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Keywords:
fuzzy numbers; Hukuhara difference; random variables; second-order fuzzy stochastic processes; mean-square calculus
Summary:
The purpose of this paper is to generalize and develop a mean-square calculus for fuzzy stochastic processes and study their differentiability and integrability properties. Some results for second-order fuzzy stochastic processes are presented.
References:
[1] Anastassiou, G., Gal, G. S.: On a fuzzy trigonometric approximation theorem of Weierstrass-type. J. Fuzzy Math. (2001), 701-708. MR 1859551
[2] Bede, B., Gal, S. G.: Almost periodic fuzzy-number-valued functions. Fuzzy Sets Syst. 147 (2004), 3, 385-403. DOI  | MR 2100833
[3] Bede, B., Gal, S. G.: Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations. Fuzzy Sets Syst. 151 (2005), 3, 581-599. DOI  | MR 2126175
[4] Bede, B., Rudas, I. J., Bencsik, A. L.: First order linear fuzzy differential equations under generalized differentiability. Inform. Sci. 177 (2007), 7, 1648-1662. DOI  | MR 2303177
[5] Chalco-Cano, Y., Maqui-Huamán, G. G., Silva, G., Jimenez-Gamero, M.: Algebra of generalized hukuhara differentiable interval-valued functions: Review and new properties. Fuzzy Sets Syst. 375 (2019), 53-69. DOI  | MR 3999369
[6] Dubois, D., Prade, H.: Towards fuzzy differential calculus. Part 3: Differentiation. Fuzzy Sets Syst. 8 (1982), 3, 225-233. DOI  | MR 0669414
[7] Feng, Y.: Mean-square integral and differential of fuzzy stochastic processes. Fuzzy Sets Syst. 102 (1999), 2, 271-280. DOI  | MR 1674963
[8] Feng, Y.: Convergence theorems for fuzzy random variables and fuzzy martingales. Fuzzy Sets Syst. 103 (1999), 3, 435-441. DOI  | MR 1669281 | Zbl 0939.60027
[9] Feng, Y.: Mean-square Riemann-Stieltjes integrals of fuzzy stochastic processes and their applications. Fuzzy Sets Syst. 110 (2000), 1, 27-41. DOI  | MR 1748106
[10] Feng, Y.: Fuzzy stochastic differential systems. Fuzzy Sets Syst. 115 (2000), 3, 351-363. DOI  | MR 1781454
[11] Feng, Y., Hu, L., Shu, H.: The variance and covariance of fuzzy random variables and their applications. Fuzzy Sets Systems 120 (2001), 3, 487-497. DOI  | MR 1829266 | Zbl 0984.60029
[12] Friedman, M., Ma, M., Kandel, A.: Fuzzy derivatives and fuzzy Cauchy problems using LP metric. In: Fuzzy Logic Foundations and Industrial Applications (D. Ruan, ed.), Springer, Boston 1996, pp. 57-72.
[13] Gasilov, N.: On exact solutions of a class of interval boundary value problems. Kybernetika 58 (2022), 376-399. DOI  | MR 4494097
[14] Gasilov, N., Amrahov, S. Emrah, Fatullayev, A. Golayoglu: Solution of linear differential equations with fuzzy boundary values. Fuzzy Sets Syst. 257 (2014), 169-183. DOI  | MR 3267136
[15] Gopal, D., Moreno, J. M., López, R. R.: Asymptotic fuzzy contractive mappings in fuzzy metric spaces. Kybernetika 60 (2024), 394-411. DOI  | MR 4777315
[16] Goetschel, R., Voxman, W.: Elementary fuzzy calculus. Fuzzy Sets Syst. 18 (1986), 1, 31-43. DOI  | MR 0825618 | Zbl 0626.26014
[17] Kaleva, O.: On the convergence of fuzzy sets. Fuzzy Sets Syst. 17 (1985), 1, 53-65. DOI  | MR 0808463 | Zbl 0584.54004
[18] Kaleva, O.: Fuzzy differential equations. Fuzzy Sets Syst. 24 (1987), 3, 301-317. DOI  | MR 0919058 | Zbl 1100.34500
[19] Kratschmer, V.: Limit theorems for fuzzy-random variables. Fuzzy Sets Syst. 126 (2002), 2, 253-263. DOI  | MR 1884692
[20] Malinowski, M. T.: Some properties of strong solutions to stochastic fuzzy differential equations. Inform. Sci. 252 (2013), 62-80. DOI  | MR 3123920
[21] Mazandarani, M., Xiu, L.: A review on fuzzy differential equations. IEEE Access 9 (2021), 62195-62211. DOI 
[22] Ming, M.: On embedding problems of fuzzy number space: Part 5. Fuzzy Sets Syst. 55 (1993), 3, 313-318. DOI  | MR 1223869
[23] Nguyen, H. T.: A note on the extension principle for fuzzy sets. J. Math. Anal. Appl. 64 (1978), 2, 369-380. DOI  | MR 0480044 | Zbl 0377.04004
[24] Puri, M. L., Ralescu, D. A.: Differentials of fuzzy functions. J. Math. Anal. Appl. 91 (1983), 2, 552-558. DOI  | MR 0690888
[25] Puri, M. L., Ralescu, D. A.: Fuzzy random variables. J. Math. Anal. Appl. 114 (1986), 2, 409-422. DOI  | MR 0833596 | Zbl 0605.60038
[26] Puri, M. L., Ralescu, D. A.: Convergence theorem for fuzzy martingales. J. Math. Anal. Appl. 160 (1991), 1, 107-122. DOI 10.1016/0022-247X(91)90293-9 | MR 1124080 | Zbl 0737.60005
[27] Rojas-Medar, M., Jimenez-Gamero, M., Chalco-Cano, Y., Viera-Brandao, A.: Fuzzy quasilinear spaces and applications. Fuzzy Sets Syst. 152 (2005), 2, 173-190. DOI  | MR 2138505
[28] Seikkala, S.: On the fuzzy initial value problem. Fuzzy Sets Syst. 24 (1987), 3, 319-330. DOI  | MR 0919059
[29] Stefanini, L., Bede, B.: Generalized hukuhara differentiability of interval-valued functions and interval differential equations. Nonlinear Analysis: Theory Methods Appl. 71 (2009), 3, 1311-1328. DOI  | MR 2527548
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