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Article
Open AccessSemi-supervised attribute reduction for hybrid data
Due to the high cost of labelling data, a lot of partially hybrid data are existed in many practical applications. Uncertainty measure (UM) can supply new viewpoints for analyzing data. They can help us in dis...
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Article
Uncertainty measurement of partially labeled categorical data with application to semi-supervised attribute reduction
In many practical applications of machine learning, there are a large number of partially labeled categorical data due to the high cost of labelling data. Semi-supervised learning algorithm is needed to deal w...
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Article
Uncertainty measurement for a gene space based on class-consistent technology: an application in gene selection
With the development of data mining, artificial intelligence, neural network, expert system and machine learning, information system (i-system) becomes more and more important. If the objects, attributes and info...
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Article
Finding minimal solutions to the system of addition-min fuzzy relational inequalities
In the literature, a BitTorrent-like peer-to-peer file-sharing system has been modelled as a system of addition-min fuzzy relational inequalities (FRIs). Finding all minimal solutions of such a system is consi...
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Article
Attribute reduction in an incomplete categorical decision information system based on fuzzy rough sets
Categorical data is an important class of data in machine learning. Information system based on categorical data is called a categorical information system (CIS), a CIS with missing values is known as an incom...
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Article
Correction to: Gene Selection in a Single Cell Gene Space Based on D–S Evidence Theory
The original article has been corrected.
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Article
Gene Selection in a Single Cell Gene Space Based on D–S Evidence Theory
If the samples, features and information values in a real-valued information system are cells, genes and gene expression values, respectively, then for convenience, this system is said to be a single cell gene...
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Article
Some results for the minimal optimal solution of min-max programming problem with addition-min fuzzy relational inequalities
In this study, a BitTorrent-like peer-to-peer (BT-P2P) file-sharing system is reduced into a system of fuzzy relational inequalities (FRI) with addition-min composition. To study the stability of data transmis...
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Article
Optimal feedback control for a class of fractional evolution equations with history-dependent operators
In this paper, we will study optimal feedback control problems derived by a class of Riemann-Liouville fractional evolution equations with history-dependent operators in separable reflexive Banach spaces. We f...
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Article
Existence of Solutions for a Class of Noncoercive Variational–Hemivariational Inequalities Arising in Contact Problems
The primary objective is to investigate a class of noncoercive variational–hemivariational inequalities on a Banach space. We start with several new existence results for the abstract inequalities in which our...
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Article
\(L^\infty \) -Stability of a Parametric Optimal Control Problem Governed by Semilinear Elliptic Equations
This paper studies local stability of a parametric optimal control problem governed by semilinear elliptic equations with mixed pointwise constraints. We show that if the unperturbed problem satisfies the stri...
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Article
Uncertainty measurement for a fuzzy set-valued information system
Uncertainty measurement (UM) can offer new visual angle for data analysis. A fuzzy set-valued information system (FSVIS) which means an information system (IS) where its information values are fuzzy sets. This...
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Article
The Galerkin Method and Regularization for Variational Inequalities in Reflexive Banach Spaces
This paper studies the convergence of the Galerkin method and regularization for variational inequalities with pseudomonotone operators in the sense of Brézis. Namely, we prove that under certain conditions, t...
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Article
Optimality Conditions for Approximate Pareto Solutions of a Nonsmooth Vector Optimization Problem with an Infinite Number of Constraints
In this paper, we present some new necessary and sufficient optimality conditions in terms of Clarke subdifferentials for approximate Pareto solutions of a nonsmooth vector optimization problem which has an in...
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Article
On the Split Equality Fixed Point Problem of Quasi-Pseudo-Contractive Map**s Without A Priori Knowledge of Operator Norms with Applications
In this paper, we consider the split equality fixed point problem for quasi-pseudo-contractive map**s without a priori knowledge of operator norms in Hilbert spaces, which includes split feasibility problem,...
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Article
Locally Lipschitz vector optimization problems: second-order constraint qualifications, regularity condition and KKT necessary optimality conditions
In the present paper, we are concerned with a class of constrained vector optimization problems, where the objective functions and active constraint functions are locally Lipschitz at the referee point. Some s...
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Article
Forward–Backward Splitting Method for Solving a System of Quasi-Variational Inclusions
The purpose of this paper is by using a generalized forward–backward splitting method to propose an iterative algorithm for finding a common element of the set of solutions to a system of quasi-variational inc...
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Article
Systems of variational inequalities with hierarchical variational inequality constraints for asymptotically nonexpansive and pseudocontractive map**s
The purpose of this paper is to introduce and analyze a hybrid extragradient-like implicit rule for finding a common solution of a general system of variational inequalities (GSVI) and a common fixed point pro...
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Article
A generalized forward–backward splitting method for solving a system of quasi variational inclusions in Banach spaces
The purpose of this paper is by using the generalized forward–backward splitting method and implicit midpoint rule to propose an iterative algorithm for finding a common element of the set of solutions to a sy...
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Article
A note on approximate Karush–Kuhn–Tucker conditions in locally Lipschitz multiobjective optimization
In the recent paper of Giorgi et al. (J Optim Theory Appl 171:70–89, 2016), the authors introduced the so-called approximate Karush–Kuhn–Tucker (AKKT) condition for smooth multiobjective optimization problems and...
