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Fang H, Mahmood T, Ali Z, Zeng S, Jin Y. WASPAS method and Aczel-Alsina aggregation operators for managing complex interval-valued intuitionistic fuzzy information and their applications in decision-making. PeerJ Comput Sci 2023; 9:e1362. [PMID: 37346593 PMCID: PMC10280628 DOI: 10.7717/peerj-cs.1362] [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: 01/06/2023] [Accepted: 04/03/2023] [Indexed: 06/23/2023]
Abstract
Aczel-Alsina t-norm and t-conorm are a valuable and feasible technique to manage ambiguous and inconsistent information because of their dominant characteristics of broad parameter values. The main theme of this analysis is to explore Aczel-Alsina operational laws in the presence of the complex interval-valued intuitionistic fuzzy (CIVIF) set theory. Furthermore, we derive the theory of aggregation frameworks based on Aczel-Alsina operational laws for managing the theory of CIVIF information. The CIVIF Aczel-Alsina weighted averaging (CIVIFAAWA), CIVIF Aczel-Alsina ordered weighted averaging (CIVIFAAOWA), CIVIF Aczel-Alsina hybrid averaging (CIVIFAAHA), CIVIF Aczel-Alsina weighted geometric (CIVIFAAWG), CIVIF Aczel-Alsina ordered weighted geometric (CIVIFAAOWG) and CIVIF Aczel-Alsina hybrid geometric (CIVIFAAHG) operators are proposed, and their well-known properties and particular cases are also detailly derived. Further, we derive the theory of the WASPAS method for CIVIF information and evaluate their positive and negative aspects. Additionally, we demonstrate the multi-attribute decision-making (MADM) strategy under the invented works. Finally, we express the supremacy and dominancy of the invented methods with the help of sensitive analysis and geometrical shown of the explored works.
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Affiliation(s)
- Haojun Fang
- Wuxi Vocational College of Science and Technology, Wuxi, China
| | - Tahir Mahmood
- International Islamic University Islamabad, Islamabad, Pakistan
| | - Zeeshan Ali
- International Islamic University Islamabad, Islamabad, Pakistan
| | - Shouzhen Zeng
- Ningbo University, Ningbo, China
- Zhejiang Gongshang University, Hangzhou, China
| | - Yun Jin
- Wuxi Vocational College of Science and Technology, Wuxi, China
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Firouzkouhi N, Amini A, Nazari M, Alkhatib F, Bordbar H, Cheng C, Davvaz B, Rashidi M. Advanced artificial intelligence system by intuitionistic fuzzy $$\Gamma$$-subring for automotive robotic manufacturing. Artif Intell Rev 2023. [DOI: 10.1007/s10462-023-10396-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/09/2023]
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3
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Luo Z, Hu J, Zhang Q, Wang G. Induction of interval shadowed sets from the perspective of maintaining fuzziness. Int J Approx Reason 2023. [DOI: 10.1016/j.ijar.2022.11.019] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
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4
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On shadowed set approximation methods. Soft comput 2023. [DOI: 10.1007/s00500-023-07821-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
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Bai W, Zhang C, Zhai Y, Sangaiah AK. Incomplete intuitionistic fuzzy behavioral group decision-making based on multigranulation probabilistic rough sets and MULTIMOORA for water quality inspection. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2022. [DOI: 10.3233/jifs-222385] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
Water quality inspection (WQI) is one of the primary ways to ensure the safe utilization of water resources, and complicated data modeling, fusion and analysis play a significant role in seeking the resource with the best water quality. Nevertheless, the challenges of missing data, relatively large differences in decision results and bounded rationality owned by decision-makers (DMs) in terms of WQI still exist nowadays. Thus, from the aspect of stable and behavioral decision-making in multi-granularity incomplete intuitionistic fuzzy information systems (MG-IIFISs), the paper investigates a comprehensive multi-attribute group decision-making (MAGDM) approach for the application of WQI. First, the concept of MG-IIFISs is built by modeling MAGDM problems with intuitionistic fuzzy numbers (IFNs), then a new transformation scheme is constructed for transforming MG-IIFISs into multi-granularity intuitionistic fuzzy information systems (MG-IFISs) based on the similarity principle. Second, three types of multigranulation intuitionistic fuzzy probabilistic rough sets (MG IF PRSs) are developed by referring to the MULTIMOORA (Multi-Objective Optimization by Ratio Analysis plus the full MULTIplicative form) method. Afterwards, attribute weights are objectively calculated based on the best-worst method (BWM), and a new stable and behavioral MAGDM approach is constructed by means of the TODIM (an acronym in Portuguese for interactive multi-criteria decision-making) method. At last, a case study in the setting of WQI is conducted with the support of a UCI data set, and sensitivity analysis, comparative analysis and experimental analysis are investigated to display the validity of the proposed approach. In general, the proposed approach improves the stability of decision results via MULTIMOORA and BWM, and also fully considers the bounded rationality of DMs’ psychological behaviors from the aspect of the TODIM method, which has certain advantages in the community of MAGDM studies.
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Affiliation(s)
- Wenhui Bai
- School of Computer and Information Technology, Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, Shanxi University, Taiyuan, 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, Shanxi, China
| | - Yanhui Zhai
- School of Computer and Information Technology, Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, Shanxi University, Taiyuan, Shanxi, China
| | - Arun Kumar Sangaiah
- International Graduate Institute of Artificial Intelligence, National Yunlin University of Science andTechnology, Taiwan
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6
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Parameterized maximum-entropy-based three-way approximate attribute reduction. Int J Approx Reason 2022. [DOI: 10.1016/j.ijar.2022.09.007] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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7
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Yue X, Liu S, Qian Q, Miao D, Gao C. Semi-supervised shadowed sets for three-way classification on partial labeled data. Inf Sci (N Y) 2022. [DOI: 10.1016/j.ins.2022.06.062] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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8
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Khan M, Anis S, Zuev S, Ullah H, Zeeshan M. An algorithm for identifying reference signals under the environment of complex fuzzy sets. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2022. [DOI: 10.3233/jifs-220517] [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
In this paper, we have discussed some new operations and results of set theory for complex fuzzy sets (CFSs). Moreover, we developed the basic results of CFSs under the basic operations such as complex fuzzy simple difference, bounded sum, bounded difference, dot product, bounded product, union, intersection, and Cartesian product. We explored the CFSs and discussed the related properties with examples such as complex fuzzy bounded sum over the intersection, complex fuzzy dot product over the union, etc. Identifying the reference signals under the environment of CFSs have always been a challenging. Many algorithms based on set theoretic operations and distance measures have been proposed for identifying a reference signal using any common system. But linear time invariant (LTI) system is considered easy to analyze the linear and time-varying signals. We used CFSs in signals and systems. We developed an algorithm based on convolution product and LTI system under the complex fuzzy environment. We identified a high degree of resemblance (reference signal) of the received signals to the reference signal in a linear time-invariant (LTI) system that receives an input signal and produces an output signal.
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Affiliation(s)
- Madad Khan
- Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Pakistan
| | - Saima Anis
- Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Pakistan
| | - Sergei Zuev
- Department of Computer Science and Automated Systems, Belgorod Shoukhov State University of Technology, Belgorod, Russia
| | - Hikmat Ullah
- Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Pakistan
| | - Muhammad Zeeshan
- Department of Mathematics, COMSATS University Islamabad, Islmabad Campus, Pakistan; Department of Mathematics, The University of Agriculture, Dera Ismail Khan, Pakistan
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Ali Z, Mahmood T, Panityakul T. Power Bonferroni mean operators under complex pythagorean fuzzy settings and their applications in decision-making problems. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2022. [DOI: 10.3233/jifs-212546] [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
Bonferroni means (BM) operator is the extended form of the arithmetic mean operator, used for simplifying non-dominant and non-feasible problems diagnosed in genuine life scenarios. A lot of aggregation operators are the specific parts of the BM operators under the consideration of different values of parameters which are the main parts of the BM operators. In the presence of the BM operator and a very well-known conception in the scenario of fuzzy set, called complex Pythagorean fuzzy (CPF) setting, the objective of this scenario is to diagnose the CPF power BM (CPFPBM) operator and utilize their beneficial results with important properties. Moreover, a multi-attribute decision-making (MADM) technique is evaluated in the presence of invented operators for CPF settings. In the last of this study, we diagnosed the superiority and efficiency of the invented works with the help of sensitive analysis and graphical illustrations to enhance the gap of the research works.
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Affiliation(s)
- Zeeshan Ali
- Department of Mathematics & Statistics, International Islamic University Islamabad, Pakistan
| | - Tahir Mahmood
- Department of Mathematics & Statistics, International Islamic University Islamabad, Pakistan
| | - Thammarat Panityakul
- Division of Computational Science, Faculty ofScience, Prince of Songkla University, Hat Yai, Songkhla, Thailand
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Xiao J, Zhang Q, Ai Z, Wang G. A fast neighborhood classifier based on hash bucket with application to medical diagnosis. Int J Approx Reason 2022. [DOI: 10.1016/j.ijar.2022.05.012] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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13
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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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14
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A New Item-Based Collaborative Filtering Algorithm to Improve the Accuracy of Prediction in Sparse Data. INT J COMPUT INT SYS 2022. [DOI: 10.1007/s44196-022-00068-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022] Open
Abstract
AbstractIn memory-based collaborative filtering (CF) algorithms, the similarity and prediction method have a significant impact on the recommendation results. Most of the existing recommendation techniques have improved different similarity measures to alleviate inaccurate similarity results in sparse data, however, ignored the impact of sparse data on prediction results. To enhance the adaptability to sparse data, we propose a new item-based CF algorithm, which consists of the item similarity measure based vague sets and item-based prediction method with the new neighbor selection strategy. First, in the stage of similarity calculation, the Kullback–Leibler (KL) divergence based on vague sets is proposed from the perspective of user preference probability to measure item similarity. Following this, the impact of rating quantity is further considered to improve the accuracy of similarity results. Next, in the prediction stage, we relax the limit of depending on explicitly ratings and integrate more rating information to adjust prediction results. Experimental results on benchmark data sets show that, compared with other representative algorithms, our algorithm has better prediction and recommendation quality, and effectively alleviates the data sparseness problem.
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Zhang X, Chen J. Three-hierarchical three-way decision models for conflict analysis: A qualitative improvement and a quantitative extension. Inf Sci (N Y) 2022. [DOI: 10.1016/j.ins.2021.12.012] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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16
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Yao Y, Yang J. Granular rough sets and granular shadowed sets: Three-way approximations in Pawlak approximation spaces. Int J Approx Reason 2022. [DOI: 10.1016/j.ijar.2021.11.012] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
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17
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Zhu J, Ma X, Zhan J. A regret theory-based three-way decision approach with three strategies. Inf Sci (N Y) 2022. [DOI: 10.1016/j.ins.2022.02.030] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
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20
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Power Muirhead Mean Operators for Interval-Valued Linear Diophantine Fuzzy Sets and Their Application in Decision-Making Strategies. MATHEMATICS 2021. [DOI: 10.3390/math10010070] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
It is quite beneficial for every company to have a strong decision-making technique at their disposal. Experts and managers involved in decision-making strategies would particularly benefit from such a technique in order to have a crucial impact on the strategy of their company. This paper considers the interval-valued linear Diophantine fuzzy (IV-LDF) sets and uses their algebraic laws. Furthermore, by using the Muirhead mean (MM) operator and IV-LDF data, the IV-LDF power MM (IV-LDFPMM) and the IV-LDF weighted power MM (IV-LDFWPMM) operators are developed, and some special properties and results demonstrated. The decision-making technique relies on objective data that can be observed. Based on the multi-attribute decision-making (MADM) technique, which is the beneficial part of the decision-making strategy, examples are given to illustrate the development. To demonstrate the advantages of the developed tools, a comparative analysis and geometrical interpretations are also provided.
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21
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Zhang WR. Science vs. Sophistry—A historical debate on bipolar fuzzy sets and equilibrium-based mathematics for AI&QI. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2021. [DOI: 10.3233/jifs-210692] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Abstract
The road from bipolar fuzzy sets to equilibrium-based mathematical abstraction is surveyed. A continuing historical debate on bipolarity and isomorphism is outlined. Related literatures are critically reviewed to counter plagiarism, distortion, renaming, and sophistry. Based on the debate, the term “isomorphistry” is coined. It is concluded that if isomorphism is used correctly it can be helpful in mathematics. If abused it may become isomorphistry—a kind of historical, socially constructed, entrenched, and “noble” hypocrisy hindering major scientific advances. It is shown that isomorphistry can be motivated by “denying” the originality of bipolar fuzzy sets and aimed at “justifying” plagiarism and distortion. Thus, isomorphistry is sophistry on isomorphism. Some (-,+)-bipolar isomorphistry behaviors are critiqued. YinYang vs. YangYin are distinguished. The geometrical and logical basis of equilibrium-based AI&QI computing machinery is introduced as a new computing paradigm with logically definable causality for mind-body unity. A philosophical joke on sophistry is appended.
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Affiliation(s)
- Wen-Ran Zhang
- Department of Computer Science, Georgia Southern University, Statesboro, GA, USA
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22
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Gandotra N, Kizielewicz B, Anand A, Bączkiewicz A, Shekhovtsov A, Wątróbski J, Rezaei A, Sałabun W. New Pythagorean Entropy Measure with Application in Multi-Criteria Decision Analysis. ENTROPY (BASEL, SWITZERLAND) 2021; 23:1600. [PMID: 34945906 PMCID: PMC8700080 DOI: 10.3390/e23121600] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/04/2021] [Revised: 11/16/2021] [Accepted: 11/26/2021] [Indexed: 11/17/2022]
Abstract
The purpose of this paper is to propose a new Pythagorean fuzzy entropy for Pythagorean fuzzy sets, which is a continuation of the Pythagorean fuzzy entropy of intuitionistic sets. The Pythagorean fuzzy set continues the intuitionistic fuzzy set with the additional advantage that it is well equipped to overcome its imperfections. Its entropy determines the quantity of information in the Pythagorean fuzzy set. Thus, the proposed entropy provides a new flexible tool that is particularly useful in complex multi-criteria problems where uncertain data and inaccurate information are considered. The performance of the introduced method is illustrated in a real-life case study, including a multi-criteria company selection problem. In this example, we provide a numerical illustration to distinguish the entropy measure proposed from some existing entropies used for Pythagorean fuzzy sets and intuitionistic fuzzy sets. Statistical illustrations show that the proposed entropy measures are reliable for demonstrating the degree of fuzziness of both Pythagorean fuzzy set (PFS) and intuitionistic fuzzy sets (IFS). In addition, a multi-criteria decision-making method complex proportional assessment (COPRAS) was also proposed with weights calculated based on the proposed new entropy measure. Finally, to validate the reliability of the results obtained using the proposed entropy, a comparative analysis was performed with a set of carefully selected reference methods containing other generally used entropy measurement methods. The illustrated numerical example proves that the calculation results of the proposed new method are similar to those of several other up-to-date methods.
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Affiliation(s)
- Neeraj Gandotra
- Yogananda School of AI, Computers and Data Science, Shoolini University, Solan 173229, Himachal Pradesh, India; (N.G.); (A.A.)
| | - Bartłomiej Kizielewicz
- Research Team on Intelligent Decision Support Systems, Department of Artificial Intelligence and Applied Mathematics, Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin, ul. Żołnierska 49, 71-210 Szczecin, Poland; (B.K.); (A.S.)
| | - Abhimanyu Anand
- Yogananda School of AI, Computers and Data Science, Shoolini University, Solan 173229, Himachal Pradesh, India; (N.G.); (A.A.)
| | - Aleksandra Bączkiewicz
- Institute of Management, University of Szczecin, ul. Cukrowa 8, 71-004 Szczecin, Poland; (A.B.); (J.W.)
- Doctoral School of University of Szczecin, ul. Mickiewicza 16, 70-383 Szczecin, Poland
| | - Andrii Shekhovtsov
- Research Team on Intelligent Decision Support Systems, Department of Artificial Intelligence and Applied Mathematics, Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin, ul. Żołnierska 49, 71-210 Szczecin, Poland; (B.K.); (A.S.)
| | - Jarosław Wątróbski
- Institute of Management, University of Szczecin, ul. Cukrowa 8, 71-004 Szczecin, Poland; (A.B.); (J.W.)
| | - Akbar Rezaei
- Department of Mathematics, Payame Noor University, Tehran P. O. Box 19395-3697, Iran;
| | - Wojciech Sałabun
- Research Team on Intelligent Decision Support Systems, Department of Artificial Intelligence and Applied Mathematics, Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin, ul. Żołnierska 49, 71-210 Szczecin, Poland; (B.K.); (A.S.)
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Gao C, Zhou J, Miao D, Yue X, Wan J. Granular-conditional-entropy-based attribute reduction for partially labeled data with proxy labels. Inf Sci (N Y) 2021. [DOI: 10.1016/j.ins.2021.08.067] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
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Power Aggregation Operators Based on t-Norm and t-Conorm under the Complex Intuitionistic Fuzzy Soft Settings and Their Application in Multi-Attribute Decision Making. Symmetry (Basel) 2021. [DOI: 10.3390/sym13111986] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Multi-attribute decision-making (MADM) is commonly used to investigate fuzzy information effectively. However, selecting the best alternative information is not always symmetric because the alternatives do not have complete information, so asymmetric information is often involved. In this analysis, we use the massive dominant and more consistent principle of power aggregation operators (PAOs) based on general t-norm and t-conorm, which manage awkward and inconsistent data in real-world dilemmas such as medical diagnosis, pattern recognition, cleaner production evaluation in gold mines, the analysis of the cancer risk factor, etc. The principle of averaging, geometric, Einstein, and Hamacher aggregation operators are specific cases of generalized PAOs. We combine the principle of complex intuitionistic fuzzy soft (CIFS) information with PAOs to initiate CIFS power averaging (CIFSPA), CIFS weighted power averaging (CIFSWPA), CIFS ordered weighted power averaging (CIFSOWPA), CIFS power geometric (CIFSPG), CIFS weighted power geometric (CIFSWPG), and CIFS ordered weighted power geometric (CIFSOWPG), and their flexible laws are elaborated. Certain specific cases (such as averaging, Einstein, and Hamacher operators) of the explored operators are also illustrated with the help of different t-norm and t-conorm operators. A MADM process is presented under the developed operators based on the CIFS environment. Finally, to investigate the supremacy of the demonstrated works, we employed a sensitivity analysis and geometrical expressions of the initiated operators with numerous prevailing works to verify the efficiency of the proposed works. This manuscript shows how to make decisions when there is asymmetric information about enterprises.
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Three-Way Multi-Attribute Decision Making Based on Outranking Relations under Intuitionistic Fuzzy Environments. Symmetry (Basel) 2021. [DOI: 10.3390/sym13081384] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
With the increasing complexity of the human social environment, it is impossible to describe each object in detail with accurate numbers when solving multiple attribute decision-making (MADM) problems. Compared with the fuzzy set (FS), the intuitionistic fuzzy set (IFS) not only has obvious advantages in allocating ambiguous values to the object to be considered, but also takes into account the degree of membership and non-membership, so it is more suitable for decision makers (DMs) to deal with complex realistic problems. Therefore, it is of great significance to propose a MADM method under an intuitionistic fuzzy environment. Moreover, compared with the traditional 2WD, by putting forward the option of delay, the decision-making risk can be effectively reduced using three-way decision (3WD). In addition, the binary relations between objects in the decision-making process have been continuously generalized, such as equivalence relation which have symmetrical relationship, dominance relation and outranking relation, which are worthy of study. In this paper, we propose 3WD-MADM method based on IF environment and the objective IFS is calculated by using the information table. Then, the hybrid information table is used to solve the supplier selection problem to demonstrate the effectiveness of the proposed method.
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