jzs-10870

Cut Set Theorems for Rectangular 𝑳-fuzzy Complex Numbers and 𝑳-multi-fuzzy Complex Numbers

Pishtiwan O. Sabir1*&Aram N. Qadir2 

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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