Journal of Intelligent & Fuzzy Systems - Volume 37, issue 4

Authors: Zheng, Qinghe | Tian, Xinyu | Jiang, Nan | Yang, Mingqiang

Article Type: Research Article

Abstract: Nowadays, despite the popularity of deep convolutional neural networks (CNNs), the efficient training of network models remains challenging due to several problems. In this paper, we present a layer-wise learning based stochastic gradient descent method (LLb-SGD) for gradient-based optimization of objective functions in deep learning, which is simple and computationally efficient. By simulating the cross-media propagation mechanism of light in the natural environment, we set an adaptive learning rate for each layer of neural networks. In order to find the proper local optimum quickly, the dynamic learning sequence spanning different layers adaptively adjust the descending speed of objective function in …multi-scale and multi-dimensional environment. To the best of our knowledge, this is the first attempt to introduce an adaptive layer-wise learning schedule with a certain degree of convergence guarantee. Due to its generality and robustness, the method is insensitive to hyper-parameters and therefore can be applied to various network architectures and datasets. Finally, we show promising results compared to other optimization methods on two image classification benchmarks using five standard networks. Show more

Keywords: Deep learning, deep CNNs, non-convex optimization, SGD, layer-wise learning

DOI: 10.3233/JIFS-190861

Citation: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 4, pp. 5641-5654, 2019

Authors: Han, Yefan | Qu, Shaojian | Wu, Zhong | Huang, Ripeng

Article Type: Research Article

Abstract: In the process of group decision making, perturbation of input data always reduces the quality of the optimal solution or even makes it unfeasible. Hence, the value of the optimal solution is often limited. In this paper, a robust optimization method is proposed to overcome the inherent uncertainty of input data in group decision making (such as experts’ unit adjustment cost). Firstly, the minimum cost consensus model based on norm definition is established. Then, four different forms of uncertainty sets are proposed, and the corresponding robust models of four minimum consensus cost models are established. Finally, in order to evaluate …the robustness of the solutions obtained by the robust consensus model, the results with different parameters are compared. The robust consensus model is also compared with the minimum cost consensus model. A numerical example proves that the result of the minimum cost consensus model is too optimistic, and the robust consensus model is more robust. Show more

Keywords: Group decision making, consensus, uncertain set, robust optimization, marketing plan

DOI: 10.3233/JIFS-190863

Citation: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 4, pp. 5655-5668, 2019

Authors: Vu, Ho | Hoa, Ngo Van | An, Truong Vinh

Article Type: Research Article

Abstract: The results of this paper is motivated from some recent papers treating the problem of the existence and stability of a solution for Volterra integro-differential equations in fuzzy setting with fractional order derivative (FFVIDEs). By constructing successive approximation method in the space of fuzzy functions, we establish the Ulam-Hyers stability and Ulam-Hyers-Rassias stability for the given problems with two concepts of fuzzy-type fractional derivative.

Keywords: Ulam-hyers stability, ulam-hyers-rassias stability, fuzzy fractional integro-differential equations

DOI: 10.3233/JIFS-190952

Citation: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 4, pp. 5669-5688, 2019

Authors: Gu, Yujie | Hao, Qingwei | Shen, Jie | Zhang, Xiang | Yu, Liying

Article Type: Research Article

Abstract: Variance in fuzzy set theory, generally applied in investment decision, risk evaluation, and so on, can be described as a measurement that gauges the deviation of a fuzzy number. In this paper, in order to extend the application range and enrich the research area of variance, the concepts of variance bounds and semi-variances are defined and discussed from a theoretical point of view. With respect to some frequently-used fuzzy intervals, four relatively simple calculation formulas for upper and lower bounds of variance, and upside and downside semi-variances are put forward respectively, with the aid of which several correlation inequalities are …subsequently presented and proved. Besides, in order to depict the concepts and inequalities more distinctly, plenty of examples are introduced to make some numerical illustration. Show more

Keywords: Fuzzy interval, bounds of variance, semi-variance, inequalities

DOI: 10.3233/JIFS-181408

Citation: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 4, pp. 5689-5705, 2019

Authors: She, Kun | Chen, Yumin

Article Type: Research Article

Abstract: Rough set reduction has been used as a momentous preprocessing tool for machine learning, pattern recognition, and big data analysis. It is well known that the traditional rough set theory can only handle features with categorical values. Therefore, a neighborhood rough set model is introduced to deal with numerical data sets. Classical greedy search strategies to neighborhood rough set reduction have often failed to achieve optimal reducts. Many researchers shift to swarm intelligence algorithms, such as particle swarmoptimization, ant colony optimization and fish swarm algorithm, giving a better solution but with a large cost of computational complexity. It is beneficial …for exploring fast and effective feature reduction algorithms. In this paper, we firstly introduce a knowledge representation, named power set tree (PS-tree). It is an order tree enumerating all the subsets of a feature set. Each node of the PS-tree is a possible feature reduct. Furthermore, we develop a tree search framework for reduction question solving by the PS-tree. We present four tree search methods based on PS-tree, which are depth-first, breadth-first, uniform-cost and A * search methods. The effectiveness of these four proposed tree search methods are tested on some UCI data sets. Finally, we compare the A * search with traditional greedy search and swarm intelligence methods. The comparisons show that the selected features by A * search attain good reduction rates and simultaneously maintain the classification accuracy of whole features. Show more

Keywords: Rough sets, neighborhood rough sets, A* search, feature selection, tree search

DOI: 10.3233/JIFS-18784

Citation: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 4, pp. 5707-5718, 2019

Authors: Xiu, Zhen-Yu | Li, Qing-Guo

Article Type: Research Article

Abstract:  In this paper, the notions of (L , M )-fuzzy concave spaces, (L , M )-fuzzy interior spaces, (L , M )-fuzzy interior relations and (L , M )-fuzzy hull relations are introduced. It is proved that the category of (L , M )-fuzzy concave spaces, the category of (L , M )-fuzzy interior spaces, the category of (L , M )-fuzzy interior relation spaces and the category of (L , M )-fuzzy hull relation spaces are isomorphic. Moreover, it is proved that these categories are all isomorphic to the category of (L , M )-fuzzy convex spaces when L …is a completely distributive lattice with an order-reversing involution. Show more

Keywords: (L, M)-fuzzy concave spaces, (L, M)-fuzzy interior operators, (L, M)-fuzzy interior relations, (L, M)-fuzzy hull relations

DOI: 10.3233/JIFS-181663

Citation: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 4, pp. 5719-5730, 2019

Authors: Sun, Lin | Wang, Wei | Xu, Jiucheng | Zhang, Shiguang

Article Type: Research Article

Abstract: Gene selection as an important data preprocessing technique for cancer classification is one of the most challenging issues in the field of microarray data analysis. In this paper, to deal with gene expression data more effectively, a locally linear embedding (LLE) and neighborhood rough sets-based gene selection method using Lebesgue measure for cancer classification is proposed. First, to solve the problems that the traditional LLE method cannot effectively identify category information, and is susceptible to noise pollution and other issues, the intra-class neighborhood is defined and a new method of calculating reconstruction weight is proposed by combining with the Euclidean …distance to improve LLE. Then, the Lebesgue measure is introduced into neighborhood rough sets, a δ -neighborhood measure is defined, and the dependency degree and the significance measure are presented in neighborhood decision systems. Finally, an improved LLE and neighborhood rough sets-based gene selection algorithm is designed, where the improved LLE algorithm is used to reduce the initial dimensions of gene expression data and obtain a candidate gene subset, and the Lebesgue measure and dependency degree-based relative reduction for gene expression data is developed to further screen the candidate subset to select the final gene subset. The experimental results under several public gene expression data sets prove that the proposed method is effective for selecting the most relevant genes with high classification accuracy. Show more

Keywords: Rough sets, neighborhood rough sets, gene selection, locally linear embedding, cancer classification

DOI: 10.3233/JIFS-181904

Citation: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 4, pp. 5731-5742, 2019

Authors: Zhang, Xiaohong | Wu, Xiaoying | Mao, Xiaoyan | Smarandache, Florentin | Park, Choonkil

Article Type: Research Article

Abstract: From the perspective of semigroup theory, the characterizations of a neutrosophic extended triplet group (NETG) and AG-NET-loop (which is both an Abel-Grassmann groupoid and a neutrosophic extended triplet loop) are systematically analyzed and some important results are obtained. In particular, the following conclusions are strictly proved: (1) an algebraic system is neutrosophic extended triplet group if and only if it is a completely regular semigroup; (2) an algebraic system is weak commutative neutrosophic extended triplet group if and only if it is a Clifford semigroup; (3) for any element in an AG-NET-loop, its neutral element is unique and idempotent; (4) …every AG-NET-loop is a completely regular and fully regular Abel-Grassmann groupoid (AG-groupoid), but the inverse is not true. Moreover, the constructing methods of NETGs (completely regular semigroups) are investigated, and the lists of some finite NETGs and AG-NET-loops are given. Show more

Keywords: Semigroup, neutrosophic extended triplet group (NETG), completely regular semigroup, Clifford semigroup, Abel-Grassmann’s groupoid (AG-groupoid)

DOI: 10.3233/JIFS-181742

Citation: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 4, pp. 5743-5753, 2019

Authors: Gao, Hui | Lu, Mao | Wei, Yu

Article Type: Research Article

Abstract: In this paper, we investigate the multiple attribute decision making problems based on the Hamacher aggregation operators with dual hesitant bipolar fuzzy information. Then, motivated by the idea of Hamacher operations, we have developed some Hamacher aggregation operators for aggregating dual hesitant bipolar fuzzy information: dual hesitant bipolar fuzzy Hamacher weighted average (DHBFHWA) operator, dual hesitant bipolar fuzzy Hamacher weighted geometric (DHBFHWG) operator, dual hesitant bipolar fuzzy Hamacher ordered weighted average (DHBFHOWA) operator, dual hesitant bipolar fuzzy Hamacher ordered weighted geometric (DHBFHOWG) operator, dual hesitant bipolar fuzzy Hamacher hybrid average (DHBFHHA) operator and dual hesitant bipolar fuzzy Hamacher hybrid geometric …(DHBFHHG) operator. Then, we have utilized these operators to develop some approaches to solve the dual hesitant bipolar fuzzy multiple attribute decision making problems. Finally, a real-world example is then analyzed to illustrate the relevance and effectiveness of the proposed methodology. Show more

Keywords: Multiple attribute decision making (MADM), bipolar fuzzy set, dual hesitant bipolar fuzzy set, dual hesitant bipolar fuzzy Hamacherhybrid average (DHBFHHA) operator, dual hesitant bipolar fuzzy Hamacher hybrid geometric (DHBFHHG) operator

DOI: 10.3233/JIFS-18266

Citation: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 4, pp. 5755-5766, 2019

Authors: Lu, Cheng | Xu, Ting-Xue | Cong, Lin-Hu

Article Type: Research Article

Abstract: As the existing research of condition-based Maintenance (CBM) decision-making neglects the influence of regular detection and maintenance (RDM) on the recovery of equipment performance, it is impossible to accurately describe the state degradation characteristics and life distribution law in this case, which is not helpful to formulate reasonable and effective maintenance strategies. Aimed at this problem, a maintenance strategy combining RDM and CBM is proposed in this paper, and the performance degradation modeling and maintenance optimization model under this strategy are studied deeply. Considering the discontinuous and catastrophic performance degradation characteristics of equipment under this condition, a performance degradation model …is established by using the Inverse Gaussian process from the failure mechanism. On this basis, a combined maintenance decision model constrained by risk function is constructed. The optimal maintenance cycle and preventive maintenance threshold are obtained by optimizing the equipment maintenance cost under long-term operation conditions. The relationship between the cost rate and the maintenance strategy value is obtained through the example analysis of the equipment components, and it is proved that the joint maintenance strategy can not only prolong the service life and maintenance interval of equipment, but also reduce the maintenance risk and cost. Show more

Keywords: Regular detection and maintenance, condition-based maintenance, inverse gaussian process, cost rate, maintenance strategy

DOI: 10.3233/JIFS-181580

Citation: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 4, pp. 5767-5775, 2019

Authors: Nosrat, Azizollah | Sanei, Masoud | Payan, Ali | Hosseinzadeh Lotfi, Farhad | Razavyan, Shabnam

Article Type: Research Article

Abstract: In this paper, crisp two-stage data envelopment analysis (TSDEA) models are expanded for decision-making problems where inputs, intermediate data, and outputs are expressed with fuzzy numbers. Considering the merits of credibility theory, we propose the use of this theory in the efficiency measurement of fuzzy serially-connected two-stage systems. For determined credibility levels, we transform the fuzzy model into a linear programming problem and then obtain the credibility function and membership function for fuzzy efficiency of two-stage decision-making units (DMUs). We also explore the sensitivity and stability analysis of two-stage DMUs based on the proposed methodology. As a result, the projection …of inefficient fuzzy two-stage DMUs and the stability radius of efficient fuzzy two-stage DMUs, i.e. the region in which efficiency status is preserved, are also determined. We also provide an illustrative example to better explain the method and demonstrate its performance in comparison with other developed methods for fuzzy TSDEA. Show more

Keywords: Two-stage data envelopment analysis, fuzzy input- intermediate -output data, credibility measure, sensitivity and stability analysis

DOI: 10.3233/JIFS-181519

Citation: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 4, pp. 5777-5796, 2019