On Fuzzy Soft (n, m) Binormal Operator
Department of Mathematical Sciences, College of Education for Pure Sciences, University of Thi-Qar, Nasiriyah 64001, Iraq.
Research Article
Open Access Research Journal of Science and Technology, 2026, 16(02), 024-031.
Article DOI: 10.53022/oarjst.2026.16.2.0026
Publication history:
Received on 27 January 2026; revised on 06 March 2026; accepted on 06 March 2026
Abstract:
A new type of operators in fuzzy soft Hilbert spaces is presented and explored in this paper, which is the fuzzy soft (n,m) binormal operator. Expanding the classical concept of binormal operators to the principles of the fuzzy soft sets, we determine the essential nature of this type of operators and investigate the main characteristics of the operators. A number of theorems that explain the structural property of fuzzy soft (n,m) binormal operators are demonstrated such as a result on adjoint operators, scalar multiplication, and commutativity. In addition, we discuss the interrelationships amongst this new defined operator with other already existing classes of fuzzy soft linear operators, specifically fuzzy soft self-adjoint operator and fuzzy soft normal operator. It is proved that the (n,m) binormal property of operator products, direct sums and the tensor products, when applied under the right conditions of commuting, as well as preserving the property. The study is part of the current advancement of the operator theory in fuzzy soft mathematical framework, offering the fundamental outcomes to the continued research in the fuzzy soft functional analysis.
Keywords:
Fuzzy Soft Sets; Fuzzy Soft Hilbert Space; Fuzzy Soft Linear Operator; Fuzzy Soft Binormal Operator
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