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Ding J, Zhang C, Li D, Zhan J, Li W, Yao Y. Three-way decisions in generalized intuitionistic fuzzy environments: survey and challenges. Artif Intell Rev 2024; 57:38. [PMID: 38333110 PMCID: PMC10847217 DOI: 10.1007/s10462-023-10647-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/10/2024]
Abstract
Enhancing decision-making under risks is crucial in various fields, and three-way decision (3WD) methods have been extensively utilized and proven to be effective in numerous scenarios. However, traditional methods may not be sufficient when addressing intricate decision-making scenarios characterized by uncertain and ambiguous information. In response to this challenge, the generalized intuitionistic fuzzy set (IFS) theory extends the conventional fuzzy set theory by introducing two pivotal concepts, i.e., membership degrees and non-membership degrees. These concepts offer a more comprehensive means of portraying the relationship between elements and fuzzy concepts, thereby boosting the ability to model complex problems. The generalized IFS theory brings about heightened flexibility and precision in problem-solving, allowing for a more thorough and accurate description of intricate phenomena. Consequently, the generalized IFS theory emerges as a more refined tool for articulating fuzzy phenomena. The paper offers a thorough review of the research advancements made in 3WD methods within the context of generalized intuitionistic fuzzy (IF) environments. First, the paper summarizes fundamental aspects of 3WD methods and the IFS theory. Second, the paper discusses the latest development trends, including the application of these methods in new fields and the development of new hybrid methods. Furthermore, the paper analyzes the strengths and weaknesses of research methods employed in recent years. While these methods have yielded impressive outcomes in decision-making, there are still some limitations and challenges that need to be addressed. Finally, the paper proposes key challenges and future research directions. Overall, the paper offers a comprehensive and insightful review of the latest research progress on 3WD methods in generalized IF environments, which can provide guidance for scholars and engineers in the intelligent decision-making field with situations characterized by various uncertainties.
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Affiliation(s)
- Juanjuan Ding
- School of Computer and Information Technology, Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, Shanxi University, Taiyuan, 030006 Shanxi China
| | - Chao Zhang
- School of Computer and Information Technology, Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, Shanxi University, Taiyuan, 030006 Shanxi China
| | - Deyu Li
- School of Computer and Information Technology, Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, Shanxi University, Taiyuan, 030006 Shanxi China
| | - Jianming Zhan
- School of Mathematics and Statistics, Hubei Minzu University, Enshi, 445000 Hubei China
| | - Wentao Li
- School of Computer and Information Technology, Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, Shanxi University, Taiyuan, 030006 Shanxi China
- College of Artificial Intelligence, Southwest University, Chongqing, 400715 China
| | - Yiyu Yao
- Department of Computer Science, University of Regina, Regina, Saskatchewan S4S 0A2 Canada
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Ding W, Li X, Shen X. Three-way group decisions using evidence theory under hesitant fuzzy linguistic environment. Sci Rep 2023; 13:22766. [PMID: 38123581 PMCID: PMC10733337 DOI: 10.1038/s41598-023-49086-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2023] [Accepted: 12/04/2023] [Indexed: 12/23/2023] Open
Abstract
In the actual decision-making process, there will be situations where decision-makers with hesitant attitudes have difficulties in evaluating alternatives numerically, and hesitant fuzzy linguistic term sets can provide decision-makers with an effective way to describe hesitancy in linguistic terms. In multi-attribute group decision-making, each decision maker typically holds different preferences. If the variation in decision makers' assessment weights across evaluations of each attribute for every alternative is not adequately accounted for, it can result in a problem of coarse-grained calculations, leading to information loss. Additionally, the three-way decision model faces significant challenges in information fusion within the context of the hesitant fuzzy linguistic environment. Therefore, we propose a new three-way decision-making model under the hesitant fuzzy linguistic environment. The model obtains the confidence of different decision makers in attribute evaluations through the fusion of D-S evidence theory, and can perform more fine-grained fusion calculations on the evaluation information of different decision makers. In addition, the model considers the cost function of each alternative in different decision-making actions under hesitant fuzzy linguistic environment, calculates the two thresholds of each alternative in the three-way decision model, and derives the decision rules. The effectiveness of the model is verified through a numerical example and two comparative experiments, therefore, the model can be applied in intelligent classification or recommendation systems of hesitant fuzzy linguistic information systems.
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Affiliation(s)
- Wenke Ding
- School of Computer and Information Engineering, Henan University, Kaifeng, 475004, China
- Henan Engineering Research Center of Intelligent Technology and Application, Henan University, Kaifeng, 475004, China
| | - Xingchen Li
- School of Computer and Information Engineering, Henan University, Kaifeng, 475004, China.
| | - Xiajiong Shen
- School of Computer and Information Engineering, Henan University, Kaifeng, 475004, China
- Henan Engineering Research Center of Intelligent Technology and Application, Henan University, Kaifeng, 475004, China
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Three-way decision for probabilistic linguistic conflict analysis via compounded risk preference. Inf Sci (N Y) 2023. [DOI: 10.1016/j.ins.2023.02.067] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/05/2023]
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Zhong Y, Wu P, Chen C, Min C, Yong X. A three-way decisions approach based on double hierarchy linguistic aggregation operators of strict t-norms and t-conorms. INT J MACH LEARN CYB 2023; 14:1-24. [PMID: 37360882 PMCID: PMC10131538 DOI: 10.1007/s13042-023-01832-7] [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: 07/15/2022] [Accepted: 04/06/2023] [Indexed: 06/28/2023]
Abstract
With the massive increase in uncertainty of linguistic information in realistic decision making, there is a great challenge for people to make decisions in the complex linguistic environment. To overcome this challenge, this paper proposes a three-way decisions method based on aggregation operators of strict t-norms and t-conorms under double hierarchy linguistic environment. By mining the double hierarchy linguistic information, strict t-norms and t-conorms are introduced to define the operation rules and their operation examples are also given. Then, the double hierarchy linguistic weighted average (DHLWA) operator and weighted geometric (DHLWG) operator are proposed based on strict t-norms and t-conorms. Besides, some of their important properties are also proved and derived, such as idempotency, boundedness and monotonicity. Next, DHLWA and DHLWG are integrated with three-way decisions to construct our three-way decisions model. Specifically, the double hierarchy linguistic decision theoretic rough set (DHLDTRS) model is constructed by incorporating the computational model of expected loss with DHLWA and DHLWG, which can consider the various decision attitudes from decision makers more adequately. Furthermore, we also propose a novel entropy weight calculation formula to improve the entropy weight method for obtaining the weights more objectively, and integrate grey relational analysis (GRA) method to calculate the conditional probability. Based on the Bayesian minimum-loss decision rules, the solving method of our model is also propounded and the corresponding algorithm is designed. Finally, an illustrative example and experimental analysis are presented, which can validate the rationality, robustness as well as superiority of our method.
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Affiliation(s)
- Yihua Zhong
- School of Science, Southwest Petroleum University, Chendu, 610500 Sichuan China
- Institute for Artificial Intelligence, Southwest Petroleum University, Chendu, 610500 Sichuan China
| | - Ping Wu
- School of Science, Southwest Petroleum University, Chendu, 610500 Sichuan China
| | - Chuan Chen
- School of Science, Southwest Petroleum University, Chendu, 610500 Sichuan China
| | - Chao Min
- School of Science, Southwest Petroleum University, Chendu, 610500 Sichuan China
- Institute for Artificial Intelligence, Southwest Petroleum University, Chendu, 610500 Sichuan China
| | - Xue Yong
- School of Science, Southwest Petroleum University, Chendu, 610500 Sichuan China
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5
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The movement strategy of three-way decisions based on clustering. Inf Sci (N Y) 2023. [DOI: 10.1016/j.ins.2023.01.015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
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Zhan J, Wang W, R. Alcantud JC, Zhan J. A three-way decision approach with prospect-regret theory via fuzzy set pair dominance degrees for incomplete information systems. Inf Sci (N Y) 2022. [DOI: 10.1016/j.ins.2022.10.107] [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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7
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Deng J, Zhan J, Ding W, Liu P, Pedrycz W. A novel prospect-theory-based three-way decision methodology in multi-scale information systems. Artif Intell Rev 2022. [DOI: 10.1007/s10462-022-10339-6] [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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8
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Three-way conflict analysis based on interval-valued Pythagorean fuzzy sets and prospect theory. Artif Intell Rev 2022. [DOI: 10.1007/s10462-022-10327-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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9
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Wei J, Liu X, Fan W. Dynamic sparse portfolio rebalancing model: A perspective of investors’ behavior-related decisions. Knowl Based Syst 2022. [DOI: 10.1016/j.knosys.2022.109224] [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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A three-way decision method with prospect theory to multi-attribute decision-making and its applications under hesitant fuzzy environments. Appl Soft Comput 2022. [DOI: 10.1016/j.asoc.2022.109283] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
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11
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Adaptive intelligent autonomous system using artificial somatic markers and Big Five personality traits. Knowl Based Syst 2022. [DOI: 10.1016/j.knosys.2022.108995] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Zhu J, Ma X, Zhan J, Yao Y. A three-way multi-attribute decision making method based on regret theory and its application to medical data in fuzzy environments. Appl Soft Comput 2022. [DOI: 10.1016/j.asoc.2022.108975] [Citation(s) in RCA: 2] [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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13
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Wu M, Wang X, Fan J. A multiple attribute decision-making three-way model at four-branch fuzzy environment. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2022. [DOI: 10.3233/jifs-212097] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Three-way decisions (TWDs) theory is one of the core ideas of decision-theoretic rough sets (DTRSs). Reviewing the existing research results, we find that TWDs provides us with more flexible decision choices. And the traditional fuzzy number does not take into account the absence of information (indifference) in the evaluation process. In order to construct a new model which can get flexible decision results in complex decision environment, we introduce four-branch fuzzy numbers (FBFNs) to describe the evaluation information, so that the decision-makers can express the evaluation information more comprehensively. In this paper, a novel TWDs model in four-branch fuzzy environment is proposed to solve multiple-attribute decision-making (MADM) problem. The first challenge is to construct a TWDs model based on FBFNs and to develop a new linguistic interpretation of the loss functions. Then, we extend a method for aggregating the loss functions obtained from the attribute evaluation values. Finally, we use the nonlinear solution to solve the threshold, and apply TOPSIS method to solve the conditional probability of FBFNs. The effectiveness of this method is illustrated by an example, and the decision results are compared with a MADM method based on OWGA operator.
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Affiliation(s)
- Meiqin Wu
- School of Economics and Management, Shanxi University, Taiyuan, China
| | - Xinsheng Wang
- School of Economics and Management, Shanxi University, Taiyuan, China
| | - Jianping Fan
- School of Economics and Management, Shanxi University, Taiyuan, China
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Wang H, Zhang Y, Bai C. A new three-way group decision-making model based on geometric heronian mean operators with q-rung orthopair uncertain linguistic information. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2022. [DOI: 10.3233/jifs-212327] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
As an effective tool for three-way decisions (3WD) problems, decision-theoretic rough sets (DTRSs) have raised increasing attention recently. In view of the advantages of q-rung orthopair uncertain linguistic variables (q-ROULVs) in depicting uncertain information, a new DTRSs model based on q-ROULVs is proposed to solve three-way group decision-making (3WGDM) problems. Firstly, the loss function of DTRSs is depicted by q-ROULVs and a q-rung orthopair uncertain linguistic DTRSs model is constructed subsequently. Secondly, to aggregate different experts’ evaluation results on loss function in group decision-making (GDM) scenario, the q-rung orthopair uncertain linguistic geometric Heronian mean (q-ROULGHM) operator and the q-rung orthopair uncertain linguistic weighted geometric Heronian mean (q-ROULWGHM) operator are presented. Related properties of the proposed operators are investigated. Thirdly, to compare the expected loss of each alternative, a new score function of q-ROULVs is defined and the corresponding decision rules for 3WGDM are deduced. Finally, an illustrative example of venture capital in high-tech projects is provided to verify the rationality and effectiveness of our method. The influence of different conditional probabilities and parameter values on decision results is comprehensively discussed.
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Affiliation(s)
- Huidong Wang
- School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan, China
| | - Yao Zhang
- School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan, China
| | - Chuanzheng Bai
- School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan, China
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16
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Interpretable systems based on evidential prospect theory for decision-making. APPL INTELL 2022. [DOI: 10.1007/s10489-022-03276-y] [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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17
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On three perspectives for deriving three-way decision with linguistic intuitionistic fuzzy information. Inf Sci (N Y) 2022. [DOI: 10.1016/j.ins.2021.12.072] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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18
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Huang X, Zhan J, Ding W, Pedrycz W. An error correction prediction model based on three-way decision and ensemble learning. Int J Approx Reason 2022. [DOI: 10.1016/j.ijar.2022.04.002] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
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19
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Wang J, Ma X, Xu Z, Zhan J. A three-way decision approach with risk strategies in hesitant fuzzy decision information systems. Inf Sci (N Y) 2022. [DOI: 10.1016/j.ins.2021.12.079] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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20
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Three-way multi-criteria group decision-making method in a fuzzy β-covering group approximation space. Inf Sci (N Y) 2022. [DOI: 10.1016/j.ins.2022.03.055] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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21
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22
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Three-way group consensus decision based on hierarchical social network consisting of decision makers and participants. Inf Sci (N Y) 2022. [DOI: 10.1016/j.ins.2021.11.057] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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23
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24
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Ye J, Zhan J, Ding W, Fujita H. A novel three-way decision approach in decision information systems. Inf Sci (N Y) 2022. [DOI: 10.1016/j.ins.2021.10.042] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
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25
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Huang X, Zhan J. TWD-R: A three-way decision approach based on regret theory in multi-scale decision information systems. Inf Sci (N Y) 2021. [DOI: 10.1016/j.ins.2021.10.014] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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26
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Wang J, Ma X, Dai J, Zhan J. A novel three-way decision approach under hesitant fuzzy information. Inf Sci (N Y) 2021. [DOI: 10.1016/j.ins.2021.07.054] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Zhang K, Dai J, Zhan J. A new classification and ranking decision method based on three-way decision theory and TOPSIS models. Inf Sci (N Y) 2021. [DOI: 10.1016/j.ins.2021.03.039] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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29
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Jiang H, Hu BQ. A novel three-way group investment decision model under intuitionistic fuzzy multi-attribute group decision-making environment. Inf Sci (N Y) 2021. [DOI: 10.1016/j.ins.2021.05.026] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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30
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Deng J, Zhan J, Wu WZ. A three-way decision methodology to multi-attribute decision-making in multi-scale decision information systems. Inf Sci (N Y) 2021. [DOI: 10.1016/j.ins.2021.03.058] [Citation(s) in RCA: 23] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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31
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32
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A Markov regime switching model for asset pricing and ambiguity measurement of stock market. Neurocomputing 2021. [DOI: 10.1016/j.neucom.2020.12.103] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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33
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Gao K, Yang Y, Zhang T, Li A, Qu X. Extrapolation-enhanced model for travel decision making: An ensemble machine learning approach considering behavioral theory. Knowl Based Syst 2021. [DOI: 10.1016/j.knosys.2021.106882] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
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