SOME FUNDAMENTAL RESULTS ON FUZZY CALCULUS

[1] S. Abbasbandy and B. Asady, Ranking of fuzzy numbers by sign distance, Information Sciences,
176 ( 2006), 2405–2416.
[2] S. Abbasbandy and S. Hajighasemi, A Fuzzy Distance between Two Fuzzy Numbers, Communications
in Computer and Information Science, 81 (2010), 376–382.
[3] T. Allahviranloo, S. Abbasbandy and S. Hajighasemi, A new similarity measure for generalized
fuzzy numbers, Neural Computing and Applications, 21 (2012), 289–294.
[4] T. Allahviranloo, A. Armand and Z. Gouyandeh, Fuzzy fractional differential equations under
generalized fuzzy Caputo derivative, Journal of Intelligent and Fuzzy Systems, 26 (2014),
1481–1490.
[5] T. Allahviranloo, A. Armand, Z. Gouyandeh and H. Ghadiri, Existence and uniqueness of
solutions for fuzzy fractional Volterra–Fredholm integro–differential equations, Journal of
Fuzzy Set Valued Analysis, 2013 (2013), 1–9.
[6] A. Armand and Z. Gouyandeh, Solving two–point fuzzy boundary value problem using variational
iteration method, Communications on Advanced Computational Science with Applications,
2013 (2013), 1–10.
[7] G. A. Anastassiou, Fuzzy Mathematics:Approximation Theory, Studies in Fuzziness and Soft
Computing, Springer–Verlag Berlin Heidelberg,2010.
[8] R. J. Aumann, Integrals of set–valued functions, Journal of Mathematical Analysis and Applications,
12 (1965), 1–12.
[9] B. Bede, I. J. Rudas and A. L. Bencsik, First order linear fuzzy differential equations under
generalized differentiability, Information Sciences, 177 (2007), 1648–1662.
[10] B. Bede and S. Gal, Generalizations of the differentiability of fuzzy number valued functions
with applications to fuzzy differential equations, Fuzzy Sets and Systems, 151 ( 2005), 581–
599.
[11] B. Bede and L. Stefanini, Generalized differentiability of fuzzy–valued functions, Fuzzy Sets
and Systems, 230 (2013), 119–141.
[12] Y. Chalco-Canoa, A. Rufi´an-Lizanab, H. Rom´an–Floresa and M. D. Jim´enez-Gameroa, Calculus
for interval–valued functions using generalized Hukuhara derivative and applications,
Fuzzy Sets and Systems, 219 (2013), 49–67.
[13] L. H. Chen and H. W. Lu, The preference order of fuzzy numbers, Computers and Mathematics
with Applications, 44 (2002), 1455–1465.
[14] A. Chwastyk and W. Kosiski, Fuzzy calculus with aplications, Mathematica applicanda, 41
(2013), 47–96.
[15] W. Congxin and M. Ming, On embedding problem of fuzzy number space: part 3, Fuzzy Sets
and Systems, 16 (1992), 281–286.
[16] D. Dubois and H. Prade, Towards fuzzy differential calculus–part 1, Fuzzy Sets and Systems,
8 (1982), 1–17.
[17] D. Dubois and H. Prade, Towards fuzzy differential calculus–part 2, Fuzzy Sets and Systems,
8 (1982), 105–116.
[18] D. Dubois and H. Prade, Towards fuzzy differential calculus–part 3, Fuzzy Sets and Systems,
8 (1982), 225–234.
[19] D. Dubois and H. Prade, Operations on fuzzy numbers, International Journal of Systems
Science, 9 (1978), 613–626.

[20] Z. Gouyandeh, T. Allahviranloo, S. Abbasbandy and A. Armand, A fuzzy solution of heat
equation under generalized Hukuhara differentiability by fuzzy Fourier transform, Fuzzy Sets
and Systems, 309 (2017), 81–97.
[21] M. Hukuhara, Int´egration des applications mesurables dont la valeur est un compact convexe,
Funkcialaj Ekvacioj, 10 (1967), 205–229.
[22] R. Jain, Decision making in the presence of fuzzy variables, IEEE Trans. Systems Man
Cybernetics, 6 (1976), 698–703.
[23] O. Kaleva, Fuzzy differential equations, Fuzzy Sets and Systems, 24 (1987), 301–317.
[24] O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems, 12 (1984),
215–229.
[25] A. Khastan and J. J. Nieto, A boundary value problem for second order fuzzy differential
equations, Nonlinear Analysis, 72 (2010), 3583–3593.
[26] V. Lakshmikantham and R. N. Mohapatra, Theory of fuzzy differential equations and inclusions,
Taylor and Francis, 2003.
[27] V. Lakshmikantham, T. GnanaBhaskar and J. VasundharaDevi, Theory of Set Differential
Equations in Metric Spaces, Cambridge Scientific Publishers, 2006.
[28] X. W. Liu and S. L. Han, Ranking fuzzy numbers with preference weighting function expectations,
Computers and Mathematics with Applicatmns, 49 (2005), 1731–1753.
[29] M. Ma, M. Friedman and A. Kandel, Numerical solutions of fuzzy differential equations,
Fuzzy Sets and Systems, 105 (1999), 133–138.
[30] M. Mizumoto and K. Tanaka, The four operations of arithmetic on fuzzy numbers, Systems
Computers Controls, 7 (1976), 73–81.
[31] D. Mon, C. Cheng and J. Lin, Evaluating weapon system using fuzzy analytic hierarchy
process based on entropy weight, Fuzzy Sets and Systems, 62 (1994), 127–134.
[32] C. V. Negoita and D. Ralescu, Applications of Fuzzy Sets to Systems Analysis, Wiley, New
York, 1975.
[33] M. L. Puri and D. A. Ralescu, Differentials of fuzzy functions, Journal of Mathematical
Analysis and Applications, 114 (1986), 409–422.
[34] L. Stefanini, A generalization of Hukuhara difference and division for interval and fuzzy
arithmetic, Fuzzy Sets and Systems, 161 (2010), 1564–1584.
[35] L. Stefanini and B. Bede, Generalized Hukuhara differentiability of interval–valued functions
and interval differential equations, Nonlinear Analysis, 71 (2009), 1311–1328.
[36] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338–353.