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Shaheen T, Khan HB, Ali W, Najam S, Uddin MZ, Mehedi Hassan M. A Novel generalization of sequential decision-theoretic rough set model and its application. Heliyon 2024; 10:e33784. [PMID: 39040370 PMCID: PMC11261872 DOI: 10.1016/j.heliyon.2024.e33784] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2024] [Revised: 06/26/2024] [Accepted: 06/26/2024] [Indexed: 07/24/2024] Open
Abstract
This paper introduces a refined and broadened version of decision-theoretic rough sets (DTRSs) named Generalized Sequential Decision-Theoretic Rough Set (GSeq-DTRS), which integrates the three-way decision (3WD) methodology. Operating through multiple levels, this iterative approach aims to comprehensively explore the boundary region. It introduces the concept of generalized granulation, departing from conventional equivalence-relation-based structures to incorporate similarity/tolerance relations. GSeq-DTRS addresses the limitations encountered by its predecessor, Seq-DTRS, particularly in managing sequential procedures and integrating new attributes. A notable advancement is its seamless handling of continuous-scale datasets through a defined Generalized Granular Structure (GGS), enabling classification across multiple levels without necessitating reduction of attributes. A refined version of conditional probability (CP), aligned with tolerance classes, enhances the approach, supported by a meticulously designed algorithm. Extensive experimental analysis conducted on two datasets sourced from https://www.kaggle.com demonstrates the efficacy of the procedure for both continuous and discrete datasets, effectively classifying probable elements into POS or NEG regions based on their membership. Unlike traditional Seq-DTRS, it does not require reduction of attributes at each new level. Additionally, the algorithm exhibits lower sensitivity to parametric values and yields results in fewer iterations. Thus, its potential impact on decision-making processes is readily apparent.
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Affiliation(s)
- Tanzeela Shaheen
- Department of Mathematics, Air University, PAF Complex E-9 Islamabad, 44230, Pakistan
| | - Hamrah Batool Khan
- Department of Mathematics, Air University, PAF Complex E-9 Islamabad, 44230, Pakistan
| | - Wajid Ali
- Department of Mathematics, Air University, PAF Complex E-9 Islamabad, 44230, Pakistan
| | - Shaheryar Najam
- Department of Electrical Engineering, Riphah International University, Islamabad, Pakistan
| | - Md. Zia Uddin
- Software and Service Innovation, SINTEF Digital, Oslo, 0373, Norway
| | - Mohammad Mehedi Hassan
- Information Systems Department, College of Computer and Information Sciences, King Saud University, Riyadh, 11543, Saudi Arabia
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Hao F, Gao J, Bisogni C, Loia V, Pei Z, Nasridinov A. Exploring invariance of concept stability for attribute reduction in three-way concept lattice. Soft comput 2022. [DOI: 10.1007/s00500-022-07671-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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3
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Huang J, Lin Y, Li J. Rule reductions of decision formal context based on mixed information. APPL INTELL 2022. [DOI: 10.1007/s10489-022-04194-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Wang Z, Qi J, Shi C, Ren R, Wei L. Multiview granular data analytics based on three-way concept analysis. APPL INTELL 2022. [DOI: 10.1007/s10489-022-04145-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
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5
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Knowledge points navigation based on three-way concept lattice for autonomous learning. Pattern Recognit Lett 2022. [DOI: 10.1016/j.patrec.2022.10.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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6
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A constructing approach to multi-granularity object-induced three-way concept lattices. Int J Approx Reason 2022. [DOI: 10.1016/j.ijar.2022.08.017] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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7
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Neighborhood based concept lattice. APPL INTELL 2022. [DOI: 10.1007/s10489-022-03828-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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8
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Lattice-theoretic three-way formal contexts and their concepts. Soft comput 2022. [DOI: 10.1007/s00500-022-07294-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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9
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Yan M, Li J. Knowledge discovery and updating under the evolution of network formal contexts based on three-way decision. Inf Sci (N Y) 2022. [DOI: 10.1016/j.ins.2022.04.010] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
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10
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Chen Y, Zhu P. Three-way recommendation for a node and a community on social networks. INT J MACH LEARN CYB 2022. [DOI: 10.1007/s13042-022-01571-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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11
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The updating methods of object-induced three-way concept in dynamic formal contexts. APPL INTELL 2022. [DOI: 10.1007/s10489-022-03646-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
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12
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Zhai Y, Qi J, Li D, Zhang C, Xu W. The structure theorem of three-way concept lattice. Int J Approx Reason 2022. [DOI: 10.1016/j.ijar.2022.04.007] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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13
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A heuristic concept construction approach to collaborative recommendation. Int J Approx Reason 2022. [DOI: 10.1016/j.ijar.2022.04.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Hao F, Yang Y, Min G, Loia V. Incremental construction of three-way concept lattice for knowledge discovery in social networks. Inf Sci (N Y) 2021. [DOI: 10.1016/j.ins.2021.07.031] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Qian T, Yang Y, He X. The Feature Description of Formal Context Based on the Relationships among Concept Lattices. ENTROPY 2021; 23:e23111397. [PMID: 34828095 PMCID: PMC8625367 DOI: 10.3390/e23111397] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/11/2021] [Revised: 10/17/2021] [Accepted: 10/20/2021] [Indexed: 11/16/2022]
Abstract
Three-way concept analysis (3WCA) is extended research of formal concept analysis (FCA) by combining three-way decision. The three-way object oriented concept lattice (OEOL) is one of the important data structures which integrates rough set, concept lattice and three-way decision in 3WCA. In the paper, we investigate the characteristics of formal context based on the isomorphic relationship among the kinds of concept lattices with OEOL. Firstly, II-dual intersectable attributes and II-dual intersectable context are proposed and the relationship between the type I-dual intersectable context(dual intersectable context) and the type II-dual intersectable context are studied. In addition, the relationship among the kinds of concept lattices with OEOL are studied when the formal context is both I-dual intersectable context and II-dual intersectable context. Finally, the inverse problems of the above conclusions are discussed and the following two conclusions are obtained: (1) the formal context is the type II-dual intersectable context, when the object oriented concept lattice and OEOL are isomorphic. (2) In addition, the formal context is the type I-dual intersectable context, when the concept lattice and OEOL are anti-isomorphic.
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Affiliation(s)
- Ting Qian
- College of Science, Xi’an Shiyou University, Xi’an 710065, China;
- Correspondence:
| | - Yongwei Yang
- School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, China;
| | - Xiaoli He
- College of Science, Xi’an Shiyou University, Xi’an 710065, China;
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Yang H, Qin K. Neutrosophic three-way concept lattice and its application in conflict analysis. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2021. [DOI: 10.3233/jifs-210481] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
The theory of three-way concept analysis has been developed into an effective tool for data analysis and knowledge discovery. In this paper, we propose neutrosophic three-way concept lattice by combining neutrosophic set with three-way concept analysis and present an approach for conflict analysis by using neutrosophic three-way concept lattice. Firstly, we propose the notion of neutrosophic formal context, in which the relationships between objects and attributes are expressed by neutrosophic numbers. Three pairs of concept derivation operators are proposed. The basic properties of object-induced and attribute-induced neutrosophic three-way concept lattices are examined. Secondly, we divide the neutrosophic formal context into three classical formal contexts and propose the notions of the candidate neutrosophic three-way concepts and the redundant neutrosophic three-way concepts. Two approaches of constructing object-induced (attribute-induced) neutrosophic three-way concept lattices are presented by using candidate, redundant and original neutrosophic three-way concepts respectively. Finally, we apply the neutrosophic formal concept analysis to the conflict analysis and put forward the corresponding optimal strategy and the calculation method of the alliance.
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Affiliation(s)
- Han Yang
- College of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan, PR China
| | - Keyun Qin
- College of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan, PR China
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Hao F, Gao J, Bisogni C, Min G, Loia V, De Maio C. Stability of three-way concepts and its application to natural language generation. Pattern Recognit Lett 2021. [DOI: 10.1016/j.patrec.2021.06.005] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Zhang C, Li J, Lin Y. Matrix-based reduction approach for one-sided fuzzy three-way concept lattices. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2021. [DOI: 10.3233/jifs-202573] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Three-way concept analysis is a mathematical model of the combination of formal concept analysis and three-way decision, and knowledge discovery plays a significant impact on formal fuzzy contexts since such datasets are frequently encountered in real life. In this paper, a novel type of one-sided fuzzy three-way concept lattices is presented in a given formal fuzzy context with its complement, in which a ternary classification is available. In such case, we comprehensively explore the connections between the proposed models and classical fuzzy concept lattices among elements, sets, and orders. Furthermore, approaches to granular matrix-based reductions are investigated, by which granular consistent sets, and granular reducts via discernibility Boolean matrices are tectonically put forward. At last, the demonstrated results are performed by several experiments which enrich the research of three-way concept analysis.
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Affiliation(s)
- Chengling Zhang
- School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, China
| | - Jinjin Li
- School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, China
| | - Yidong Lin
- School of Mathematical Sciences, Xiamen University, Xiamen, China
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