Cut Set Theorems for Rectangular 𝑳-fuzzy Complex
Numbers and 𝑳-multi-fuzzy Complex Numbers
Pishtiwan O. Sabir1*&Aram N. Qadir2
Abstract
References
1 Department of Mathematics, College of Science, University of Sulaimani, Sulaimani, Iraq
2 Department of Mathematics, College of Education, University of Garmian, Kalar, Iraq
*Corresponding author Email: pishtiwan.sabir@univsul.edu.iq
Abstract
In this paper, the properties of the lower cut set and the upper cut set of
rectangular 𝐿-fuzzy complex numbers are studied and it is showed that the (ℓ)-
upper cut and [ℓ]-upper cut on this type of fuzzy numbers are satisfied under 𝛽
and 𝛼 preserving mapping, respectively. The inclusion properties on the set of
cut set types are proved and some decompositions of this type of number and its
characterizations are discussed. The basic arithmetic operations between
rectangular 𝐿-fuzzy complex numbers are introduced and some representations
of them are obtained. Furthermore, the notions of rectangular 𝐿-multi-fuzzy
complex numbers are demonstrated and some fundamental theorems and rules
were presented for calculating binary operations between them. Some modulus
and inequalities on the set of 𝐿-multi-fuzzy quantities are derived.
Key Words:
Cut set, 𝐿-fuzzy set, 𝐿-
fuzzy number, 𝐿-fuzzy
complex number, 𝐿-
multi-fuzzy complex
number.
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