[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
Skip to main content
Springer Nature Link
Log in

On Possibilistic Mean Value, Variance, Covariance and Correlation of Fuzzy Numbers

  • Chapter
Towards Intelligent Engineering and Information Technology

Part of the book series: Studies in Computational Intelligence ((SCI,volume 243))

Abstract

In 2001 we introduced the notions of possibilistic mean value and variance of fuzzy numbers. In this paper we give a short survey of these notations and show some examples of their application from the literature.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
GBP 19.95
Price includes VAT (United Kingdom)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
GBP 199.50
Price includes VAT (United Kingdom)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
GBP 249.99
Price includes VAT (United Kingdom)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
GBP 249.99
Price includes VAT (United Kingdom)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Carlsson, C., Fullér, R.: Capital Budgeting Problems with Fuzzy Cash Flows. Mathware and Soft Computing 6, 81–89 (1999)

    MATH  Google Scholar 

  2. Carlsson, C., Fullér, R.: Real Option Evaluation in Fuzzy Environment. In: Proceedings of the International Symposium of Hungarian Researchers on Computational Intelligence, Budapest Polytechnic, pp. 69–77 (2000)

    Google Scholar 

  3. Carlsson, C., Fullér, R.: On Possibilistic Mean Value and Variance of Fuzzy Numbers. Fuzzy Sets and Systems 122, 315–326 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  4. Carlsson, C., Fullér, R.: On Optimal Investment Timing with Fuzzy Real Options. In: Proceedings of the EUROFUSE 2001 Workshop on Preference Modelling and Applications, pp. 235–239 (2001)

    Google Scholar 

  5. Carlsson, C., Fullér, R., Majlender, P.: Project Selection with Fuzzy Real Options. In: Proceedings of the Second International Symposium of Hungarian Researchers on Computational Intelligence, pp. 81–88 (2001)

    Google Scholar 

  6. Carlsson, C., Fullér, R.: Project Scheduling with Fuzzy Real Options. In: Trappl, R. (ed.) Cybernetics and Systems ’2002, Proceedings of the Sixteenth European Meeting on Cybernetics and Systems Research, Vienna, April 2-4, pp. 511–513. Austrian Society for Cybernetic Studies (2002)

    Google Scholar 

  7. Carlsson, C., Fullér, R., Majlender, P.: A Possibilistic Approach to Selecting Portfolios with Highest Utility Score. Fuzzy Sets and Systems 131, 13–21 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  8. Carlsson, C., Fullér, R.: A Fuzzy Approach to Real Option Valuation. Fuzzy Sets and Systems 139, 297–312 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  9. Carlsson, C., Fullér, R., Majlender, P.: On Possibilistic Correlation. Fuzzy Sets and Systems 155, 425–445 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  10. Carlsson, C., Fullér, R., Majlender, P.: A Fuzzy Real Options Model for R&D Project Evaluation. In: Liu, Y., Chen, G., Ying, M. (eds.) Proceedings of the Eleventh IFSA World Congress, Beijing, China, July 28-31, pp. 1650–1654. Tsinghua University Press and Springer, Beijing (2005)

    Google Scholar 

  11. Carlsson, C., Fullér, R., Heikkil, M., Majlender, P.: A Fuzzy Approach to R&D Project Portfolio Selection. International Journal of Approximate Reasoning 44, 93–105 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  12. Dubois, D., Prade, H.: The Mean Value of a Fuzzy Number. Fuzzy Sets and Systems 24, 279–300 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  13. Dubois, D., Prade, H.: Possibility Theory: An Approach to Computerized Processing of Uncertainty. Plenum Press, New York (1988)

    MATH  Google Scholar 

  14. Fullér, R., Majlender, P.: On Weighted Possibilistic Mean and Variance of Fuzzy Numbers. Fuzzy Sets and Systems 136, 363–374 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  15. Fullér, R., Majlender, P.: On Interactive Fuzzy Numbers. Fuzzy Sets and Systems 143, 355–369 (2004)

    Article  MathSciNet  Google Scholar 

  16. Goetschel, R., Voxman, W.: Elementary Fuzzy Calculus. Fuzzy Sets and Systems 18, 31–43 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  17. Jaynes, E.T.: Probability Theory: The Logic of Science. Cambridge University Press, Cambridge (2003)

    MATH  Google Scholar 

  18. Zadeh, L.A.: L. A. Zadeh, Concept of a Linguistic Variable and its Application to Approximate Reasoning. I, II, III, Information Sciences 8, 199–249, 301-357 (1975); 9, 43–80 (1975)

    MathSciNet  Google Scholar 

  19. Zhang, W.-G., Wang, Y.-L., Chen, Z.-P., Nie, Z.-K.: Possibilistic Mean-Variance Models and Efficient Frontiers for Portfolio Selection Problem. Information Sciences 177(13), 2787–2801 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  20. Dutta, P., Chakraborty, D., Roy, A.R.: Continuous Review Inventory Model in Mixed Fuzzy and Stochastic Environment. Applied Mathematics and Computation 188(1), 970–980 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  21. Thavaneswaran, A., Thiagarajah, K.: Appadoo SS Fuzzy Coefficient Volatility (FCV) Models with Applications. Mathematical and Computer Modelling 45(7-8), 777–786 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  22. Vercher, E., Bermudez, J.D., Segura, J.V.: Fuzzy Portfolio Optimization under Downside Risk Measures. Fuzzy Sets and Systems 158(7), 769–782 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  23. Thiagarajah, K., Appadoo, S.S., Thavaneswaran, A.: Option Valuation Model with Adaptive Fuzzy Numbers. Computers and Mathematics with Applications 53, 831–841 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  24. Fang, Y., Lai, K.K., Wang, S.Y.: Portfolio Rebalancing Model with Transaction Costs Based on Fuzzy Decision Theory. European Journal of Operational Research 175(2), 879–893 (2006)

    Article  MATH  Google Scholar 

  25. Yoshida, Y., Yasuda, M., Nakagami, J.I., et al.: A New Evaluation of Mean Value for Fuzzy Numbers and its Application to American Put Option under Uncertainty. Fuzzy Sets and Systems 157(19), 2614–2626 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  26. Dubois, D.: Possibility Theory and Statistical Reasoning. Computational Statistics & Data Analysis 51(1), 47–69 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  27. Stefanini, L., Sorini, L., Guerra, M.L.: Parametric Representation of Fuzzy Numbers and Application to Fuzzy Calculus. Fuzzy Sets and Systems 157(18), 2423–2455 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  28. Beynon, M.J., Munday, M.: The Elucidation of Multipliers and their Moments in Fuzzy Closed Leontief Input-Output Systems. Fuzzy Sets and Systems 157(18), 2482–2494 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  29. Hashemi, S.M., Modarres, M., Nasrabadi, E., et al.: Fully Fuzzified Linear Programming, Solution and Duality. Journal of Intelligent & Fuzzy Systems 17(3), 253–261 (2006)

    MATH  Google Scholar 

  30. Facchinetti, G., Pacchiarotti, N.: Evaluations of Fuzzy Quantities. Fuzzy Sets and Systems 157(7), 892–903 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  31. Bodjanova, S.: Median Alpha-Levels of a Fuzzy Number. Fuzzy Sets and Systems 157(7), 879–891 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  32. Sheen, J.N.: Generalized Fuzzy Numbers Comparison by Geometric Moments. WSEAS Transactions on Systems 5(6), 1237–1242 (2006)

    Google Scholar 

  33. Liu, X.: On the Maximum Entropy Parameterized Interval Approximation of Fuzzy Numbers. Fuzzy Sets and Systems 157, 869–878 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  34. Cheng, C.B.: Fuzzy Process Control: Construction of Control Charts with Fuzzy Numbers. Fuzzy Sets and Systems 154(2), 287–303 (2005)

    Article  MathSciNet  Google Scholar 

  35. Ayala, G., Leon, T., Zapater, V.: Different Averages of a Fuzzy Set with an Application to Vessel Segmentation. IEEE Transactions on Fuzzy Systems 13(3), 384–393 (2005)

    Article  Google Scholar 

  36. Hong, D.H., Kim, K.T.: A Note on Weighted Possibilistic Mean. Fuzzy Sets and Systems 148(2), 333–335 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  37. Jahanshahloo, G.R., Soleimani-damaneh, M., Nasrabadi, E.: Measure of Efficiency in DEA with Fuzzy Input-Output Levels: a Methodology for Assessing. Ranking and Imposing of Weights Restrictions, Applied Mathematics and Computation 156(1), 175–187 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  38. Roventa, E., Spircu, T.: Averaging Procedures in Defuzzification Processes. Fuzzy Sets and Systems 136, 375–385 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  39. Facchinetti, G.: Ranking Functions Induced by Weighted Average of Fuzzy Numbers. Fuzzy Optimization and Decision Making 1, 313–327 (2002)

    Article  MATH  Google Scholar 

  40. Zhang, W.-G., Chen, Q., Lan, H.-L.: A Portfolio Selection Method Based on Possibility Theory. In: Cheng, S.-W., Poon, C.K. (eds.) AAIM 2006. LNCS, vol. 4041, pp. 367–374. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  41. Yoshida, Y.: A Defuzzification Method of Fuzzy Numbers Induced from Weighted Aggregation Operations. In: Torra, V., Narukawa, Y., Valls, A., Domingo-Ferrer, J. (eds.) MDAI 2006. LNCS (LNAI), vol. 3885, pp. 161–171. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  42. Yoshida, Y.: Mean Values of Fuzzy Numbers with Evaluation Measures and the Measurement of Fuzziness. In: Proceedings of the 9th Joint Conference on Information Sciences, JCIS 2006 (2006) (art. no. 298), doi:10.2991/jcis.2006.298

    Google Scholar 

  43. Yoshida, Y.: Mean Values of Fuzzy Numbers and the Measurement of Fuzziness by Evaluation Measures. In: 2006 IEEE Conference on Cybernetics and Intelligent Systems, pp. 1–6 (2006) (art. no. 4017804)

    Google Scholar 

  44. Zarandi, M.H.F., Pourakbar, M., Turksen, I.B.: An Intelligent Agent-based System for Reduction of Bullwhip Effect in Supply Chains. In: IEEE International Conference on Fuzzy Systems, pp. 663–670 (2006) (art. no. 1681782)

    Google Scholar 

  45. Liu, H., Brown, D.J.: An Extension to Fuzzy Qualitative Trigonometry and its Application to Robot Kinematics. In: IEEE International Conference on Fuzzy Systems, pp. 1111–1118 (2006) (art. no. 1681849)

    Google Scholar 

  46. Wang, X., Xu, W., Zhang, W.-G., Hu, M.: Weighted Possibilistic Variance of Fuzzy Number and its Application in Portfolio Theory. In: Wang, L., Jin, Y. (eds.) FSKD 2005. LNCS, vol. 3613, pp. 148–155. Springer, Heidelberg (2005)

    Google Scholar 

  47. Dubois, D., Fargier, H., Fortin, J.: The Empirical Variance of a Set of Fuzzy Intervals. In: IEEE International Conference on Fuzzy Systems, pp. 885–890 (2005)

    Google Scholar 

  48. Zhang, W.-G., Wang, Y.: Using fuzzy possibilistic mean and variance in portfolio selection model. In: Hao, Y., Liu, J., Wang, Y.-P., Cheung, Y.-m., Yin, H., Jiao, L., Ma, J., Jiao, Y.-C. (eds.) CIS 2005. LNCS (LNAI), vol. 3801, pp. 291–296. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  49. Zhang, W.-G., Liu, W.-A., Wang, Y.-L.: A Class of Possibilistic Portfolio Selection Models and Algorithms. In: Deng, X., Ye, Y. (eds.) WINE 2005. LNCS, vol. 3828, pp. 464–472. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  50. Sato, T., Takahashi, S., Huang, C., Inoue, H.: Option Pricing with Fuzzy Barrier Conditions. In: Liu, Y., Chen, G., Ying, M. (eds.) Proceedings of the Eleventh International Fuzzy systems Association World Congress, July 28-31, pp. 380–384. Tsinghua University Press and Springer, Beijing (2005)

    Google Scholar 

  51. Zhang, J.-P., Li, S.-M.: Portfolio Selection with Quadratic Utility Function under Fuzzy Envirornment. In: 2005 International Conference on Machine Learning and Cybernetics, ICMLC 2005, pp. 2529–2533 (2005)

    Google Scholar 

  52. Yoshida, Y.: Mean Values of Fuzzy Numbers by Evaluation Measures and its Measurement of Fuzziness. In: Proceedings - International Conference on Computational Intelligence for Modelling, Control and Automation, CIMCA 2005 and International Conference on Intelligent Agents, Web Technologies and Internet, vol. 2, pp. 163–169 (2005) (art. no. 1631462)

    Google Scholar 

  53. Blankenburg, B., Klusch, M.: BSCA-F: Efficient Fuzzy Valued Stable Coalition Forming among Agents. In: Proceedings - 2005 IEEE/WIC/ACM International Conference on Intelligent Agent Technology, IAT 2005, pp. 732–738 (2005) (art. no. 1565632)

    Google Scholar 

  54. Lazo, J.G.L., Vellasco, M.M.B.R., Pacheco, M.A.C.: Determination of Real Options Value by Monte Carlo Simulation and Fuzzy Numbers. In: Proceedings - HIS 2005: Fifth International Conference on Hybrid Intelligent Systems, pp. 488–493 (2005) (art. no. 1587794)

    Google Scholar 

  55. Yoshida, Y.: A mean estimation of fuzzy numbers by evaluation measures. In: Negoita, M.G., Howlett, R.J., Jain, L.C. (eds.) KES 2004. LNCS, vol. 3214, pp. 1222–1229. Springer, Heidelberg (2004)

    Google Scholar 

  56. Garcia, F.A.A.: Fuzzy Real Option Valuation in a Power Station Reengineering Project Soft Computing with Industrial Applications. In: Proceedings of the Sixth Biannual World Automation Congress, pp. 281–287 (2004)

    Google Scholar 

  57. Collan, M.: Fuzzy Real Investment Valuation Model for Very Large Industrial Real Investments. In: Soft Computing with Industrial Applications - Proceedings of the Sixth Biannual World Automation Congress, pp. 379–384 (2004)

    Google Scholar 

  58. Spircu, L., Spircuin, T.: Fuzzy Treatment of American Call Options. In: Proceedings of the Tenth International Conference on Information Processing and Management of Uncertainty in Knowledge-based Systems IPMU 2004, Perugia, Italy, July 4-9, pp. 1841–1846 (2004)

    Google Scholar 

  59. Wang, X., Xu, W.-J., Zhang, W.-G.: A Class of Weighted Possibilistic Mean-Variance Portfolio Selection Problems. In: Proceedings of 2004 International Conference on Machine Learning and Cybernetics, vol. 4, pp. 2036–2040 (2004)

    Google Scholar 

  60. Wang, G.-X., Zhao, C.-H.: Characterization of Discrete Fuzzy Numbers and Application in Adaptive Filter Algorithm. In: Proceedings of 2004 International Conference on Machine Learning and Cybernetics, vol. 3, pp. 1850–1854 (2004)

    Google Scholar 

  61. Fang, Y., Lai, K.K., Wang, S.-Y.: A Fuzzy Approach to Portfolio Rebalancing with Transaction Costs. In: Sloot, P.M.A., Abramson, D., Bogdanov, A.V., Gorbachev, Y.E., Dongarra, J., Zomaya, A.Y. (eds.) ICCS 2003. LNCS, vol. 2658, pp. 10–19. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  62. Zhang, W.-G., Nie, Z.-K.: On Possibilistic Variance of Fuzzy Numbers. In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds.) RSFDGrC 2003. LNCS, vol. 2639, pp. 398–402. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  63. Dai, Z., Scott, M.J., Mourelatos, Z.P.: Incorporating Epistemic Uncertainty in Robust Design. In: Proceedings of the 2003 ASME Design Engineering Technical Conferences (DETC 2003), Chicago, Illinois, USA, September 2-6 (2003) (DAC-48713.pdf)

    Google Scholar 

  64. Peschland, G.M., Schweiger, H.F.: Reliability Analysis in Geotechnics with Finite Elements - Comparison of Probabilistic, Stochastic and Fuzzy Set Methods. In: Proceedings of the 3rd International Symposium on Imprecise Probabilities and Their Applications (ISIPTA 2003), Carleton Scientific Proceedings in Informatics, July 14–17, 2003, vol. 18, University of Lugano, Lugano (2003)

    Google Scholar 

  65. Zhang, W.-G., Zhang, Q.-M., Nie, Z.-K.: A Class of Fuzzy Portfolio Selection Problems. In: International Conference on Machine Learning and Cybernetics, vol. 5, pp. 2654–2658 (2003)

    Google Scholar 

  66. Daz-Hermida, F., Carinena, P., Bugarn, A., Barro, S.: Modelling of Task-oriented Vocabularies: An Example in Fuzzy Temporal Reasoning. In: IEEE International Conference on Fuzzy Systems, vol. 1, pp. 43–46 (2001)

    Google Scholar 

  67. Saeidifar, A., Pasha, E.: The Possibilistic Moments of Fuzzy Numbers and their Applications. Journal of Computational and Applied Mathematics 223, 1028–1042 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  68. Chrysas, K.A., Papadopoulos, B.K.: On Theoretical Pricing of Options with Fuzzy Estimators. Journal of Computational and Applied Mathematics 223, 552–566 (2009)

    Article  MathSciNet  Google Scholar 

  69. Thavaneswaran, A., Appadoo, S.S., Paseka, A.: Weighted Possibilistic Moments of Fuzzy Numbers with Applications to GARCH Modeling and Option Pricing. Mathematical and Computer Modelling 9, 352–368 (2009)

    Article  MathSciNet  Google Scholar 

  70. Gong, Y.-B.: Method for Fuzzy Multi-Attribute Decision Making with Preference on Alternatives and Partial Weights Information. Kongzhi yu Juece/Control and Decision 23, 507–510 (2008)

    MATH  Google Scholar 

  71. Beynon, M.J., Munday, M.: Considering the effects of imprecision and uncertainty in ecological footprint estimation: An approach in a fuzzy environment. Ecological Economics 67, 373–383 (2008)

    Article  Google Scholar 

  72. Liu, H., Brown, D.J., Coghill, G.M.: Fuzzy Qualitative Robot Kinematics. IEEE Transactions on Fuzzy Systems 16, 808–822 (2008)

    Article  Google Scholar 

  73. Huang, X.: Mean-Semivariance Models for Fuzzy Portfolio Selection. Journal of Computational and Applied Mathematics 217, 1–8 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  74. Appadoo, S.S., Bhatt, S.K., Bector, C.R.: Application of Possibility Theory to Investment Decisions. Fuzzy Optimization and Decision Making 7, 35–57 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  75. Lalla, M., Facchinetti, G., Mastroleo, G.: Vagueness Evaluation of the Crisp Output in a Fuzzy Inference System. Fuzzy Sets and Systems 159, 3297–3312 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  76. Cong, G.D., Zhang, J.L., Chen, T., Lai, K.K.: A Variable Precision Fuzzy Rough Group Decision-Making Model for IT Offshore Outsourcing Risk Evaluation. Journal of Global Information Management 16(2), 18–34 (2008)

    Google Scholar 

  77. Allahviranloo, T., Hosseinzadeh Lotfi, F., Kiasary, M.K., Kiani, N.A., Alizadeh, L.: Solving Fully Fuzzy Linear Programming Problem by the Ranking Function. Applied Mathematical Sciences 2(1), 19–32 (2008)

    MATH  MathSciNet  Google Scholar 

  78. Huang, X.: Risk Curve and Fuzzy Portfolio Selection. Computers and Mathematics With Applications 55, 1102–1112 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  79. Soleimani-damaneh, M.: Fuzzy Upper Bounds and their Applications. Chaos, Solitons And Fractals 36(2), 217–225 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  80. Zarandi, M.H.F., Pourakbar, M., Turksen, I.B.: A Fuzzy Agent-based Model for Reduction of Bullwhip Effect in Supply Chain Systems. Expert Systems With Applications 34(3), 1680–1691 (2008)

    Article  Google Scholar 

  81. Yoshida, Y.: A Risk-Sensitive Portfolio with Mean and Variance of Fuzzy Random Variables. In: Huang, D.-S., Wunsch II, D.C., Levine, D.S., Jo, K.-H. (eds.) ICIC 2008. LNCS, vol. 5227, pp. 358–366. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  82. Yanbing, G., Jiguo, Z.: A Method for Fuzzy Multi-Attribute Decision Making with Preference Information in the Form of Fuzzy Complementary Judgment Matrix. In: Proceedings of 5th International Conference on Fuzzy Systems and Knowledge Discovery, FSKD 2008, vol. 3, pp. 336–340 (2008) (art. no. 4666265)

    Google Scholar 

  83. Gong, Y., Zhang, J.: A new Method for Assessing the Weights of Fuzzy Opinions in Group Decision Environment. In: Proceedings of International Conference on Intelligent Computation Technology and Automation, ICICTA 2008, vol. 1, pp. 836–839 (2008) (art. no. 4659604)

    Google Scholar 

  84. Hsu, H.-W., Wang, H.-F.: Closed-Loop Green Supply Chain Logistics Model with Uncertain Reverse Parameters. In: 2008 International Conference on Wireless Communications, Networking and Mobile Computing, WiCOM 2008 (2008) (art. no. 4679358)

    Google Scholar 

  85. Yoshida, Y.: A Risk-Minimizing Portfolio Model with Fuzziness. In: IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2008), June 1-6, 2008, pp. 909–914 (2008)

    Google Scholar 

  86. Tupac, Y.J., Lazo, J.G., Faletti, L., Pacheco, M.A., Vellasco, M.M.B.R.: Decision Support System for Economic Analysis of E&P Projects under Uncertainties. In: Society of Petroleum Engineers - Intelligent Energy Conference and Exhibition: Intelligent Energy 2008, vol. 2, pp. 1115–1124 (2008)

    Google Scholar 

  87. Saeidifar, A., Pasha, E.: The Possibilistic Moments of Fuzzy Numbers and their Applications. Journal of Computational and Applied Mathematics 223, 1028–1042 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  88. Chen, C.-C., Tang, H.-C.: Degenerate Correlation and Information Energy of Interval-valued Fuzzy Numbers. International Journal of Information and Management Sciences 19, 119–130 (2008)

    MATH  MathSciNet  Google Scholar 

  89. Bede, B., Bhaskar, T.G., Lakshmikantham, V.: Perspectives of Fuzzy Initial Value Problems. Communications in Applied Analysis 11(3-4), 339–358 (2007)

    MATH  MathSciNet  Google Scholar 

  90. Hong, D.H., Kim, K.T.: A Maximal Variance Problem. Applied Mathematics Letters 20(10), 1088–1093 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  91. Mizukoshi, M.T., Barros, L.C., Chalco-Cano, Y., Roman-Flores, H., Bassanezi, R.C.: Fuzzy Differential Equations and the Extension Principle. Information Sciences 177(17), 3627–3635 (2007)

    Article  MATH  Google Scholar 

  92. Matia, F., Jimenez, A., Al-Hadithi, B.M., et al.: The Fuzzy Kalman Filter: State Estimation Using Possibilistic Techniques. Fuzzy Sets and Systems 157(16), 2145–2170 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  93. Liu, X.: On the Maximum Entropy Parameterized Interval Approximation of Fuzzy Numbers. Fuzzy Sets and Systems 157, 869–878 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  94. Ayala, G., Leon, T., Zapater, V.: Different Averages of a Fuzzy Set with an Application to Vessel Segmentation. IEEE Transactions on Fuzzy Systems 13(3), 384–393 (2005)

    Article  Google Scholar 

  95. Cheng, C.B.: Fuzzy Process Control: Construction of Control Charts with Fuzzy Numbers. Fuzzy Sets and Systems 154(2), 287–303 (2005)

    Article  MathSciNet  Google Scholar 

  96. Bodjanova, S.: Median Value and Median Interval of a Fuzzy Number. Information Sciences 172(1-2), 73–89 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  97. Hong, D.H., Kim, K.T.: A Note on Weighted Possibilistic Mean. Fuzzy Sets and Systems 148(2), 333–335 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  98. Wang, X., Xu, W., Zhang, W.-G., Hu, M.: Weighted Possibilistic Variance of Fuzzy Number and its Application in Portfolio Theory. In: Wang, L., Jin, Y. (eds.) FSKD 2005. LNCS (LNAI), vol. 3613, pp. 148–155. Springer, Heidelberg (2005)

    Google Scholar 

  99. Zhang, W.-G., Wang, Y.-L.: Portfolio Selection: Possibilistic Mean-Variance Model and Possibilistic Efficient Frontier. In: Megiddo, N., Xu, Y., Zhu, B. (eds.) AAIM 2005. LNCS, vol. 3521, pp. 203–213. Springer, Heidelberg (2005)

    Google Scholar 

  100. Zhang, J.-P., Li, S.-M.: Portfolio Selection with Quadratic Utility Function under Fuzzy Enviornment. In: 2005 International Conference on Machine Learning and Cybernetics, ICMLC 2005, pp. 2529–2533 (2005)

    Google Scholar 

  101. Blankenburg, B., Klusch, M.: BSCA-F: Efficient Fuzzy Valued Stable Coalition Forming Among Agents. In: Proceedings - 2005 IEEE/WIC/ACM International Conference on Intelligent Agent Technology, IAT 2005, pp. 732–738 (2005) (art. no. 1565632)

    Google Scholar 

  102. Garcia, F.A.A.: Fuzzy Real Option Valuation in a Power Station Reengineering Project Soft Computing with Industrial Applications. In: Proceedings of the Sixth Biannual World Automation Congress, pp. 281–287 (2004)

    Google Scholar 

  103. Wang, X., Xu, W.-J., Zhang, W.-G.: A Class of Weighted Possibilistic Mean-Variance Portfolio Selection Problems. In: Proceedings of 2004 International Conference on Machine Learning and Cybernetics, vol. 4, pp. 2036–2040 (2004)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IAMSR, Åbo Akademi University, Joukahaisenkatu 3-5, FIN-20520, Åbo, Finland

    Christer Carlsson & Robert Fullér

Authors
  1. Christer Carlsson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Robert Fullér
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. John von Neumann Fac. Informatics, Dept. Intelligent Engineering Systems, Budapest Tech., 1034, Budapest, Hungary

    Imre J. Rudas  & János Fodor  & 

  2. Systems Research Instiute, PAN Warszawa, Newelska 6, 01-447, Warszawa, Poland

    Janusz Kacprzyk

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Carlsson, C., Fullér, R. (2009). On Possibilistic Mean Value, Variance, Covariance and Correlation of Fuzzy Numbers. In: Rudas, I.J., Fodor, J., Kacprzyk, J. (eds) Towards Intelligent Engineering and Information Technology. Studies in Computational Intelligence, vol 243. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03737-5_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-03737-5_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03736-8

  • Online ISBN: 978-3-642-03737-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation