# ON THE PETTIS INTEGRAL OF FUZZY MAPPINGS IN BANACH SPACES

Park, Chun-Kee

• Published : 2007.10.31
• 42 6

#### Abstract

In this paper, we introduce the Pettis integral of fuzzy mappings in Banach spaces using the Pettis integral of closed set-valued mappings. We investigate the relations between the Pettis integral, weak integral and integral of fuzzy mappings in Banach spaces and obtain some properties of the Pettis integral of fuzzy mappings in Banach spaces.

#### Keywords

Pettis integral of closed set-valued mappings;weak integral;integral and Pettis integral of fuzzy mappings in Banach spaces

#### References

1. K. Amri and C. Hess, On the Pettis integral of closed valued multifunctions, Set-Valued Analysis 8 (2000), 329-360 https://doi.org/10.1023/A:1026547222209
2. R. J. Aumann, Integrals of set-valued functions, J. Math. Anal. Appl. 12 (1965), 1-12 https://doi.org/10.1016/0022-247X(65)90049-1
3. O. Kaleva, Fuzzy differential equations, Fuzzy Sets and Systems 24 (1987), 301-317 https://doi.org/10.1016/0165-0114(87)90029-7
4. N. Papageoriou, On the theory of Banach space valued multifunctions, J. Multivariate Anal. 17 (1985), 185-206 https://doi.org/10.1016/0047-259X(85)90078-8
5. J. Wu and C. Wu, The w-derivatives of fuzzy mappings in Banach spaces, Fuzzy Sets and Systems 119 (2001), 375-381 https://doi.org/10.1016/S0165-0114(98)00468-0
6. X. Xiaoping, H. Minghu, and M. Ming, Random fuzzy number integrals in Banach spaces, Fuzzy Sets and Systems 66 (1994), 97-111 https://doi.org/10.1016/0165-0114(94)90303-4
7. X. Xiaoping, X. Wang, and L. Wu On the convergence and representation of random fuzzy number integrals, Fuzzy Sets and Systems 103 (1999), 115-125 https://doi.org/10.1016/S0165-0114(97)00150-4
8. W. Z. Wu, W. X. Zhang, and R. M. Wang, Set valued Bartle integrals, J. Math. Anal. Appl. 255 (2001), 1-20 https://doi.org/10.1006/jmaa.2000.6976