Volume 27 , Issue 2 , PP: 287-296, 2026 | Cite this article as | XML | Html | PDF | Full Length Article
K. Meenakshi 1 * , Pavithra S. 2 , S. Sathish 3 , Prabakaran N. 4
Doi: https://doi.org/10.54216/IJNS.270224
This article defines the central tendency fuzzy measures, which include the weighted fuzzy possiblistic mean and the fuzzy probability mean involving octagonal fuzzy numbers. The same is supported by a fuzzy variant of the Black-Scholes option model, in which uncertain pricing parameters such as volatility, interest rate, and stock price are described using octagonal fuzzy numbers.
Weighted fuzzy possiblistic mean , Interval-valued fuzzy expectation , Octagonal fuzzy numbers , Black-Scholes variant fuzzy option model
[1] Andres-Sanchez, J. D., An Empirical Assessment of Fuzzy Black and Scholes Pricing Option Model in Spanish Stock Option Market. Journal of Intelligent and Fuzzy Systems 33, (2017) 2509-2521.DOI:
[2] C. Carlsson, R. Fuller, On possibilistic mean and variance of fuzzy numbers, Fuzzy Sets and Systems122, (2001), 315–326.
[3] Cheng-Few Lee, Gwo-Hshiung Tzeng, Shin-Yun Wang, A new application of fuzzy set theory to the Black–Scholes option pricing model, Expert Systems with Applications Vol. 29, 2 (2005) 330-342.
[4] U. Cherubini, Fuzzy measures and asset prices: Accounting for information ambiguity, Applied Mathematical Finance 4, (1997), 135-149.
[5] Konstantinos A. Chrysafis, Basil K. Papadopoulos, On theoretical pricing of options with fuzzy estimators, Journal of Computational and Applied Mathematics 223(2), (2009), 552-566.
[6] F. Black, M. Scholes, The pricing of options and corporate liabilities, Journal of Political Economy 81, (1973), 637–659.
[7] K.R. French, Stock returns and the weekend effect, Journal of Financial Economics 8, (1980), 55–69.
[8] R. Fuller, P. Majlender, On weighted possibilistic mean and variance of fuzzy numbers, Fuzzy Sets and Systems 136, (2003), 363–374.
[9] H. Ghaziri, S. Elfakhani, J. Assi, Neural networks approach to pricing options, Neural Network World10, C(2000), 271–277..
[10] M.L. Guerra, L. Sorini, L. Stefanini, Option price sensitivities through fuzzy numbers, Computers and Mathematics with Applications 61(3), (2011), 515–526.
[11] S. Heilpern, The expected value of a fuzzy number, Fuzzy Sets and Systems 47, (1992), 81–86.
[12] S.L. Heston, A closed-form solution for options with stochastic volatility with applications to bond and currency options, Review of financial studies 6(2), (1993), 327–343.
[13] M. Jimenez and J.A. Rivas, Fuzzy number approximation, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 6(01), (1998), 69–78.
[14] J.D. MacBeth and L.J. Merville, An empirical examination of the Black-Scholes call option pricing model The Journal of Finance 34(5), (1979), 1173–1186.
[15] L. Maciel, F. Gomide, and R. Ballini, Evolving fuzzy- GARCH pproach for financial volatility modeling and forecasting, Computational Economics 48(3), (2016), 379–398.
[16] Malini, S. SU, Felbin C. Kennedy, An approach for solving fuzzy transportation problem using octagonal fuzzy numbers, Applied Mathematical Sciences 54, (2013), 2661-2673.
[17] Maria Letizia Guerra, Laerte Sorini, Luciano Stefanini, Option price sensitivities through fuzzy numbers, Computers and Mathematics with Applications Volume 61, Issue 3, (2011), 515-526.
[18] S. Mixon, The implied volatility term structure of stock index options, Journal of Empirical Finance14(3), (2007), 333–354.
[19] S. Muzzioli and B. De Baets, Fuzzy approaches to option price modeling, IEEE Transactions on Fuzzy Systems 25(2), (2017), 392–401.
[20] H.T. Nguyen, A note on the extension principle for fuzzy sets, Journal of Mathematical Analysis and Applications 64, (1978), 369–380.
[21] P. Nowak and M. Romaniuk, A fuzzy approach to option pricing in a Levy process setting, International Journal of Applied Mathematics and Computer Science 23(3), (2013), 613–622.
[22] M.R. Simonelli, Fuzziness in valuing financial instruments by certainty equivalents, European Journal of Operational Research, 135, (2001) 296–302.
[23] A. Thavanaeswaran, J. Singh, S.S. Appadoo, Option pricing for some volatility models, The Journal of Risk Finance 7 (2006) 425–445.
[24] A. Thavaneswaran, S.S. Appadoo, A. Paseka, Weighted possibilistic moments of fuzzy numbers with applications to GARCH modeling and option pricing, Mathematical and Computer Modelling 49 (1–2), (2009), 352–368.
[25] K. Thiagarajah, S.S. Appadoo, A. Thavaneswaran, Option valuation model with adaptive fuzzy numbers, Computers and Mathematics with Applications Vol. 53, 5 (2007), 831–841.
[26] K. Thiagarajah, A. Thavanaeswaran, Fuzzy random coefficient volatility models with financial applications, Journal of Risk Finance 7 (2006), 503–524.
[27] N.N. Trenev, A refinement of the Black-Scholes formula of pricing options, Cybernetics and Systems Analysis 37, (2001), 911-917.
[28] H.C. Wu, Using fuzzy sets theory and Black–Scholes formula to generate pricing boundaries of European options, Applied Mathematics and Computation 185, (2007), 136–146.
[29] Y. Yoshida, The valuation of European options in uncertain environment, European Journal of Operational Research 145, (2003), 221–229.
[30] Z. Zmeskal, Applications of the fuzzy-stochastic methodology to appraising the firm value as a European call option, European Journal of Operational Research 135, (2001), 303-310.