Correlations from conjugate and dual intuitionistic fuzzy triangular norms and conorms

Reiser, Renata; Visintin, Lidiane; Benitez, Ibero; Bedregal, Benjamín R. C.

doi:10.1109/ifsa-nafips.2013.6608605

Cited by 8 publications

(2 citation statements)

References 9 publications

(15 reference statements)

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“…An A-IFS considers the informations of these degrees and also providing the hesitation (uncertainty) margin related to the Atanassov's intuitionistic fuzzy index (A-IFIx), as reported by approach. This approach leads to a great numbers of studies, all of them are closely connected with the correlation coefficient (A-CC) [Reiser et al 2013, Bertei et al 2016, Bertei and Reiser 2018, Bertei et al 2021] between two intuitionistic fuzzy sets, mainly those applied to processes of decision-making, such as clustering analysis [Meng et al 2016], digital image processing and medical diagnosis [Bertei and Reiser 2019].…”

Section: Introductionmentioning

confidence: 99%

An Application for Medical Diagnosis Using Correlation Coefficient With Modal Operators and Operator Identifying and Unary

Bertei

Reiser

Foss

2021

Anais Do VI Workshop-Escola De Informática Teórica (WEIT 2021)

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This paper aims to study the Atanassov's correlation coefficient (A-CC) between two of Atanassov's intuitionistic fuzzy sets (A-IFS), obtained as images of intuitionistic fuzzy modal operators. The composition of modal operators are investigated, verifying under which conditions an A-CC preserves the main properties related to conjugate and complement operations performed on A-IFS. In addition, a simulation based on the proposal methodology using operators described above is applied to a medical diagnosis analysis.

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Section: Introductionmentioning

confidence: 99%

An Application for Medical Diagnosis Using Correlation Coefficient With Modal Operators and Operator Identifying and Unary

Bertei

Reiser

Foss

2021

Anais Do VI Workshop-Escola De Informática Teórica (WEIT 2021)

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“…In our previous work [1,2], it is shown that the conjugate of an interval-valued Atanassov's intuitionistic fuzzy negation not only preserves the main properties of its corresponding fuzzy negation but also of two other ones, the intuitionistic fuzzy negation and intervalvalued fuzzy negation. Moreover, we introduce an extension of the intuitionistic fuzzy index as well as study basic concepts related to the correlation index in the sense of [3], 2 which are discussed in terms of fuzzy connectives, by considering the Atanassov's Intuitionistic Fuzzy Logic.…”

Section: Introductionmentioning

confidence: 99%

Correlation Analysis of Intuitionistic Fuzzy Connectives

Bertei¹,

Zanotelli²,

Cardoso³

et al. 2017

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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Quantum computing simulation through reduction and decomposition optimizations with a case study of Shor's algorithm

Ávila

Reiser

Pilla

2016

Concurrency and Computation

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Because of the expansion of transformations and read/write memory states by tensor products in multidimensional quantum applications, the exponential increase in temporal and spatial complexities constitutes one of the main challenges for quantum computing simulations. Simulation of these systems is very relevant to develop and test new quantum algorithms. In order to overcome the increase in simulation complexity, this work presents reduction and decomposition optimizations for the Distributed Geometric Machine environment. By exploring properties as the sparsity of the Identity operator and partiality of dense unitary transformations, better storage and distribution of quantum information are achieved. The main improvements are reached by decreasing replication and void elements inherited from quantum operators. In the evaluation of this proposal, Hadamard transformations from 21 to 28 qubits and Quantum Fourier Transforms from 26 to 28 qubits were simulated over CPU, sequentially and in parallel, and in graphics processing unit, showing reduced temporal complexity and, consequently, shorter simulation time. Moreover, evaluations of the Shor's algorithm considering 2n C 3 qubits in the order-finding quantum algorithm were simulated up to 25 qubits. When comparing our implementations running on the same hardware with language-integrated quantum operation, academic release version, our new simulator was faster and allowed for the simulation of more qubits. the clever use of the Identity operator (Id-operator) and by splitting independent operations. Instead of executing the QT in a single step, they are divided in sub-QTs, and only the different values from Id-operators are stored.Although the number of steps required for simulation is increased, simulation time is greatly reduced even when steps are sequentially executed. Besides, these sub-steps may be executed in parallel and distributed computations among GPUs. Relative speedups of more than 10,000 were achieved for the most demanding transformations when compared with previous works [2], thus making QC simulation more affordable and interesting for a range of algorithms.Reduction and decomposition optimizations are proposed from design to implementation of quantum algorithms (QAs) in the Distributed Geometric Machine environment (D-GM environment) [3]. By exploring properties as sparsity of the Id-operator and partiality of density unitary transformations, the results achieved present better storage and distribution of quantum information.Additionally, the structure of mixed partial processes [4] preserve control over the increase in the size of read/write memory states in the calculation of a QT, contributing to increase the scalability of QTs and regarding hardware-GPUs memory limit.The main improvements are achieved by decreasing replication and void elements inherited from such operators. In the evaluation of this proposal, Hadamard transformations from 21 to 28 qubits and the Quantum Fourier Transforms from 26 to 28 qubits were both simulated over a sin...

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Correlations from conjugate and dual intuitionistic fuzzy triangular norms and conorms

Cited by 8 publications

References 9 publications

An Application for Medical Diagnosis Using Correlation Coefficient With Modal Operators and Operator Identifying and Unary

An Application for Medical Diagnosis Using Correlation Coefficient With Modal Operators and Operator Identifying and Unary

Correlation Analysis of Intuitionistic Fuzzy Connectives

Quantum computing simulation through reduction and decomposition optimizations with a case study of Shor's algorithm

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