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Decision Sciences

Research :: Navorsing :: Patlisiso

The Department of Decision Sciences remains, together with the other departments of the School of Economics Sciences, at the forefront of research in the College of Economic and Management Sciences. The research done in the Department reflects the interdisciplinary approach typical of operations research and related subjects.

NRF rating

Three staff members in the Department have received National Research Foundation (NRF) ratings: Proff Fouché, Luhandjula and PH Potgieter.

Research groups

Although a considerable amount of research is conducted in staff members' personal capacity, the following distinct groups operate in the Department.

Computability and Complexity in Decision Sciences (CCDS)

The research group Computability and Complexity in Decision Sciences (CCDS) at the University of South Africa (Unisa) in Pretoria is one of South Africa’s pre-eminent centres for research in theoretical computer science (including foundations of quantum computing) as well as being at the forefront of research into computational and fractal properties of sample paths of Brownian motion (BM) and images of sets under BM. The group has also investigated computational and constructive aspects of economic models and was the main South African partner in a two-year project, funded under the South Africa-Hungary Science and Technology Agreement (NRF UID: 62110) entitled Computers and Algorithms in Mathematical Economics and Finance.

The work of the leader of the group, Professor Willem Fouché, has been published in leading journals, such as Advances in Mathematics, Journal of the London Mathematical Society, The Journal of Symbolic Logic and Journal of Number Theory. The distinguished international gatherings that he has been invited to address include the 1999–2000 winter meeting of the Association for Symbolic Logic in Washington DC (January 2000) and the Prague Midsummer Combinatorial Workshop XII in July 2005. During the World Mathematical Year 2000 Fouché received a gold medal from the South African Mathematical Society (SAMS) for his achievements. He was awarded the Chancellor’s Prize for research at the University of South Africa in 2005.

Individual CCDS members regularly speak at conferences abroad as well as in South Africa. Members have also participated in joint SA/German and SA/Swiss scientific programmes over the past three years. The group is also active in the high-performance computing initiative at the University of South Africa and has substantial computing resources at its disposal as well as considerable practical expertise in the area of computer applications.

Quantum Information and Computation (QuIC) Research Group

The Unisa QuIC group has been active for 7 years, and has collaborated on research problems to do with the universality and programmability of quantum computers, as well as other related topics. The work is truly multi-, inter and trans-disciplinary (MIT), straddling the disciplines of quantum physics, computer science and mathematics and engineering. Several papers and conference contributions have resulted from the group's work.

Reflexive Research Workgroup

The Decision Sciences Tuition Reflexive Research Workgroup holds regular meetings and has several projects which are planned and already underway, including an investigation into Computer/ Internet / MyUnisa access by undergraduate students.

Selected recent publications and research outputs

Papers accepted or published: 

  • Fouché, WL: Fractals generated by algorithmically random Brownian Motion.  Mathematical theory and computational practice.  Lecture Notes Computer Science.  Springer Verlag.  Volume 5635. pp 208-217.
  • Conradie, WJ (Stellenbosch), de Wet T (Stellenbosch), Jankowitz, MD (Unisa):  Performance of nonlinear smoother in signal recovery.  Applied Stochastic Models in Business and Industry. 25, 425-444.  DOI: 10.1002/ASMMB.774
  • Potgieter, P: Nonstandard analysis, Fractal Properties and Brownian Motion.  Fractals 17, 117 - 129 (2009).
  • Potgieter, P: Arithmetic progressions in salem-type subsets of the integers.  Journal of Fourier Analysis and Applications, Volume 17, pp 1138-1151 (2011).
  • Potgieter, PH: Fractal asset returns, arbitrage and option pricing.  Chaos, Solitions and Fractals.  42(3), 1792 - 1795.
  • Adeyeoluwa, S: Multi-objective Stochastic Linear Programming: An Overview.  American Journal of Operations Research.  Volume 1, Issue 4, 2011.
  • Strydom, MC: 'n Bydrae tot die rangordebepaling van akademiese tydskrifte.  Litnet Akademies. Volume 8. Issue 1, pp 1-8, 2011.
  • Edmond J. Vanderperre E (Research fellow of the Department Decision Sciences), Stanislav S. (Thailand), Overall availability of a robot with internal safety device, Computers Industrial Engineering 56 (2009) 236240.

Papers submitted:

  • Adeyefa, AS and Luhandjula, MK: Multiobjective Stochastic Linear Programming : An Overview.  Submitted.
  • Fouché, WL: Countably Dense Random Sets of Reals, Kolmogorov Complexity and Brownian Motion.  Invited lecture. Abstract submitted for conference:  Continuity, Computability, Constructivity:  From Logic to Algorithms, CCA 2009,  Cologne.  Accepted for conference proceedings.
  • Luhandjula, MK and Joubert, JW: Randomness and Fuzziness in an Optimization setting.
  • Luhandjula, MK: Embedding Theorem for Fuzzy random variable and its application to Fuzzy Stochastic Optimization.
  • Potgieter, PH: International mobile roaming - economic issues and regulation. Abstract accepted for: International Telecommunications Society Fourth Africa-Asia-Australasia conference, International Telecommunications Society, Perth, 2009.

Conferences and Workships attended

Potgieter, PH:

  • Future Models for Energy and Water Management under a Regulated Environment 20 - 22 July 2009, Queensland University of Technology, Brisbane
  • 3rd Annual Organizational Economics Workshop 24 July 2009, University of Sydney
Fouché, WL:
  • Fifth Conference on Computability in Europe, CiE 2009, Heidelberg, Germany, July 2009.
  • Continuity, Computability, Constructivity: From Logic to Algorithms, CCA 2009, Joint meeting of the following bi-national projects:
    • Computations over non-discrete structures: models, semantics and complexity (Germany-Russia)
    • From continuity to computability (Germany-South Africa)
    • Logic and algorithms for continuous data spaces (Germany-United Kingdom), Cologne, Germany, July 2009. (Invited speaker)

Research events in the department

Dr Nies from the University Auckland visited Professor Fouché during 22 - 29 September 2009 and they started to write a paper for the Bulletin of Symbolic Logic. Dr Nies presented two lectures on the interplay between randomness and computing, a topic on which he is a leading expert. He has also invited members of Professor Fouché's research group for short academic visits to his university.

We have an ongoing weekly seminar series on Fourier analysis and randomness which is attended by members from our department as well as members from the mathematics department at Unisa.

One of our doctoral students, Mr Munapo has presented four talks on his doctoral research to our department.

Mr Munapo and Mrs Fick have attended the ORSSA congress in Stellenbosch, where they presented short talks. 

Selected Research Publications

This list is not complete and not necessarily up to date. Researchers in the department are more likely to have recent publications on their own web pages.

  • M Fick, CJ Swanepoel
    Recursive Decompounding in Afrikaans,
    Lecture Notes in Artificial Intelligence 6836:  Text, Speech and Dialogue:,  14th International Conference,  TSD  2011.

  • MF Immelman, LGC Scheepers
    The effects of Data Reduction on LiDAR-based Digital Elevation Models,
    Proceedings:  The 4th International Congress on Image and Signal Processing,  Volume 3,  CISP  2011.

  • MK Luhandjula
    On Fuzzy random-valued Optimization,
    American Journal of Operations Research,  Volume 1, No. 4,  2011.

  • MK Luhandjula, S Adeyeoluwa,
    Multiobjective Programming Problems with Fuzzy Random Coefficients,
    Advances in Fuzzy Sets and Systems,  Volume 7, No. 1,  2011.

  • M Mulaudzi, J Mukuddem, IM Schoeman, B de Waal, J Manale, MA Petersen
    Optimal Allocation Between Subprime Structured Mortgage Products and Treasuries,
    Proceedings of World Academy of Science, Engineering and Technology,  Volume 7, No. 17,  2011.

  • MA Petersen, M Mulaudzi, J Mukuddem, IM Schoeman, B de Waal
    Stochastic control of credit default insurance for subprime residential mortgage-backed securities,
    Optimal control Applications & Methods,  Volume Online, 1-26,  2011.

  • P Potgieter
    Arithmetic progressions in salem-type subsets of the integers,
    Journal of Fourier Analysis and Applications,  Volume 17, 1138-1151,  2011.

  • S Adeyeoluwa and MK Luhandjula
    Multi-objective Stochastic Linear Programming: An Overview,
    American Journal of Operations Research,  Volume 1, No. 4,  2011.

  • MC Strydom
    'n Bydrae tot die rangordebepaling van akademiese tydskrifte,
    Litnet Akademies,  Volume 8, No 1, 1-8,  2011.

  • B Swart
    Pricing of single stock futures and dividend risk,
    Investment Analysts Journal,  Volume 73, 37-42,  2011.

  • G Davie
    Dobbelstrategieë vir toevalsrye (Gambling strategies for random sequences),
    Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie,  Volume 29, No. 1,  2010.

  • D Maposa, E Mudimu and O Ngwenya
    A Multivariate Analysis of Variance (ANOVA) of the Performance of Sorghum Lines in Different Agro-Ecological Regions of Zimbabwwe,
    African Journal of Agricultural Research,  5(3):196-203, 4 February 2010

  • Petrus H Potgieter and Elemér E Rosinger
    Output concepts for accelerated Turing machines,
    Natural Computing,  Volume 9,  Maart / April 2010.

  • PH Potgieter and F Lyons
    Prysrisikobestuur - is daar pit in?,
    Afgriland ,  Number 4, 853-864,   2010.

  • M Fick and CJ Swanepoel
    Afrikaanse Lettergreepverdelingspatrone (Afrikaans Syllabification Patterns),
    Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie,  vol 29, No 2,   Junie 2010.

  • Munapo, E
    Project activity analysis without the network model,
    South African Journal of Industrial Engineering,  vol 21(1): 81-92, 2010.

  • C Sigauke, D Maposa, E Mudimu and P Nyamugure
    Volatility modelling using ARIMA-GARCH models in a hyperinflationary economic environment: The Zimbabwean experience,
    SASA 2010 peer-reviewed proceedings.   

  • Petrus H Potgieter,
    International mobile roaming - economic issues and regulation,
    In Electronic proceedings of the ITS Africa-Asia-Australia regional conference,  ITS, 2009.

  • W L Fouché,
    Fractals generated by algorithmically random Brownian motion,
    K. Ambos-Spies, B. Löwe and W Merkle (Eds.): CiE 2009,  LNCS 5635, (2009) 208217.

  • Petrus H Potgieter,
    Fractal asset returns, arbitrage and option pricing,
    Chaos, Solitons & Fractals,  42(3): 1792-1795, 2009.

  • WL Fouché,
    Dynamics of a generic Brownian motion: Recursive aspects,
    In: From Gödel to Einstein: Computability between Logic and Physics,  Theoretical Computer Science A,  394 (2008), 175-186.

  • WL Fouché, J Heidema, G Jones, PH Potgieter,
    Universality and programmability of quantum computers,
    Theoretical Computer Science,  403, 121 - 129, (2008).

  • Willem L Fouché,
    Subrecursive Complexity of Identifying the Ramsey Structure of Posets,
    Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms,   CiE June (2008), Springer-Verlag - Lecture Notes in Computer Science.

  • WL Fouché,
    An algorithmic construction of quantum circuits of high descriptive complexity,
    Electronic Notes in Theoretical Computer Science, 221,   (2008), 61-69.

  • Petrus H Potgieter and Elemér E. Rosinger
    Ultrafilter and non-standard Turing machines.,
    In Proceedings of the 7th international conference on Unconventional Computing, Vienna, Austria, pages 220-227,  (2008). Springer-Verlag. ISBN 978-3-540-85193-6.

  • PH Potgieter
    Computable counter-examples to the Brouwer fixed-point theorem.,
    In Costas Dimitracopoulos Arnold Beckmann and Benedikt Lowe, editors, Logic and Theory of Algorithms, Fourth Conference on Computability in Europe, CiE 2008, Local Proceedings, pages 377-386,  (2008).

  • PH Potgieter
    Elementêre topologie en berekeningsuniversaliteit,
    Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie, 27(4):287-293,  December (2008).

  • JW Joubert, MK Luhandjula, O Ncube, G le Roux & F de Wet
    An optimization model for the management of a South African game ranch,
    Agricultural Systems, 92 (2007).

  • WJ Conradie, T de Wet and MD Jankowitz
    Exact and asymptotic distribution of LULU smoothers.,
    Computational and Mathematical Organization Theory, 186 (2006).

  • WL Fouché,
    Brownian motion and Kolmogorov complexity,
    to appear in: Logical Approaches to Computational Barriers, University of Wales Swansea, Computer Science Report Series Arnold Beckmann, Ulrich Berger, Benedikt Lwe, & John V Tucker (eds.), (2006).

  • MK Luhandjula
    Fuzzy stochastic linear programming: Survey and future research directions,
    European Journal of Operational Research, 174 (2006).

  • PH Potgieter,
    Deutsch's Universality and Programmability of Quantum Computers (Revisited) (with G Jones, J Heidema & WL Fouché),
    to appear in proceedings of Theoretical and Experimental Foundations of Recent Quantum Technologies, (Durban, July 2006).

  • PH Potgieter,
    Hypercomputing the Mandelbrot Set?,
    to appear in Logical Approaches to Computational Barriers, University of Wales Swansea, Computer Science Report Series (proceedings of Computability in Europe 2006).

  • Barbara Swart & Antoinetta Venter
    What is quantitative finance?,
    South African Journal of Science, 102 March/April (2006).

  • Linda Smit & Barbara Swart
    Calculating the Price of Bond Convexity,
    The Journal of Portfolio Management, (2006).

  • EJ Vanderperre
    On Gaver's parallel system: The idle time,
    Technical report, Unisa, November (2006).

  • EJ Vanderperre
    A functional equation related to a multiple cold standby system,
    Technical report, Unisa, August (2006).

  • EJ Vanderperre
    On the idle time of a repairman attending a renewable cold standby system,
    Technical report, Unisa, March (2006).

  • EJ Vanderperre
    Long-run availability of a warm standby system,
    Technical report, Unisa, March (2006).

  • EJ Vanderperre
    A Markov time related to a priority system,
    Mathematical Problems in Engineering, (2006).

  • EJ Vanderperre
    Point availability of a renewable T-Cell,
    Mathematical Problems in Engineering, (2006).

  • WJ Conradie, T de Wet and MD Jankowitz
    An overview of LULU Smoothers with application to financial data,
    J.STUD.ECON.ECONOMETRICS, 29(1) (2005).

  • WL Fouché, J Heidema & PH Potgieter,
    Kwantumberekening,
    SA Tydskrif vir Natuurwetenskappe en Tegnologie, 24 (2005), 60-83.

  • WL Fouché, L Pretorius & C Swanepoel,
    The Ramsey degrees of bipartite graphs: A primitive recursive proof,
    Discrete Math, 292 (2005).

  • PH Potgieter,
    Zeno Machines and Hypercomputation
    to appear in Theoretical Computer Science, (2005).

  • PH Potgieter,
    Kwantumberekening (with J. Heidema & WL Fouché, with English abstract: Quantum computation),
    SA Tydskrif vir Natuurwetenskap en Tegnologie (ISSN 0254-3486), Vol 24, Issue 3, September, 60-83 (2005).

  • EJ Vanderperre,
    A Sokhotski-Plemelj problem related to a renewable T-cell,
    Electronic version of the article published in ORiON, 2005, Volume 21, number 2, pages 147-155.

  • S Rodtook, SS Makhanov & EJ Vanderperre,
    A filter bank for rotatiionally invariant image recognition,
    Electronic version of the article published in ORiON, 2005, Volume 21, number 2, pages 125-138.

  • EJ Vanderperre
    On rhe reliability of a renewable multiple cold standby system,
    Mathematical Problems in Engineering, 3 (2005).

  • EJ Vanderperre & SS Makhanov,
    A Markov time related to a robot-safety device system,
    Journal of the Operations Research Societies of Belgium, France and Italy, 3 (2005).

  • EJ Vanderperre & SS Makhanov,
    Long-run availability of a priority system: A numerical approach.,
    Mathematical Problems in Engineering, 1 (2005).

  • PH Potgieter,
    Die voorgeskiedenis van kwantumberekening (with English abstract: The pre-history of quantum computation),
    SA Tydskrif vir Natuurwetenskap en Tegnologie (ISSN 0254-3486), Vol 23, Issue 1/2, Mar/Jun, 2-6 (2004).

  • EJ Vanderperre
    On Gaver's parallel system (with V.S. Yadavalli and S.S. Makhanov),
    South African Journal of Industrial Engineering, 75 (2004).

  • EJ Vanderperre,
    Reliability analysis of a renewable multiple cold standby system,,
    Operations Research Letters 32 (2004), 288--292.

  • M Fick,
    Neurale netwerke as moontlike woordafkappingstegniek vir Afrikaans,
    Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie 22 (2003).

  • RJ Fossati & JS Wolvaardt,
    The construction of drape surfaces with constrained first derivates,
    Orion 17 (2003), 65--80.

  • PH Potgieter,
    A multifractal model for South African rand exchange rates,
    Economic & Financial modelling Autumn (2002).

  • EJ Vanderperre & SS Makhanov,
    On Gaver's parallel system sustained by a cold standby unit and attended by two repairmen,
    Operations Research Letters 30 (2002), 43--48.

  • EJ Vanderperre & SS Makhanov,
    Risk analysis of a robot-safety device system,
    International Journal of Reliability, Quality and Safety Engineering 9 (2002), 79--87.

  • A Venter & DP Laurie,
    A double adaptive integration algorithm using stratified rules,
    Bit 42 (2002), 183--193.

  • PO de Wet,
    Constructing a large number of nonisomorphic graphs of order n,
    Morehead Electronic Journal of Applicable Mathematics 1 (2001), MATH-2000-02.

  • PH Potgieter,
    Assesing recent rand volatility,
    Southern African Business Review, Volume 5 Number 1 (July 2001).
    http://www.sabusinessreview.co.za/July2001/general_articles/potgieter.htm

  • L Zietsman, NFJ van Rensburg & AJ van der Merwe,
    Analysis of the solvability of a model for the vibrations of a damaged beam,
    Applicable Analysis 78 (2001), 9--20.

  • WL Fouche, LM Pretorius & CJ Swanepoel, 
    Partitions of factorisations of parameter words,
    Discrete Mathematics 231 (2001), 169--175.

  • SS Makhanov & EJ Vanderperre,
    Optimal adaptive blur identification of noisy images,
    Yugoslav Journal of Operations Research 11 (2001), 105--112.

  • EJ Vanderperre,
    Point availability of a robot-safety device,
    Operations Research Letters 28 (2001), 143--148.

    WL Fouche,
    Discrepancies of hypergraphs of high Kolmogorov complexity,
    Journal of Combinatorial Mathematics and Combinatorial Computing 33 (2000), 199--207.

  • WL Fouche,
    The descriptive complexity of Brownian motion,
    Advances in Mathematics 155 (2000), 317--343.

  • LM Pretorius & CJ Swanepoel,
    Partitions of countable posets,
    Journal of Combinatorial Mathematics and Combinatorial Computing 33 (2000), 289--297.

  • EJ Vanderperre,
    A Sokhotski-Plemelj problem related to a robot-safety device system,
    Operations Research Letters 27 (2000), 67--71.

  • EJ Vanderperre,
    Long-run availability of a two-unit standby system subjected to a priority rule,
    Bulletin of the Belgian Mathematical Society Simon Stevin 7 (2000), 355--364.

  • L Zietsman, NFJ van Rensburg & AJ van der Merwe,
    A numerical study of the vibrations of a damaged beam,
    Mathematical and Computer Modelling 31 (2000), 51--60.

  • GN Engelbrecht,
    On the relevance of game theory in strategic thinking,
    Scientia Militaria 29 (1999), 36--52.

  • WL Fouche, LM Pretorius & CJ Swanepoel
    Partition theorems for factorisations of ascending parameter words,
    Discrete Mathematics 197/198 (1999), 331--350.

  • C le Roux,
    Existence and uniqueness of the flow of second-grade fluids with slip boundary conditions,
    Archive for Rational Mechanics and Analysis 148 (1999), 309--356.

  • EJ Vanderperre,
    On hazard rates modelled by mixtures of exponential distributions,
    Belgian Journal of Operations Research, Statistics and Computer Science 39 (1999), 31--38.

  • CA van der Merwe et al,
    Dysfunction of sensory nerves during attacks of hypokalernic periodic paralysis,
    Neuromuscular Disorders 9 (1999), 227--231.