Special Issue "General Algebraic Structures 2020"

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: closed (30 December 2020).

Special Issue Editors

Prof. Dr. Hee Sik Kim
E-Mail Website
Guest Editor
Department of Mathematics, Research Institute of Natural Sciences, Hanyang University, Seoul 04763, Korea
Interests: BCK/BCI-algebras; fuzzy algebras; groupoid theory (= general algebraic structures); semirings; Fibonacci numbers
Special Issues and Collections in MDPI journals
Prof. Dr. Wiesław A. Dudek
E-Mail Website
Guest Editor
Faculty of Pure and Applied Mathematics, Wroclaw University of Science and Technology, 50-370 Wroclaw, Poland
Interests: quasigroups; BCK-algebras; fuzzy algebras
Special Issues and Collections in MDPI journals

Special Issue Information

Dear Colleagues,

This issue is a continuation of the previous successful Special Issue “General Algebraic Structures”.

R. H. Bruck's famous book, A Survey of Binary Systems, mainly discussed loops and semigroups. It is necessary to organize several groupoids dealing with various axioms. The area of “general algebraic structures” contains several groupoids, i.e., sets with a single binary operation satisfying some conditions. The well-known topics, e.g., groups, semigroups, monoids, BCK/BCI-algebra, are not included in this area. It contains lots of generalized algebraic structures of these well-known mathematical structures simply by deleting/weakening/changing the axioms.

The notion of BCK/BCI-algebra was introduced by K. Iséki in 1965, alongside its generalizations, e.g., BCH-algebra, BH-algebra, BZ-algebra, BCC-algebra, pre-BCK-algebra, and near-BCK-algebra. The notion of d-algebra was introduced by deleting two complicated axioms from BCK-algebra. After that, many algebraic structures appeared, e.g., B-, BE-, BF-, BG-, BM-, BN-, BO-, BP-, C-, CI-, Q, and QS-algebra. Other important algebraic structures are implicative algebra, positive implication algebra, selective groupoids, pogroupoids, weak-zero groupoids, etc. These algebras have some inter-relationships with each other and have more room for further research.

This Special Issue of Mathematics (MDPI) will provide an opportunity to construct an area of general algebraic structures and will encourage researchers to publish their investigations in this area.

We will consider any paper in the area of general algebraic structures for possible publication. We will exclude papers on well-known algebras, e.g., groups, rings, fields, semigroups, lattices and posets, BCK/BCI-algebra, and fuzzy algebraic theory.

Prof. Dr. Hee Sik Kim
Prof. Dr. Wiesław A. Dudek
Guest Editors

Manuscript Submission Information

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Keywords

  • General algebraic structures
  • Sets with a single binary operations (groupoids)
  • Generalized groups
  • Implicative algebra
  • Generalized BCK/BCI-algebra

Published Papers (4 papers)

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Research

Open AccessArticle
Automated Maintenance Data Classification Using Recurrent Neural Network: Enhancement by Spotted Hyena-Based Whale Optimization
Mathematics 2020, 8(11), 2008; https://doi.org/10.3390/math8112008 - 11 Nov 2020
Viewed by 422
Abstract
Data classification has been considered extensively in different fields, such as machine learning, artificial intelligence, pattern recognition, and data mining, and the expansion of classification has yielded immense achievements. The automatic classification of maintenance data has been investigated over the past few decades [...] Read more.
Data classification has been considered extensively in different fields, such as machine learning, artificial intelligence, pattern recognition, and data mining, and the expansion of classification has yielded immense achievements. The automatic classification of maintenance data has been investigated over the past few decades owing to its usefulness in construction and facility management. To utilize automated data classification in the maintenance field, a data classification model is implemented in this study based on the analysis of different mechanical maintenance data. The developed model involves four main steps: (a) data acquisition, (b) feature extraction, (c) feature selection, and (d) classification. During data acquisition, four types of dataset are collected from the benchmark Google datasets. The attributes of each dataset are further processed for classification. Principal component analysis and first-order and second-order statistical features are computed during the feature extraction process. To reduce the dimensions of the features for error-free classification, feature selection was performed. The hybridization of two algorithms, the Whale Optimization Algorithm (WOA) and Spotted Hyena Optimization (SHO), tends to produce a new algorithm—i.e., a Spotted Hyena-based Whale Optimization Algorithm (SH-WOA), which is adopted for performing feature selection. The selected features are subjected to a deep learning algorithm called Recurrent Neural Network (RNN). To enhance the efficiency of conventional RNNs, the number of hidden neurons in an RNN is optimized using the developed SH-WOA. Finally, the efficacy of the proposed model is verified utilizing the entire dataset. Experimental results show that the developed model can effectively solve uncertain data classification, which minimizes the execution time and enhances efficiency. Full article
(This article belongs to the Special Issue General Algebraic Structures 2020)
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Open AccessArticle
Filters in Strong BI-Algebras and Residuated Pseudo-SBI-Algebras
Mathematics 2020, 8(9), 1513; https://doi.org/10.3390/math8091513 - 04 Sep 2020
Viewed by 567
Abstract
The concept of basic implication algebra (BI-algebra) has been proposed to describe general non-classical implicative logics (such as associative or non-associative fuzzy logic, commutative or non-commutative fuzzy logic, quantum logic). However, this algebra structure does not have enough characteristics to describe residual implications [...] Read more.
The concept of basic implication algebra (BI-algebra) has been proposed to describe general non-classical implicative logics (such as associative or non-associative fuzzy logic, commutative or non-commutative fuzzy logic, quantum logic). However, this algebra structure does not have enough characteristics to describe residual implications in depth, so we propose a new concept of strong BI-algebra, which is exactly the algebraic abstraction of fuzzy implication with pseudo-exchange principle (PEP). Furthermore, in order to describe the characteristics of the algebraic structure corresponding to the non-commutative fuzzy logics, we extend strong BI-algebra to the non-commutative case, and propose the concept of pseudo-strong BI (SBI)-algebra, which is the common extension of quantum B-algebras, pseudo-BCK/BCI-algebras and other algebraic structures. We establish the filter theory and quotient structure of pseudo-SBI- algebras. Moreover, based on prequantales, semi-uninorms, t-norms and their residual implications, we introduce the concept of residual pseudo-SBI-algebra, which is a common extension of (non-commutative) residual lattices, non-associative residual lattices, and also a special kind of residual partially-ordered groupoids. Finally, we investigate the filters and quotient algebraic structures of residuated pseudo-SBI-algebras, and obtain a unity frame of filter theory for various algebraic systems. Full article
(This article belongs to the Special Issue General Algebraic Structures 2020)
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Open AccessArticle
Multipolar Intuitionistic Fuzzy Hyper BCK-Ideals in Hyper BCK-Algebras
Mathematics 2020, 8(8), 1373; https://doi.org/10.3390/math8081373 - 16 Aug 2020
Viewed by 643
Abstract
In 2020, Kang et al. introduced the concept of a multipolar intuitionistic fuzzy set of finite degree, which is a generalization of a k-polar fuzzy set, and applied it to a BCK/BCI-algebra. The specific purpose of this study was to apply the [...] Read more.
In 2020, Kang et al. introduced the concept of a multipolar intuitionistic fuzzy set of finite degree, which is a generalization of a k-polar fuzzy set, and applied it to a BCK/BCI-algebra. The specific purpose of this study was to apply the concept of a multipolar intuitionistic fuzzy set of finite degree to a hyper BCK-algebra. The notions of the k-polar intuitionistic fuzzy hyper BCK-ideal, the k-polar intuitionistic fuzzy weak hyper BCK-ideal, the k-polar intuitionistic fuzzy s-weak hyper BCK-ideal, the k-polar intuitionistic fuzzy strong hyper BCK-ideal and the k-polar intuitionistic fuzzy reflexive hyper BCK-ideal are introduced herein, and their relations and properties are investigated. These concepts are discussed in connection with the k-polar lower level set and the k-polar upper level set. Full article
(This article belongs to the Special Issue General Algebraic Structures 2020)
Open AccessArticle
On Multipolar Intuitionistic Fuzzy B-Algebras
Mathematics 2020, 8(6), 907; https://doi.org/10.3390/math8060907 - 03 Jun 2020
Viewed by 490
Abstract
In this paper, we discuss the notion of an m-polar fuzzy (normal) subalgebra in B-algebras and its related properties. We consider characterizations of an m-polar fuzzy (normal) subalgebra. We define the concept of an m-polar intuitionistic fuzzy (normal) subalgebra [...] Read more.
In this paper, we discuss the notion of an m-polar fuzzy (normal) subalgebra in B-algebras and its related properties. We consider characterizations of an m-polar fuzzy (normal) subalgebra. We define the concept of an m-polar intuitionistic fuzzy (normal) subalgebra in a B-algebra, and we characterize the m-polar intuitionistic fuzzy (normal) subalgebra. Given an m-polar fuzzy set, we construct a simple m-polar fuzzy set and discuss on m-polar intuitionistic fuzzy subalgebras of B-algebras. Full article
(This article belongs to the Special Issue General Algebraic Structures 2020)
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