05.023 DOI

Jung J. Computational reputation model based on selecting consensus choices: An empirical study on semantic wiki platform. Expert Syst Appl. 2012; 39: 9002–9007. 10.1016/j.eswa.2012.02.035 DOI

Schallehn E, Sattler K, Saake G. Efficient similarity-based operations for data integration. Data Knowl Eng. 2004; 48: 361–387. 10.1016/j.datak.2003.08.004 DOI

Kashkoush M, ElMaraghy H. Matching Bills of Materials Using Tree Reconciliation. Procedia CIRP. 2013; 7: 169–174. 10.1016/j.procir.2013.05.029 DOI

Alhaj-Dibo M, Maquin D, Ragot J. Data reconciliation: A robust approach using a contaminated distribution. Control Eng Pract. 2008; 16: 159–170. 10.1016/j.conengprac.2007.01.003 DOI

Mousavi S, Gigerenzer G. Risk, uncertainty, and heuristics. J Bus Res. 2014; 67: 1671–1678. 10.1016/j.jbusres.2014.02.013 DOI

Sundar S, Singh A. New heuristic approaches for the dominating tree problem. Appl Soft Comput. 2013; 13: 4695–4703. 10.1016/j.asoc.2013.07.014 DOI

Dohnal M, Vykydal J, Kvapilik M, Bures P. Practical uncertainty assessment of reasoning paths (fault trees) under total uncertainty ignorance. J Loss Prev Process Ind. 1992; 5: 125–131. 10.1016/0950-4230(92)80009-W DOI

Fitch EC, Hong I. Hydraulic component design and selection. Stillwater: BarDyne; 2004.

Dimitri P B, Tsitsiklis J N. Introduction to Probability. Belmont, Mass.: Athena Scientific; 2008.

Rokach L, Maimon O. Data Mining with Decision Trees: Theory and Applications. Singapore: World Scientific; 2008.

Rutkowski L, Jaworski M, Pietruczuk L, Duda P. The CART decision tree for mining data streams. Information Sciences. 2014; 266: 1–15. 10.1016/j.ins.2013.12.060 DOI

Parsons S, Dohnal M. The qualitative and semiqualitative analysis of environmental problems. Environ Softw. 1995; 10: 75–85. 10.1016/0266-9838(95)00008-9 DOI

Janssens D, Wets G, Brijs T, Vanhoof K, Arentze T, Timmermans H. Integrating Bayesian networks and decision trees in a sequential rule-based transportation model. Eur J Oper Res. 2006; 175: 16–34. 10.1016/j.ejor.2005.03.022 DOI

Vandaele N, Landrieux B, Vandaele C, Landrieux C, Decouttere C. The sustainable reconciliation between technological, financial and people aspects in R&D portfolio assessment. Proceedings of the 6th International Conference on Management of Innovation and Technology, ICMIT 2012. 10.1109/ICMIT.2012.6225779 DOI

Narasimhan S, Jordache C. Data Reconciliation and Gross Error Detection: An Intelligent Use of Process Data. 1st ed Houston: Gulf Professional Publishing; 1999.

Monekosso D, Remagnino P. Data reconciliation in a smart home sensor network. Expert Syst Appl. 2013; 40: 3248–3255. 10.1016/j.eswa.2012.12.037 DOI

Zhang Z, Shao Z, Chen X, Wang K, Qian J. Quasi-weighted least squares estimator for data reconciliation. Comput Chem Eng. 2010; 34: 154–162. 10.1016/j.compchemeng.2009.09.007 DOI

Ubando A, Culaba A, Aviso K, Ng D, Tan R. Fuzzy mixed-integer linear programming model for optimizing a multi-functional bioenergy system with biochar production for negative carbon emissions. Clean Technol Environ Policy. 2014; 16: 1537–1549. 10.1007/s10098-014-0721-z DOI

Tan R, Briones L, Culaba A. Fuzzy data reconciliation in reacting and non-reacting process data for life cycle inventory analysis. J Clean Prod. 2007; 15: 944–949. 10.1016/j.jclepro.2005.09.001 DOI

Tanaka H, Asai K. Fuzzy linear programming problems with fuzzy numbers. Fuzzy Sets Syst. 1984; 13: 1–10. 10.1016/0165-0114(84)90022-8 DOI

Watson S. The meaning of probability in probabilistic safety analysis. Reliab Eng Syst Saf. 1994; 45: 261–269. 10.1016/0951-8320(94)90142-2 DOI

Fedrizzi M, Kacprzyk J, Verdegay JL. A survey of fuzzy optimization and mathematical programming In: Fedrizzi M, Kacprzyk J, Roubens M, editors. Interactive Fuzzy Optimization. Lecture Notes in Economics and Mathematical Systems. Berlin: Springer; 1991. pp. 15–28.

Lai YJ, Hwang CI. Fuzzy mathematical programming: Methods and applications. Berlin: Springer-Verlag; 1992.

Guua S, Wu Y. Two-phase approach for solving the fuzzy linear programming problems. Fuzzy Sets Syst. 1999; 107: 191–195. 10.1016/S0165-0114(97)00304-7 DOI

Huang G, Moore RD. Grey linear programming, its solving approach, and its application. Int J Syst Sci. 1993; 24: 159–172. 10.1080/00207729308949477 DOI

Brooke A, Kendrick D, Meeraus A. GAMS: User’s Guide. Redwood City, California: The Scientific Press; 1988.

Kikuchi S. A method to defuzzify the fuzzy number: Transportation problem application. Fuzzy Sets Syst. 2000; 116: 3–9. 10.1016/S0165-0114(99)00033-0 DOI

Nie G, Zhang L, Liu Y, Zheng X, Shi Y. Decision analysis of data mining project based on Bayesian risk. Expert Syst Appl. 2009; 36: 4589–4594. 10.1016/j.eswa.2008.05.014 DOI

Rose LM. Engineering investment decisions: planning under uncertainty. Amsterdam: Elsevier; 1976.

Eaton JW, Bateman D, Hauberg S. Gnu Octave Version 3. 0. 1 Manual: A High-Level Interactive Language for Numerical Computations. 1st ed CreateSpace Independent Publishing Platform; 2009.

Basgalupp MP, Barros RC, De Carvalho A, Freitas AA. Evolving decision trees with beam search-based initialization and lexicographic multi-objective evaluation. Inf Sci. 2014; 258: 160–181. 10.1016/j.ins.2013.07.025 DOI

Cao S, Dehmer M, Shi Y. Extremality of degree-based graph entropies. Inf Sci. 2014; 278: 22–33. 10.1016/j.ins.2014.03.133 DOI