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Symmetry
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Symmetry/Asymmetry and Fuzzy Systems
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Symmetry/Asymmetry and Fuzzy Systems

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 31912

Special Issue Editors

Dr. Yiming Tang

E-Mail Website
Guest Editor
School of Computer and Information, Hefei University of Technology, Hefei 230009, Anhui, China
Interests: machine learning; image processing; fuzzy mathematics; fuzzy system; affective computing
Dr. Yong Zhang

E-Mail Website
Guest Editor
College of Electronics and Information Engineering, Shenzhen University, Shenzhen 518060, China
Interests: fuzzy system; multimedia information security; video analysis and retrieval; cloud computing; system integration and optimization
Prof. Dr. Zhaohong Deng

E-Mail Website
Guest Editor
School of Artificial Intelligence and Computer Science, Jiangnan University, Wuxi 214122, China
Interests: fuzzy computing; fuzzy system; uncertain artificial intelligence; neural computing; machine learning; data mining; smart health; medically assisted diagnosis; multimedia data mining
Dr. Xiaohui Yuan

E-Mail Website
Guest Editor
College of Engineering, University of North Texas, Denton, TX 76207, USA
Interests: fuzzy system; computer vision; image processing; data mining; machine learning; artificial intelligence
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In recent years, fuzzy systems have played a vital role in automatic control, pattern recognition, decision analyses, man–machine dialogue systems, affective computing, etc. They characterize the input, output and state variables on fuzzy sets, which integrate fuzzy rules, fuzzy reasoning, fuzzy logic and uncertain artificial intelligence, skilled in imitating the comprehensive inference of humans to deal with uncertain information processing difficult-to-solve problems with conventional mathematical methods. Hence, computer applications can be extended to humanities, social sciences and complex systems.

In fuzzy systems, there often exists a large number of symmetric/asymmetric phenomena, as well as many symmetric/asymmetric structures in the implementation mechanism or practical application of fuzzy systems, for example, the fuzzier and defuzzier constituting a symmetric structure. Additionally, the symmetric implicational method is a recently proposed fuzzy reasoning strategy in the fuzzy system, with symmetry and asymmetry having aroused great interest in many researchers, becoming a novel academic focus. Therefore, this Special Issue welcomes original research and review articles regarding all aspects of symmetry/asymmetry and fuzzy systems.

Dr. Yiming Tang
Dr. Yong Zhang
Prof. Dr. Zhaohong Deng
Dr. Xiaohui Yuan
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • fuzzy systems
  • fuzzy logic
  • fuzzy reasoning
  • fuzzy control
  • symmetry and asymmetry
  • artificial intelligence logic
  • collaborative computing
  • machine learning
  • computer vision
  • granular computing

Published Papers (21 papers)

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Research

17 pages, 300 KiB  
Article
Two Improved Constraint-Solving Algorithms Based on lmaxRPC3rm
by Xirui Pan, Zhuyuan Cheng and Yonggang Zhang
Symmetry 2023, 15(12), 2151; https://doi.org/10.3390/sym15122151 - 03 Dec 2023
Viewed by 882
Abstract
The Constraint Satisfaction Problem (CSP) is a significant research area in artificial intelligence, and includes a large number of symmetric or asymmetric structures. A backtracking search combined with constraint propagation is considered to be the best CSP-solving algorithm, and the consistency algorithm is [...] Read more.
The Constraint Satisfaction Problem (CSP) is a significant research area in artificial intelligence, and includes a large number of symmetric or asymmetric structures. A backtracking search combined with constraint propagation is considered to be the best CSP-solving algorithm, and the consistency algorithm is the main algorithm used in the process of constraint propagation, which is the key factor in constraint-solving efficiency. Max-restricted path consistency (maxRPC) is a well-known and efficient consistency algorithm, whereas the lmaxRPC3rm algorithm is a classic lightweight algorithm for maxRPC. In this paper, we leverage the properties of symmetry to devise an improved pruning strategy aimed at efficiently diminishing the problem’s search space, thus enhancing the overall solving efficiency. Firstly, we propose the maxRPC3sim algorithm, which abandons the two complex data structures used by lmaxRPC3rm. We can render the algorithm to be more concise and competitive compared to the original algorithm while ensuring that it maintains the same average performance. Secondly, inspired by the RCP3 algorithm, we propose the maxRPC3simR algorithm, which uses the idea of residual support to cut down the redundant operation of the lmaxRPC3rm algorithm. Finally, combining the domain/weighted degree (dom/wdeg) heuristic with the activity-based search (ABS) heuristic, a new variable ordering heuristic, ADW, is proposed. Our heuristic prioritizes the selection of variables with symmetry for pruning, further enhancing the algorithm’s pruning capabilities. Experiments were conducted on both random and structural problems separately. The results indicate that our two algorithms generally outperform other algorithms in terms of performance on both problem classes. Moreover, the new heuristic algorithm demonstrates enhanced robustness across different problem types when compared to various existing algorithms. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry and Fuzzy Systems)
22 pages, 3611 KiB  
Article
Symmetric Multi-Scale Residual Network Ensemble with Weighted Evidence Fusion Strategy for Facial Expression Recognition
by Juan Liu, Min Hu, Ying Wang, Zhong Huang and Julang Jiang
Symmetry 2023, 15(6), 1228; https://doi.org/10.3390/sym15061228 - 08 Jun 2023
Viewed by 1039
Abstract
To extract facial features with different receptive fields and improve the decision fusion performance of network ensemble, a symmetric multi-scale residual network (SMResNet) ensemble with a weighted evidence fusion (WEF) strategy for facial expression recognition (FER) was proposed. Firstly, aiming at the defect [...] Read more.
To extract facial features with different receptive fields and improve the decision fusion performance of network ensemble, a symmetric multi-scale residual network (SMResNet) ensemble with a weighted evidence fusion (WEF) strategy for facial expression recognition (FER) was proposed. Firstly, aiming at the defect of connecting different filter groups of Res2Net only from one direction in a hierarchical residual-like style, a symmetric multi-scale residual (SMR) block, which can symmetrically extract the features from two directions, was improved. Secondly, to highlight the role of different facial regions, a network ensemble was constructed based on three networks of SMResNet to extract the decision-level semantic of the whole face, eyes, and mouth regions, respectively. Meanwhile, the decision-level semantics of three regions were regarded as different pieces of evidence for decision-level fusion based on the Dempster-Shafer (D-S) evidence theory. Finally, to fuse the different regional expression evidence of the network ensemble, which has ambiguity and uncertainty, a WEF strategy was introduced to overcome conflicts within evidence based on the support degree adjustment. The experimental results showed that the facial expression recognition rates achieved 88.73%, 88.46%, and 88.52% on FERPlus, RAF-DB, and CAER-S datasets, respectively. Compared with other state-of-the-art methods on three datasets, the proposed network ensemble, which not only focuses the decision-level semantics of key regions, but also addresses to the whole face for the absence of regional semantics under occlusion and posture variations, improved the performance of facial expression recognition in the wild. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry and Fuzzy Systems)
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20 pages, 2681 KiB  
Article
The Facial Expression Data Enhancement Method Induced by Improved StarGAN V2
by Baojin Han and Min Hu
Symmetry 2023, 15(4), 956; https://doi.org/10.3390/sym15040956 - 21 Apr 2023
Cited by 3 | Viewed by 1933
Abstract
Due to the small data and unbalanced sample distribution in the existing facial emotion datasets, the effect of facial expression recognition is not ideal. Traditional data augmentation methods include image angle modification, image shearing, and image scrambling. The above approaches cannot solve the [...] Read more.
Due to the small data and unbalanced sample distribution in the existing facial emotion datasets, the effect of facial expression recognition is not ideal. Traditional data augmentation methods include image angle modification, image shearing, and image scrambling. The above approaches cannot solve the problem that is the high similarity of the generated images. StarGAN V2 can generate different styles of images across multiple domains. Nevertheless, there are some defects in gener-ating these facial expression images, such as crooked mouths and fuzzy facial expression images. To service such problems, we improved StarGAN V2 by solving the drawbacks of creating pictures that apply an SENet to the generator of StarGAN V2. The generator’s SENet can concentrate at-tention on the important regions of the facial expression images. Thus, this makes the generated symmetrical expression image more obvious and easier to distinguish. Meanwhile, to further im-prove the quality of the generated pictures, we customized the hinge loss function to reconstruct the loss functions that increase the boundary of real and fake images. The created facial expression pictures testified that our improved model could solve the defects in the images created by the original StarGAN V2. The experiments were conducted on the CK+ and MMI datasets. The correct recognition rate of the facial expressions on the CK+ was 99.2031%, which is a 1.4186% higher accuracy than that of StarGAN V2. The correct recognition rate of the facial expressions on the MMI displays was 98.1378%, which is 5.059% higher than that of the StarGAN V2 method. Furthermore, contrast test outcomes proved that the improved StarGAN V2 performed better than most state-of-the-art methods. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry and Fuzzy Systems)
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16 pages, 350 KiB  
Article
The Linguistic Concept’s Reduction Methods under Symmetric Linguistic-Evaluation Information
by Hui Cui, Ansheng Deng, Guanli Yue, Li Zou and Luis Martinez
Symmetry 2023, 15(4), 813; https://doi.org/10.3390/sym15040813 - 27 Mar 2023
Viewed by 1304
Abstract
Knowledge reduction is a crucial topic in formal concept analysis. There always exists uncertain, symmetric linguistic-evaluation information in social life, which leads to high complexity in the process of knowledge representation. In order to overcome this problem, we are focused on studying the [...] Read more.
Knowledge reduction is a crucial topic in formal concept analysis. There always exists uncertain, symmetric linguistic-evaluation information in social life, which leads to high complexity in the process of knowledge representation. In order to overcome this problem, we are focused on studying the linguistic-concept-reduction methods in an uncertain environment with fuzzy linguistic information. Based on three-way decisions and an attribute-oriented concept lattice, we construct a fuzzy-object-induced three-way attribute-oriented linguistic (FOEAL) concept lattice, which provides complementary conceptual structures of a three-way concept lattice with symmetric linguistic-evaluation information. Through the granular concept of the FOEAL lattice, we present the corresponding linguistic concept granular consistent set and granular reduction. Then, we further employ the linguistic concept discernibility matrix and discernibility function to calculate the granular reduction set. A similar issue on information entropy is investigated to introduce a method of entropy reduction for the FOEAL lattice, and the relation between the linguistic concept granular reduction and entropy reduction is discussed. The efficiency of the proposed method is depicted by some examples and comparative analysis. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry and Fuzzy Systems)
22 pages, 4373 KiB  
Article
EMSI-BERT: Asymmetrical Entity-Mask Strategy and Symbol-Insert Structure for Drug–Drug Interaction Extraction Based on BERT
by Zhong Huang, Ning An, Juan Liu and Fuji Ren
Symmetry 2023, 15(2), 398; https://doi.org/10.3390/sym15020398 - 02 Feb 2023
Cited by 2 | Viewed by 1258
Abstract
Drug-drug interaction (DDI) extraction has seen growing usage of deep models, but their effectiveness has been restrained by limited domain-labeled data, a weak representation of co-occurring entities, and poor adaptation of downstream tasks. This paper proposes a novel EMSI-BERT method for drug–drug interaction [...] Read more.
Drug-drug interaction (DDI) extraction has seen growing usage of deep models, but their effectiveness has been restrained by limited domain-labeled data, a weak representation of co-occurring entities, and poor adaptation of downstream tasks. This paper proposes a novel EMSI-BERT method for drug–drug interaction extraction based on an asymmetrical Entity-Mask strategy and a Symbol-Insert structure. Firstly, the EMSI-BERT method utilizes the asymmetrical Entity-Mask strategy to address the weak representation of co-occurring entity information using the drug entity dictionary in the pre-training BERT task. Secondly, the EMSI-BERT method incorporates four symbols to distinguish different entity combinations of the same input sequence and utilizes the Symbol-Insert structure to address the week adaptation of downstream tasks in the fine-tuning stage of DDI classification. The experimental results showed that EMSI-BERT for DDI extraction achieved a 0.82 F1-score on DDI-Extraction 2013, and it improved the performances of the multi-classification task of DDI extraction and the two-classification task of DDI detection. Compared with baseline Basic-BERT, the proposed pre-training BERT with the asymmetrical Entity-Mask strategy could obtain better effects in downstream tasks and effectively limit “Other” samples’ effects. The model visualization results illustrated that EMSI-BERT could extract semantic information at different levels and granularities in a continuous space. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry and Fuzzy Systems)
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16 pages, 311 KiB  
Article
Pythagorean Fuzzy Partial Correlation Measure and Its Application
by Dongfang Yan, Keke Wu, Paul Augustine Ejegwa, Xianyang Xie and Yuming Feng
Symmetry 2023, 15(1), 216; https://doi.org/10.3390/sym15010216 - 12 Jan 2023
Cited by 5 | Viewed by 1067
Abstract
The process of computing correlation among attributes of an ordinary database is significant in the analysis and classification of a data set. Due to the uncertainties embedded in data classification, encapsulating correlation techniques using Pythagorean fuzzy information is appropriate to curb the uncertainties. [...] Read more.
The process of computing correlation among attributes of an ordinary database is significant in the analysis and classification of a data set. Due to the uncertainties embedded in data classification, encapsulating correlation techniques using Pythagorean fuzzy information is appropriate to curb the uncertainties. Although correlation coefficient between Pythagorean fuzzy data (PFD) is an applicable information measure, its output is not reliable because of the intrinsic effect of other interfering PFD. Due to the fact that the correlation coefficients in a Pythagorean fuzzy environment could not remove the intrinsic effect of the interfering PFD, the notion of Pythagorean fuzzy partial correlation measure (PFPCM) is necessary to enhance the measure of precise correlation between PFD. Because of the flexibility of Pythagorean fuzzy sets (PFSs), we are motivated to initiate the study on Pythagorean fuzzy partial correlation coefficient (PFPCC) based on a modified Pythagorean fuzzy correlation measure (PFCM). Examples are given to authenticate the choice of the modified PFCM in the computational process of PFPCC. For application, we discuss a case of pattern recognition and classification using the proposed PFPCC after computing the simple correlation coefficient between the patterns based on the modified correlation technique. To be precise, the contributions of the work include the enhancement of an existing PFCC approach, development of PFPCC using the enhanced PFCC, and the application of the developed PFPCC in pattern recognition and classifications. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry and Fuzzy Systems)
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13 pages, 785 KiB  
Article
A Novel Approach for Minimizing Processing Times of Three-Stage Flow Shop Scheduling Problems under Fuzziness
by Alhanouf Alburaikan, Harish Garg and Hamiden Abd El-Wahed Khalifa
Symmetry 2023, 15(1), 130; https://doi.org/10.3390/sym15010130 - 02 Jan 2023
Cited by 3 | Viewed by 1109
Abstract
The purpose of this research is to investigate a novel three-stage flow shop scheduling problem with an ambiguous processing time. The uncertain information is characterized by Pentagonal fuzzy numbers. To solve the problem, in this paper, two different strategies are proposed; one relies [...] Read more.
The purpose of this research is to investigate a novel three-stage flow shop scheduling problem with an ambiguous processing time. The uncertain information is characterized by Pentagonal fuzzy numbers. To solve the problem, in this paper, two different strategies are proposed; one relies on the idea of a ranking function, and the other on the close interval approximation of the pentagonal fuzzy number. For persons that need to be more specific in their requirements, the close interval approximation of the Pentagonal fuzzy number is judged to be the best appropriate approximation interval. Regarding the rental cost specification, these methods are used to reduce the rental cost for the concerned devices. In addition, a comparison of our suggested approach’s computed total processing time, total machine rental cost, and machine idle time to the existing approach is introduced. A numerical example is shown to clarify the benefits of the two strategies and to help the readers understand it better. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry and Fuzzy Systems)
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17 pages, 320 KiB  
Article
A Novel Software Trustworthiness Evaluation Strategy via Relationships between Criteria
by Hongwei Tao, Qiaoling Cao, Haoran Chen, Yang Xian, Songtao Shang and Xiaoxu Niu
Symmetry 2022, 14(11), 2458; https://doi.org/10.3390/sym14112458 - 20 Nov 2022
Cited by 2 | Viewed by 1007
Abstract
Software trustworthiness evaluation is regarded as a multi-criteria decision-making problem. However, most current software trustworthiness evaluation methods do not consider the relationships between criteria. In this paper, we present a software trustworthiness evaluation strategy via the relationships between criteria. Because the trustworthy attribute [...] Read more.
Software trustworthiness evaluation is regarded as a multi-criteria decision-making problem. However, most current software trustworthiness evaluation methods do not consider the relationships between criteria. In this paper, we present a software trustworthiness evaluation strategy via the relationships between criteria. Because the trustworthy attribute degree is evaluated by a criterion, a trustworthy attribute measurement method based on fuzzy theory is first proposed, and the relationships between criteria are described by cooperative and conflicting degrees between criteria. Then, a measure formula for the symmetric substitutivity between criteria is proposed, and the cooperative degree between criteria is taken as the approximation of the symmetric substitutivity between criteria. With the help of the symmetric substitutivity between criteria, the software trustworthiness measurement model obtained by axiomatic approaches is applied to aggregate the degree to which each optional software product meets each objective. Finally, the candidate software products are sorted according to the trustworthiness aggregation results, and the optimal product is obtained from the alternative software products on the basis of the sorting results. The theoretical rationality of the measurement model is validated by proving that it satisfies the desirable properties of software trustworthiness measures, and its effectiveness is demonstrated through a case study. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry and Fuzzy Systems)
16 pages, 297 KiB  
Article
The Submodular Inequality of Aggregation Operators
by Qigao Bo and Gang Li
Symmetry 2022, 14(11), 2354; https://doi.org/10.3390/sym14112354 - 08 Nov 2022
Viewed by 890
Abstract
Aggregation operators have become an essential tool in many applications. The functional equations related to aggregation operators play an important role in fuzzy sets and fuzzy logic theory. The modular equation is strongly connected with the distributivity equation and can be considered as [...] Read more.
Aggregation operators have become an essential tool in many applications. The functional equations related to aggregation operators play an important role in fuzzy sets and fuzzy logic theory. The modular equation is strongly connected with the distributivity equation and can be considered as a constrained associative equation. In this paper, we consider the submodular inequality, which can be viewed as a generalization of the modular equation. First, we discuss the submodular inequality of two general aggregation operators under duality and isomorphism. Moreover, one result of the submodular inequality is presented for the ordinal sum aggregation operators. In the cases of triangular norms and triangular conorms, we present the solutions and validate the symmetry in the related results for some classes of aggregation operators. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry and Fuzzy Systems)
20 pages, 7733 KiB  
Article
SPM: Sparse Persistent Memory Attention-Based Model for Network Traffic Prediction
by Xue-Sen Ma, Gong-Hui Jiang and Biao Zheng
Symmetry 2022, 14(11), 2319; https://doi.org/10.3390/sym14112319 - 04 Nov 2022
Viewed by 1306
Abstract
The network traffic prediction (NTP) model can help operators predict, adjust, and control network usage more accurately. Meanwhile, it also reduces network congestion and improves the quality of the user service experience. However, the characteristics of network traffic data are quite complex. NTP [...] Read more.
The network traffic prediction (NTP) model can help operators predict, adjust, and control network usage more accurately. Meanwhile, it also reduces network congestion and improves the quality of the user service experience. However, the characteristics of network traffic data are quite complex. NTP models with higher prediction accuracy tend to have higher complexity, which shows obvious asymmetry. In this work, we target the conflict between low complexity and high prediction performance and propose an NTP model based on a sparse persistent memory (SPM) attention mechanism. SPM can accurately capture the sparse key features of network traffic and reduce the complexity of the self-attention layer while ensuring prediction performance. The symmetric SPM encoder and decoder replace the high complexity feed-forward sub-layer with an attention layer to reduce the complexity. In addition, by adding an attention layer to persistently memorize key features, the prediction performance of the model could be further improved. We evaluate our method on two real-world network traffic datasets. The results demonstrate that the SPM-based method outperforms the state-of-the-art (SOTA) approaches in NTP results by 33.0% and 21.3%, respectively. Meanwhile, the results of RMSE and R2 are also optimal. When measured by temporal performance, SPM reduces the complexity and reduces the training time by 22.2% and 30.4%, respectively, over Transformer. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry and Fuzzy Systems)
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13 pages, 323 KiB  
Article
Fuzzy Reasoning for Mixture of Fuzzy/Intuitionistic Fuzzy Information Based on Triple I Method
by Mucong Zheng and Yan Liu
Symmetry 2022, 14(10), 2184; https://doi.org/10.3390/sym14102184 - 18 Oct 2022
Viewed by 740
Abstract
Generalized modus ponens (GMP) is a basic model of approximate reasoning. GMP in fuzzy propositions is called fuzzy modus ponen (FMP) and it is called intuitionistic fuzzy modus ponens (IFMP) when fuzzy propositions are generalized to intuitionistic fuzzy propositions. In this paper, we [...] Read more.
Generalized modus ponens (GMP) is a basic model of approximate reasoning. GMP in fuzzy propositions is called fuzzy modus ponen (FMP) and it is called intuitionistic fuzzy modus ponens (IFMP) when fuzzy propositions are generalized to intuitionistic fuzzy propositions. In this paper, we aim to investigate fuzzy reasoning methods for GMP with mixture of fuzzy/intuitionistic fuzzy information. For mixed types of GMP, we present two basic methods to solve GMP problems based on the triple I method (TIM). One is to transform the GMP problem into two FMP problems by decomposition and aggregate the solutions of TIM for FMP problems to obtain the solution for GMP problem. The other is to transform the GMP problem into the IFMP problem by expansion and aggregate the solutions of TIM for the IFMP problem to obtain the solution for the GMP problem. These two methods are called the decomposition triple I method (DTIM) and expansion triple I method (ETIM), respectively. We analyze the relationship between DTIM and ETIM. Furthermore, we discuss the reversibility of DTIM and ETIM. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry and Fuzzy Systems)
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20 pages, 2885 KiB  
Article
A Heuristic Integrated Scheduling Algorithm via Processing Characteristics of Various Machines
by Wei Zhou, Pengwei Zhou, Ying Zheng and Zhiqiang Xie
Symmetry 2022, 14(10), 2150; https://doi.org/10.3390/sym14102150 - 14 Oct 2022
Cited by 2 | Viewed by 1105
Abstract
Complex products with a tree-like structure usually have an asymmetric structure. Therefore, in order to avoid the separation of equipment and operation correlation during the scheduling, the structural attributes of products and the use of equipment resources should be fully considered. However, this [...] Read more.
Complex products with a tree-like structure usually have an asymmetric structure. Therefore, in order to avoid the separation of equipment and operation correlation during the scheduling, the structural attributes of products and the use of equipment resources should be fully considered. However, this feature is ignored in the current research works on the scheduling of multi-variety and small batch products. This leads to increased idle time for equipment and an extended makespan for products. To avoid this situation, a heuristic integrated scheduling algorithm via processing characteristics of various machines (HIS-PCVM) is proposed. In the integrated scheduling, the algorithm first divides the equipment into two categories: the special equipment and the general equipment according to the resources of the production scheduling system. Then, different scheduling methods are designed according to the equipment categories. The makespan of the product is further optimized through various combination methods. Moreover, the constraint audit strategy to guarantee the constraint relationship between the operations is optimized. The earliest scheduling time strategy is proposed to improve the parallelism and serial tightness of the operations. These strategies reduce the idle time of equipment effectively. Experimental results show that the proposed algorithm has a better application effect in reducing the makespan of complex products, both with asymmetric structures and symmetric structures. This also shows that the algorithm is effective in improving the utilization rate of equipment. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry and Fuzzy Systems)
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16 pages, 936 KiB  
Article
An Entity Linking Algorithm Derived from Graph Convolutional Network and Contextualized Semantic Relevance
by Bingjing Jia, Chenglong Wang, Haiyan Zhao and Lei Shi
Symmetry 2022, 14(10), 2060; https://doi.org/10.3390/sym14102060 - 03 Oct 2022
Cited by 3 | Viewed by 1595
Abstract
In the era of big data, a large amount of unstructured text data springs up every day. Entity linking involves relating the mentions found in the texts to the corresponding entities, which stand for objective things in the real world, in a knowledge [...] Read more.
In the era of big data, a large amount of unstructured text data springs up every day. Entity linking involves relating the mentions found in the texts to the corresponding entities, which stand for objective things in the real world, in a knowledge base. This task can help computers understand semantics in the texts correctly. Although there have been numerous approaches employed in research such as this, some challenges are still unresolved. Most current approaches utilize neural models to learn important features of the entity and mention context. However, the topic coherence among the referred entities is frequently ignored, which leads to a clear preference for popular entities but poor accuracy for less popular ones. Moreover, the graph-based models face much noise information and high computational complexity. To solve the problems above, the paper puts forward an entity linking algorithm derived from the asymmetric graph convolutional network and the contextualized semantic relevance, which can make full use of the neighboring node information as well as deal with unnecessary noise in the graph. The semantic vector of the candidate entity is obtained by continuously iterating and aggregating the information from neighboring nodes. The contextualized relevance model is a symmetrical structure that is designed to realize the deep semantic measurement between the mentions and the entities. The experimental results show that the proposed algorithm can fully explore the topology information of the graph and dramatically improve the effect of entity linking compared with the baselines. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry and Fuzzy Systems)
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26 pages, 7028 KiB  
Article
A Triple-Structure Network Model Based upon MobileNet V1 and Multi-Loss Function for Facial Expression Recognition
by Baojin Han, Min Hu, Xiaohua Wang and Fuji Ren
Symmetry 2022, 14(10), 2055; https://doi.org/10.3390/sym14102055 - 02 Oct 2022
Cited by 5 | Viewed by 2554
Abstract
Existing facial expression recognition methods have some drawbacks. For example, it becomes difficult for network learning on cross-dataset facial expressions, multi-region learning on an image did not extract the overall image information, and a frequency multiplication network did not take into account the [...] Read more.
Existing facial expression recognition methods have some drawbacks. For example, it becomes difficult for network learning on cross-dataset facial expressions, multi-region learning on an image did not extract the overall image information, and a frequency multiplication network did not take into account the inter-class and intra-class features in image classification. In order to deal with the above problems, in our current research, we raise a symmetric mode to extract the inter-class features and intra-class diversity features, and then propose a triple-structure network model based upon MobileNet V1, which is trained via a new multi-branch loss function. Such a proposed network consists of triple structures, viz., a global branch network, an attention mechanism branch network, and a diversified feature learning branch network. To begin with, the global branch network is used to extract the global features of the facial expression images. Furthermore, an attention mechanism branch network concentrates to extract inter-class features. In addition, the diversified feature learning branch network is utilized to extract intra-class diverse features. The network training is performed by using multiple loss functions to decrease intra-class differences and inter-class similarities. Finally, through ablation experiments and visualization, the intrinsic mechanism of our triple-structure network model is proved to be very reasonable. Experiments on the KDEF, MMI, and CK+ datasets show that the accuracy of facial expression recognition using the proposed model is 1.224%, 13.051%, and 3.085% higher than that using MC-loss (VGG16), respectively. In addition, related comparison tests and analyses proved that our raised triple-structure network model reaches better performance than dozens of state-of-the-art methods. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry and Fuzzy Systems)
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17 pages, 415 KiB  
Article
An Intelligent Genetic Scheme for Multi-Objective Collaboration Services Scheduling
by Wei Guo, Lanju Kong, Xudong Lu and Lizhen Cui
Symmetry 2022, 14(10), 2037; https://doi.org/10.3390/sym14102037 - 29 Sep 2022
Cited by 1 | Viewed by 1189
Abstract
The optimization of collaborative service scheduling is the main bottleneck restricting the efficiency and cost of collaborative service execution. It is helpful to reduce the cost and improve the efficiency to deal with the scheduling problem correctly and effectively. The traditional genetic algorithm [...] Read more.
The optimization of collaborative service scheduling is the main bottleneck restricting the efficiency and cost of collaborative service execution. It is helpful to reduce the cost and improve the efficiency to deal with the scheduling problem correctly and effectively. The traditional genetic algorithm can solve the multi-objective problem more comprehensively than the optimization algorithm, such as stochastic greedy algorithm. But in the actual situation, the traditional algorithm is still one-sided. The intelligent genetic scheme (IGS) proposed in this paper enhances the expansibility and diversity of the algorithm on the basis of traditional genetic algorithm. In the process of initial population selection, the initial population generation strategy is changed, a part of the population is randomly generated and the selection process is iteratively optimized, which is a selection method based on population asymmetric exchange to realize selection. Mutation factors enhance the diversity of the population in the adaptive selection based on individual innate quality. The proposed IGS can not only maintain individual diversity, increase the probability of excellent individuals, accelerate the convergence rate, but also will not lead to the ultimate result of the local optimal solution. It has certain advantages in solving the optimization problem, and provides a new idea and method for solving the collaborative service optimization scheduling problem, which can save manpower and significantly reduce costs on the premise of ensuring the quality. The experimental results show that Intelligent Genetic algorithm (IGS) not only has better scalability and diversity, but also can increase the probability of excellent individuals and accelerate the convergence speed. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry and Fuzzy Systems)
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19 pages, 965 KiB  
Article
A Text Classification Model via Multi-Level Semantic Features
by Keji Mao, Jinyu Xu, Xingda Yao, Jiefan Qiu, Kaikai Chi and Guanglin Dai
Symmetry 2022, 14(9), 1938; https://doi.org/10.3390/sym14091938 - 17 Sep 2022
Cited by 5 | Viewed by 2168
Abstract
Text classification is a major task of NLP (Natural Language Processing) and has been the focus of attention for years. News classification as a branch of text classification is characterized by complex structure, large amounts of information and long text length, which in [...] Read more.
Text classification is a major task of NLP (Natural Language Processing) and has been the focus of attention for years. News classification as a branch of text classification is characterized by complex structure, large amounts of information and long text length, which in turn leads to a decrease in the accuracy of classification. To improve the classification accuracy of Chinese news texts, we present a text classification model based on multi-level semantic features. First, we add the category correlation coefficient to TF-IDF (Term Frequency-Inverse Document Frequency) and the frequency concentration coefficient to CHI (Chi-Square), and extract the keyword semantic features with the improved algorithm. Then, we extract local semantic features with TextCNN with symmetric-channel and global semantic information from a BiLSTM with attention. Finally, we fuse the three semantic features for the prediction of text categories. The results of experiments on THUCNews, LTNews and MCNews show that our presented method is highly accurate, with 98.01%, 90.95% and 94.24% accuracy, respectively. With model parameters two magnitudes smaller than Bert, the improvements relative to the baseline Bert+FC are 1.27%, 1.2%, and 2.81%, respectively. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry and Fuzzy Systems)
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20 pages, 15813 KiB  
Article
ELM-Based Active Learning via Asymmetric Samplers: Constructing a Multi-Class Text Corpus for Emotion Classification
by Xuefeng Shi, Min Hu, Fuji Ren, Piao Shi and Xiao Sun
Symmetry 2022, 14(8), 1698; https://doi.org/10.3390/sym14081698 - 16 Aug 2022
Cited by 1 | Viewed by 1316
Abstract
A high-quality annotated text corpus is vital when training a deep learning model. However, it is insurmountable to acquire absolute abundant label-balanced data because of the huge labor and time costs needed in the labeling stage. To alleviate this situation, a novel active [...] Read more.
A high-quality annotated text corpus is vital when training a deep learning model. However, it is insurmountable to acquire absolute abundant label-balanced data because of the huge labor and time costs needed in the labeling stage. To alleviate this situation, a novel active learning (AL) method is proposed in this paper, which is designed to scratch samples to construct multi-class and multi-label Chinese emotional text corpora. This work shrewdly leverages the superiorities, i.e., less learning time and generating parameters randomly possessed by extreme learning machines (ELMs), to initially measure textual emotion features. In addition, we designed a novel combined query strategy called an asymmetric sampler (which simultaneously considers uncertainty and representativeness) to verify and extract ideal samples. Furthermore, this model progressively modulates state-of-the-art prescriptions through cross-entropy, Kullback–Leibler, and Earth Mover’s distance. Finally, through stepwise-assessing the experimental results, the updated corpora present more enriched label distributions and have a higher weight of correlative emotional information. Likewise, in emotion classification experiments by ELM, the precision, recall, and F1 scores obtained 7.17%, 6.31%, and 6.71% improvements, respectively. Extensive emotion classification experiments were conducted by two widely used classifiers—SVM and LR—and their results also prove our method’s effectiveness in scratch emotional texts through comparisons. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry and Fuzzy Systems)
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18 pages, 1833 KiB  
Article
Dynamic Behavior of a Fractional-Type Fuzzy Difference System
by Lili Jia, Changyou Wang, Xiaojuan Zhao and Wei Wei
Symmetry 2022, 14(7), 1337; https://doi.org/10.3390/sym14071337 - 28 Jun 2022
Cited by 2 | Viewed by 1037
Abstract
In this paper, our aim is to study the following fuzzy system: [...] Read more.
In this paper, our aim is to study the following fuzzy system: xn+1=Axn−1xn−2+Bxn−3D+Cxn−4, n=0,1,2,⋯, where {xn} is a sequence of positive fuzzy numbers and the initial conditions x−4,x−3,x−2,x−1,x0 and the parameters A,B,C,D are positive fuzzy numbers. Firstly, the existence and uniqueness of positive fuzzy solutions of the fuzzy system are proved. Secondly, the dynamic behavior of the equilibrium points for the fuzzy system are studied by means of the fuzzy sets theory, linearization method and mathematical induction. Finally, the results obtained in this paper are simulated by using the software package MATLAB 2016, and the numerical results not only show the dynamic behavior of the solutions for the fuzzy system, but also verify the effectiveness of the proposed results. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry and Fuzzy Systems)
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16 pages, 1619 KiB  
Article
Compressed-Encoding Particle Swarm Optimization with Fuzzy Learning for Large-Scale Feature Selection
by Jia-Quan Yang, Chun-Hua Chen, Jian-Yu Li, Dong Liu, Tao Li and Zhi-Hui Zhan
Symmetry 2022, 14(6), 1142; https://doi.org/10.3390/sym14061142 - 01 Jun 2022
Cited by 19 | Viewed by 1693
Abstract
Particle swarm optimization (PSO) is a promising method for feature selection. When using PSO to solve the feature selection problem, the probability of each feature being selected and not being selected is the same in the beginning and is optimized during the evolutionary [...] Read more.
Particle swarm optimization (PSO) is a promising method for feature selection. When using PSO to solve the feature selection problem, the probability of each feature being selected and not being selected is the same in the beginning and is optimized during the evolutionary process. That is, the feature selection probability is optimized from symmetry (i.e., 50% vs. 50%) to asymmetry (i.e., some are selected with a higher probability, and some with a lower probability) to help particles obtain the optimal feature subset. However, when dealing with large-scale features, PSO still faces the challenges of a poor search performance and a long running time. In addition, a suitable representation for particles to deal with the discrete binary optimization problem of feature selection is still in great need. This paper proposes a compressed-encoding PSO with fuzzy learning (CEPSO-FL) for the large-scale feature selection problem. It uses the N-base encoding method for the representation of particles and designs a particle update mechanism based on the Hamming distance and a fuzzy learning strategy, which can be performed in the discrete space. It also proposes a local search strategy to dynamically skip some dimensions when updating particles, thus reducing the search space and reducing the running time. The experimental results show that CEPSO-FL performs well for large-scale feature selection problems. The solutions obtained by CEPSO-FL contain small feature subsets and have an excellent performance in classification problems. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry and Fuzzy Systems)
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24 pages, 622 KiB  
Article
Maximal Product and Symmetric Difference of Complex Fuzzy Graph with Application
by Muhammad Shoaib, Waqas Mahmood, Qin Xin and Fairouz Tchier
Symmetry 2022, 14(6), 1126; https://doi.org/10.3390/sym14061126 - 30 May 2022
Cited by 5 | Viewed by 1282
Abstract
A complex fuzzy set (CFS) is described by a complex-valued truth membership function, which is a combination of a standard true membership function plus a phase term. In this paper, we extend the idea of a fuzzy graph (FG) to a complex fuzzy [...] Read more.
A complex fuzzy set (CFS) is described by a complex-valued truth membership function, which is a combination of a standard true membership function plus a phase term. In this paper, we extend the idea of a fuzzy graph (FG) to a complex fuzzy graph (CFG). The CFS complexity arises from the variety of values that its membership function can attain. In contrast to a standard fuzzy membership function, its range is expanded to the complex plane’s unit circle rather than [0,1]. As a result, the CFS provides a mathematical structure for representing membership in a set in terms of complex numbers. In recent times, a mathematical technique has been a popular way to combine several features. Using the preceding mathematical technique, we introduce strong approaches that are properties of CFG. We define the order and size of CFG. We discuss the degree of vertex and the total degree of vertex of CFG. We describe basic operations, including union, join, and the complement of CFG. We show new maximal product and symmetric difference operations on CFG, along with examples and theorems that go along with them. Lastly, at the base of a complex fuzzy graph, we show the application that would be important for measuring the symmetry or asymmetry of acquaintanceship levels of social disease: COVID-19. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry and Fuzzy Systems)
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16 pages, 333 KiB  
Article
ZL-Completions for ZL-Semigroups
by Shuhua Su, Qingguo Li and Qi Li
Symmetry 2022, 14(3), 578; https://doi.org/10.3390/sym14030578 - 15 Mar 2022
Cited by 1 | Viewed by 1245
Abstract
In this paper, we generalize a common completion pattern of ordered semigroups to the fuzzy setting. Based on a standard L-completion ZL, we introduce the notion of a ZL-semigroup as a generalization of an L-ordered semigroup, where [...] Read more.
In this paper, we generalize a common completion pattern of ordered semigroups to the fuzzy setting. Based on a standard L-completion ZL, we introduce the notion of a ZL-semigroup as a generalization of an L-ordered semigroup, where L is a complete residuated lattice. For this asymmetric mathematical structure, we define a ZL-completion of it to be a complete residuated L-ordered semigroup together with a join-dense L-ordered semigroup embedding satisfying the universal property. We prove that: (1) For every compositive ZL, the category CSL of complete residuated L-ordered semigroups is a reflective subcategory of the category SZL of ZL-semigroups; (2) for an arbitrary ZL, there is an adjunction between SZL and the category SZL→E of weakly ZL-continuous L-ordered semigroup embeddings of ZL-semigroups. By appropriate specialization of ZL, the results can be applied to the DML-completion, certain completions associated with fuzzy subset systems, etc. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry and Fuzzy Systems)
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