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Regularity Index of Uncertain Random Graph. Symmetry (Basel) 2023. [DOI: 10.3390/sym15010137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Abstract
A graph containing some edges with probability measures and other edges with uncertain measures is referred to as an uncertain random graph. Numerous real-world problems in social networks and transportation networks can be boiled down to optimization problems in uncertain random graphs. Actually, information in optimization problems in uncertain random graphs is always asymmetric. Regularization is a common optimization problem in graph theory, and the regularity index is a fundamentally measurable indicator of graphs. Therefore, this paper investigates the regularity index of an uncertain random graph within the framework of chance theory and information asymmetry theory. The concepts of k-regularity index and regularity index of the uncertain random graph are first presented on the basis of the chance theory. Then, in order to compute the k-regularity index and the regularity index of the uncertain random graph, a simple and straightforward calculating approach is presented and discussed. Furthermore, we discuss the relationship between the regularity index and the k-regularity index of the uncertain random graph. Additionally, an adjacency matrix-based algorithm that can compute the k-regularity index of the uncertain random graph is provided. Some specific examples are given to illustrate the proposed method and algorithm. Finally, we conclude by highlighting some potential applications of uncertain random graphs in social networks and transportation networks, as well as the future vision of its combination with symmetry.
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Li H, Zhang K. On the shortest path problem of uncertain random digraphs. Soft comput 2022; 26:9069-9081. [PMID: 35909949 PMCID: PMC9308943 DOI: 10.1007/s00500-022-07305-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 06/13/2022] [Indexed: 11/23/2022]
Abstract
In the field of graph theory, the shortest path problem is one of the most significant problems. However, since varieties of indeterminated factors appear in complex networks, determining of the shortest path from one vertex to another in complex networks may be a lot more complicated than the cases in deterministic networks. To illustrate this problem, the model of uncertain random digraph will be proposed via chance theory, in which some arcs exist with degrees in probability measure and others exist with degrees in uncertain measure. The main focus of this paper is to investigate the main properties of the shortest path in uncertain random digraph. Methods and algorithms are designed to calculate the distribution of shortest path more efficiently. Besides, some numerical examples are presented to show the efficiency of these methods and algorithms.
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Connectivity Index of Generalized Uncertain Graph. COMPUTATIONAL INTELLIGENCE AND NEUROSCIENCE 2022; 2022:4571530. [PMID: 35655500 PMCID: PMC9152379 DOI: 10.1155/2022/4571530] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/24/2022] [Revised: 03/26/2022] [Accepted: 04/12/2022] [Indexed: 11/18/2022]
Abstract
In the application of classical graph theory, there always are various indeterministic factors. This study studies the indeterministic factors in the connected graph by employing the uncertainty theory. First, this study puts forward two concepts: generalized uncertain graph and its connectivity index. Second, it presents a new algorithm to compute the connectivity index of an uncertain graph and generalized uncertain graph and verify this algorithm with typical examples. In addition, it proposes the definition and algorithm of α-connectivity index of generalized uncertain graph and verifies the stability and efficiency of this new algorithm by employing numerical experiments.
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On the significance of edges for connectivity in uncertain random graphs. Soft comput 2021; 25:8989-8997. [PMID: 34075307 PMCID: PMC8152216 DOI: 10.1007/s00500-021-05813-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 04/08/2021] [Indexed: 10/26/2022]
Abstract
In practical applications of graph theory, indeterminacy factors always appear in graphs. Uncertain random graph was proposed via chance theory, in which some edges exist with degrees in probability measure and others exist with degrees in uncertain measure. This paper discusses the contributions of edges for connectivity of an uncertain random graph and proposes concepts about significance of edges, according to which edges are classified. In addition, this paper presents algorithms for calculating connectivity index and significance of edges of an uncertain random graph. Examples are given to illustrate algorithms and methods.
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Uncertain programming models for multi-objective shortest path problem with uncertain parameters. Soft comput 2019. [DOI: 10.1007/s00500-019-04423-3] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Ma W, Liu Y, Zhang X. A new model and algorithm for uncertain random parallel machine scheduling problem. Soft comput 2019. [DOI: 10.1007/s00500-018-3304-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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Li S, Peng J, Zhang B. A Stock Model with Varying Stock Diffusion for Uncertain Market. INT J UNCERTAIN FUZZ 2018. [DOI: 10.1142/s0218488518500319] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The option-pricing problem is an important topic in modern finance. In this paper, we propose a stock model with varying stock diffusion based on uncertainty theory. The European option pricing formulas are derived from the proposed uncertain stock model, and some mathematical properties of these formulas are investigated. Moreover, extended uncertain stock models are introduced and discussed. Finally, numerical examples are given to illustrate the proposed model.
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Affiliation(s)
- Shengguo Li
- Institute of Uncertain Systems, Huanggang Normal University, Hubei 438000, China
- Hubei Key Laboratory of Applied Mathematics, Hubei 430062, China
| | - Jin Peng
- Institute of Uncertain Systems, Huanggang Normal University, Hubei 438000, China
- Hubei Key Laboratory of Applied Mathematics, Hubei 430062, China
| | - Bo Zhang
- School of Statistics and Mathematics, Zhongnan University of Economics and Law, Hubei 430073, China
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Chen L, Peng J, Rao C, Rosyida I. Cycle index of uncertain random graph. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2018. [DOI: 10.3233/jifs-17373] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Lin Chen
- College of Management and Economics, Tianjin University, Tianjin, China
| | - Jin Peng
- Institute of Uncertain System, Huanggang Normal University, Hubei, China
| | - Congjun Rao
- School of Science, Wuhan University of Technology, Hubei, China
| | - Isnaini Rosyida
- Department of Mathematics, Universitas Negeri Semarang, Semarang, Indonesia
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Guo Y, Tang W, Zhao R. The impacts of uncertain factors on decisions of NPO and firms. Appl Soft Comput 2017. [DOI: 10.1016/j.asoc.2016.06.015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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13
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Kar MB, Majumder S, Kar S, Pal T. Cross-entropy based multi-objective uncertain portfolio selection problem. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2017. [DOI: 10.3233/jifs-169212] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Mohuya B. Kar
- Department of Computer Science and Engineering, Heritage Institute of Technology, Kolkata, West Bengal, India
| | - Saibal Majumder
- Department of Computer Science and Engineering, National Institute of Technology, Durgapur, West Bengal, India
| | - Samarjit Kar
- Department of Mathematics, National Institute of Technology, Durgapur, West Bengal, India
| | - Tandra Pal
- Department of Computer Science and Engineering, National Institute of Technology, Durgapur, West Bengal, India
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Qin Z, Dai Y, Zheng H. Uncertain random portfolio optimization models based on value-at-risk. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2017. [DOI: 10.3233/jifs-169216] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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Ke H, Huang H, Gao X. Pricing decision problem in dual-channel supply chain based on experts’ belief degrees. Soft comput 2017. [DOI: 10.1007/s00500-017-2600-0] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Huang M, Ren L, Lee LH, Wang X, Kuang H, Shi H. Model and algorithm for 4PLRP with uncertain delivery time. Inf Sci (N Y) 2016. [DOI: 10.1016/j.ins.2015.10.030] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Wang L, Gao Z, Yang L. Criteria for the a Priori Shortest Path Generation in Uncertain Time-Varying Transportation Networks. INT J UNCERTAIN FUZZ 2015. [DOI: 10.1142/s021848851550035x] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
This paper proposes a new definition of uncertain time-varying network to capture the uncertain and dynamic characteristics of the network with discrete uncertain link travel times. To find the a priori non-dominated paths in this type of network, three comparison criteria based on the uncertain measure, namely, deterministic dominance rule, first-order uncertain dominance rule and uncertain expected value dominance rule, are proposed to generate non-dominated paths in a single time interval and a time period, as more than one path may exist between an origin and destination for a given departure time. The proposed comparison methods are then applied to solving a simple uncertain time-varying network. The computational results verify the efficiency of three dominance rules for finding non-dominated paths.
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Affiliation(s)
- Li Wang
- State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, 10004, China
| | - Ziyou Gao
- State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, 10004, China
| | - Lixing Yang
- State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, 10004, China
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