A Kernel-Based Intuitionistic Fuzzy C-Means Clustering Using a DNA Genetic Algorithm for Magnetic Resonance Image Segmentation

The Application of Genetic Algorithm in Land Use Optimization Research: A Review

Land use optimization (LUO) first considers which types of land use should exist in a certain area, and secondly, how to allocate these land use types to specific land grid units. As an intelligent global optimization search algorithm, the Genetic Algorithm (GA) has been widely used in this field. However, there are no comprehensive reviews concerning the development process for the application of the Genetic Algorithm in land use optimization (GA-LUO). This article used a bibliometric analysis method to explore current state and development trends for GA-LUO from 1154 relevant documents published over the past 25 years from Web of Science. We also displayed a visualization network from the aspects of core authors, research institutions, and highly cited literature. The results show the following: (1) The countries that published the most articles are the United States and China, and the Chinese Academy of Sciences is the research institution that publishes the most articles. (2) The top 10 cited articles focused on describing how to build GA models for multi-objective LUO. (3) According to the number of keywords that appear for the first time in each time period, we divided the process of GA-LUO into four stages: the presentation and improvement of methods stage (1995–2004), the optimization stage (2005–2008), the hybrid application of multiple models stage (2009–2016), and the introduction of the latest method stage (after 2017). Furthermore, future research trends are mainly manifested in integrating together algorithms with GA and deepening existing research results. This review could help researchers know this research domain well and provide effective solutions for land use problems to ensure the sustainable use of land resources.

Intuitionistic Center-Free FCM Clustering for MR Brain Image Segmentation

In this paper, an intuitionistic center-free fuzzy c-means clustering method (ICFFCM) is proposed for magnetic resonance (MR) brain image segmentation. First, in order to suppress the effect of noise in MR brain images, a pixel-to-pixel similarity with spatial information is defined. Then, for the purpose of handling the vagueness in MR brain images as well as the uncertainty in clustering process, a pixel-to-cluster similarity measure is defined by employing the intuitionistic fuzzy membership function. These two similarities are used to modify the center-free FCM so that the ability of the method for MR brain image segmentation could be improved. Second, on the basis of the improved center-free FCM method, a local information term, which is also intuitionistic and center-free, is appended to the objective function. This generates the final proposed ICFFCM. The consideration of local information further enhances the robustness of ICFFCM to the noise in MR brain images. Experimental results on the simulated and real MR brain image datasets show that ICFFCM is effective and robust. Moreover, ICFFCM could outperform several fuzzy-clustering-based methods and could achieve comparable results to the standard published methods like statistical parametric mapping and FMRIB automated segmentation tool.

A Nonparametric Model for Multi-Manifold Clustering with Mixture of Gaussians and Graph Consistency

Multi-manifold clustering is among the most fundamental tasks in signal processing and machine learning. Although the existing multi-manifold clustering methods are quite powerful, learning the cluster number automatically from data is still a challenge. In this paper, a novel unsupervised generative clustering approach within the Bayesian nonparametric framework has been proposed. Specifically, our manifold method automatically selects the cluster number with a Dirichlet Process (DP) prior. Then, a DP-based mixture model with constrained Mixture of Gaussians (MoG) is constructed to handle the manifold data. Finally, we integrate our model with the k-nearest neighbor graph to capture the manifold geometric information. An efficient optimization algorithm has also been derived to do the model inference and optimization. Experimental results on synthetic datasets and real-world benchmark datasets exhibit the effectiveness of this new DP-based manifold method.

KL Divergence-Based Fuzzy Cluster Ensemble for Image Segmentation

Ensemble clustering combines different basic partitions of a dataset into a more stable and robust one. Thus, cluster ensemble plays a significant role in applications like image segmentation. However, existing ensemble methods have a few demerits, including the lack of diversity of basic partitions and the low accuracy caused by data noise. In this paper, to get over these difficulties, we propose an efficient fuzzy cluster ensemble method based on Kullback-Leibler divergence or simply, the KL divergence. The data are first classified with distinct fuzzy clustering methods. Then, the soft clustering results are aggregated by a fuzzy KL divergence-based objective function. Moreover, for image segmentation problems, we utilize the local spatial information in the cluster ensemble algorithm to suppress the effect of noise. Experiment results reveal that the proposed methods outperform many other methods in synthetic and real image-segmentation problems.

Q-Neutrosophic Soft Relation and Its Application in Decision Making

Q-neutrosophic soft sets are essentially neutrosophic soft sets characterized by three independent two-dimensional membership functions which stand for uncertainty, indeterminacy and falsity. Thus, it can be applied to two-dimensional imprecise, indeterminate and inconsistent data which appear in most real life problems. Relations are a suitable tool for describing correspondences between objects. In this study we introduce and discuss Q-neutrosophic soft relations, which can be discussed as a generalization of fuzzy soft relations, intuitionistic fuzzy soft relations, and neutrosophic soft relations. Q-neutrosophic soft relation is a sub Q-neutrosophic soft set of the Cartesian product of the Q-neutrosophic soft sets, in other words Q-neutrosophic soft relation is Q-neutrosophic soft sets in a Cartesian product of universes. We also present the notions of inverse, composition of Q-neutrosophic soft relations and functions along with some related theorems and properties. Reflexivity, symmetry, transitivity as well as equivalence relations and equivalence classes of Q-neutrosophic soft relations are also defined. Some properties of these concepts are presented and supported by real life examples. Finally, an algorithm to solve decision making problems using Q-neutrosophic soft relations is developed and verified by an example to show the efficiency of this method.

The Complex Neutrosophic Soft Expert Relation and Its Multiple Attribute Decision-Making Method

This paper introduces a novel soft computing technique, called the complex neutrosophic soft expert relation (CNSER), to evaluate the degree of interaction between two hybrid models called complex neutrosophic soft expert sets (CNSESs). CNSESs are used to represent two-dimensional data that are imprecise, uncertain, incomplete and indeterminate. Moreover, it has a mechanism to incorporate the parameter set and the opinions of all experts in one model, thus making it highly suitable for use in decision-making problems where the time factor plays a key role in determining the final decision. The complex neutrosophic soft expert set and complex neutrosophic soft expert relation are both defined. Utilizing the properties of CNSER introduced, an empirical study is conducted on the relationship between the variability of the currency exchange rate and Malaysian exports and the time frame (phase) of the interaction between these two variables. This study is supported further by an algorithm to determine the type and the degree of this relationship. A comparison between different existing relations and CNSER to show the ascendancy of our proposed CNSER is provided. Then, the notion of the inverse, complement and composition of CNSERs along with some related theorems and properties are introduced. Finally, we define the symmetry, transitivity and reflexivity of CNSERs, as well as the equivalence relation and equivalence classes on CNSESs. Some interesting properties are also obtained.