Sudad M. Rasheed

Faculty of Physical and Basic Education-School of Basic Education, University of Sulaimani, Sulaimani, Iraq

DOI: https://doi.org/10.17656/jzs.10601

In this work, we focus our study on adjoint Fuzzy linear operator and self-adjoint Fuzzy linear operator acting on a Fuzzy Hilbert space (FH-Space). We have given several definitions, theorems and discuss in details, The properties of the adjoint and self-adjoint Fuzzy operators in a FH-adjoint Fuzzy operators in a FH-space.

[1] A. K. Katsaras "Fuzzy topological vector space-II", Fuzzy Sets and Systems, Vol. 12, pp. 143-154. (1984).

[2] B. Punnose and S. Kuriakose, "Fuzzy inner product space- A New Approach", J. of Fuzzy Math. Vol.14 No.2, pp. 273-282. (2006).

[3] C. Felbin "Finite dimensional Fuzzy normed linear space", Fuzzy Sets and Systems. Vol. 48, pp. 239-248. (1992).

[4] J.K.Kohil and R.Kumar "Linear mappings, Fuzzy linear spaces, Fuzzy inner product spaces and Fuzzy Co-inner product space", Bull Calcutta Math. Soc., Vol. 87, pp. 237-246. (1995).

[5] J.K.Kohil and R.Kumar, "On Fuzzy Inner Product Spaces and Fuzzy Co-Inner Product Space, Fuzzy sets and system", Bull Calcutta Math. Soc., Vol. 53, pp. 227-232. (1993).

[6] M. Goudarzi and S.M. Vaezpour, "On the definition of Fuzzy Hilbert spaces and it’s Application", J. Nonlinear Sci. Appl. Vol. 2, No. 1, pp. 46-59. (2009).

[7] P. Majundarand and S.K. Samanta "On fuzzy inner product spaces", J. Fuzzy Math. Vol. 16, No. 2, pp. 377-392. (2008).

[8] R.Biswas, "Fuzzy inner product spaces & Fuzzy norm functions", Information Sciences Vol. 53, pp. 185-190. (1991).

[9] R. Saadati and S,M. Vaezpoor, "Some results on fuzzy Banach spaces", J. appl. Math. and computing, Vol 17, Issue 1, pp 475-488. (2005).

[10] S.C. Cheng, J.N.Mordeson, "Fuzzy linear operators and Fuzzy normed linear spaces", Bull. Cal. Math. Soc. Vol. 86, pp. 429-436. (1994).

[11] T. Bag. S. K. Samanta, "Operators Fuzzy Norm and some properties Fuzzy", Inf. Eng. Vol. 7, pp. 151-164. (2015).

[12] Yongfu su. "Riesz Theorem in probabilistic inner prodict spaces" , Inter. Math. Forum, Vol. 2, No. 62, pp. 3073-3078. (2007).

Faculty of Physical and Basic Education-School of Basic Education, University of Sulaimani, Sulaimani, Iraq

DOI: https://doi.org/10.17656/jzs.10601

**Abstract**In this work, we focus our study on adjoint Fuzzy linear operator and self-adjoint Fuzzy linear operator acting on a Fuzzy Hilbert space (FH-Space). We have given several definitions, theorems and discuss in details, The properties of the adjoint and self-adjoint Fuzzy operators in a FH-adjoint Fuzzy operators in a FH-space.

**Key Words**: adjoint Fuzzy operators, self-adjoint Fuzzy operator, FH-space, FIP-space.**References**

[1] A. K. Katsaras "Fuzzy topological vector space-II", Fuzzy Sets and Systems, Vol. 12, pp. 143-154. (1984).

[2] B. Punnose and S. Kuriakose, "Fuzzy inner product space- A New Approach", J. of Fuzzy Math. Vol.14 No.2, pp. 273-282. (2006).

[3] C. Felbin "Finite dimensional Fuzzy normed linear space", Fuzzy Sets and Systems. Vol. 48, pp. 239-248. (1992).

[4] J.K.Kohil and R.Kumar "Linear mappings, Fuzzy linear spaces, Fuzzy inner product spaces and Fuzzy Co-inner product space", Bull Calcutta Math. Soc., Vol. 87, pp. 237-246. (1995).

[5] J.K.Kohil and R.Kumar, "On Fuzzy Inner Product Spaces and Fuzzy Co-Inner Product Space, Fuzzy sets and system", Bull Calcutta Math. Soc., Vol. 53, pp. 227-232. (1993).

[6] M. Goudarzi and S.M. Vaezpour, "On the definition of Fuzzy Hilbert spaces and it’s Application", J. Nonlinear Sci. Appl. Vol. 2, No. 1, pp. 46-59. (2009).

[7] P. Majundarand and S.K. Samanta "On fuzzy inner product spaces", J. Fuzzy Math. Vol. 16, No. 2, pp. 377-392. (2008).

[8] R.Biswas, "Fuzzy inner product spaces & Fuzzy norm functions", Information Sciences Vol. 53, pp. 185-190. (1991).

[9] R. Saadati and S,M. Vaezpoor, "Some results on fuzzy Banach spaces", J. appl. Math. and computing, Vol 17, Issue 1, pp 475-488. (2005).

[10] S.C. Cheng, J.N.Mordeson, "Fuzzy linear operators and Fuzzy normed linear spaces", Bull. Cal. Math. Soc. Vol. 86, pp. 429-436. (1994).

[11] T. Bag. S. K. Samanta, "Operators Fuzzy Norm and some properties Fuzzy", Inf. Eng. Vol. 7, pp. 151-164. (2015).

[12] Yongfu su. "Riesz Theorem in probabilistic inner prodict spaces" , Inter. Math. Forum, Vol. 2, No. 62, pp. 3073-3078. (2007).