Fuzzy a-Ideals of Product Operator on Bounded Fuzzy Lattices

2013 ◽  
Author(s):  
Ivan Mezzomo ◽  
Benjamin Bedregal ◽  
Regivan H.N. Santiago ◽  
Renata H.S. Reiser
Keyword(s):  
Product Operator

Influence of different fuzzy operators on analytical structure and variable gains of typical interval type-2 fuzzy PI controller

2020 ◽  
Vol 39 (3) ◽  
pp. 4319-4329
Author(s):  
Haibo Zhou ◽  
Chaolong Zhang ◽  
Shuaixia Tan ◽  
Yu Dai ◽  
Ji’an Duan ◽  
...  
Keyword(s):  
Pi Controller ◽  
Real Time Control ◽  
Fuzzy Operators ◽  
Fuzzy Operator ◽  
Analytical Structure ◽  
Product Operator ◽  
Pi Controllers ◽  
Fuzzy Pi Controller ◽  
Interval Type

The fuzzy operator is one of the most important elements affecting the control performance of interval type-2 (IT2) fuzzy proportional-integral (PI) controllers. At present, the most popular fuzzy operators are product fuzzy operator and min() operator. However, the influence of these two different types of fuzzy operators on the IT2 fuzzy PI controllers is not clear. In this research, by studying the derived analytical structure of an IT2 fuzzy PI controller using typical configurations, it is proved mathematically that the variable gains, i.e., proportional and integral gains of typical IT2 fuzzy PI controllers using the min() operator are smaller than those using the product operator. Moreover, the study highlights that unlike the controllers based on the product operator, the controllers based on the min() operator have a simple analytical structure but provide more control laws. Real-time control experiments on a linear motor validate the theoretical results.

CONSTRUCTION AND APPLICATION OF FOUR-QUBIT SWAP LOGIC GATE IN NMR QUANTUM COMPUTING

2011 ◽  
Vol 09 (02) ◽  
pp. 779-790 ◽  
Author(s):  
A. GÜN ◽  
I. ŞAKA ◽  
A. GENÇTEN
Keyword(s):  
Quantum Computing ◽  
Spin System ◽  
Matrix Representation ◽  
Pulse Sequence ◽  
Logic Gate ◽  
Logic Gates ◽  
Unitary Matrices ◽  
Quantum Logic Gates ◽  
Product Operator ◽  
The Matrix

In NMR quantum computing, spin states of spin-1/2 nuclei are called qubits. Quantum logic gates are represented by unitary matrices. As a universal gate, controlled-NOT (CNOT) is a two-qubit gate. For the IS (I = 1/2 and S = 1/2) spin system, two-qubit CNOT gate is represented by a 4 × 4 matrix. SWAP logic gate, which exchanges two quantum states, is constructed by CNOT gates. In this study, first, four-qubit CNOT gates are constructed for the IS (I = 3/2, S = 3/2) spin system. Then, by using these CNOT gates, a four-qubit SWAP logic gate is found. As an application and verification, an obtained SWAP logic gate is applied to the matrix representation of product operators for the IS (I = 3/2, S = 3/2) spin system. SWAP logic gate can also be presented by an NMR pulse sequence. By using the product operator theory, the pulse sequence of the SWAP logic gate is applied to product operators of the IS (I = 3/2, S = 3/2) spin system. The expected exchange results are obtained for both the matrix representation and the pulse sequence of SWAP logic gate.

scholarly journals Anyons and matrix product operator algebras

2017 ◽  
Vol 378 ◽  
pp. 183-233 ◽  
Author(s):  
N. Bultinck ◽  
M. Mariën ◽  
D.J. Williamson ◽  
M.B. Şahinoğlu ◽  
J. Haegeman ◽  
...  
Keyword(s):  
Operator Algebras ◽  
Matrix Product ◽  
Product Operator
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