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Wang Z, Xiao F, Cao Z. Uncertainty measurements for Pythagorean fuzzy set and their applications in multiple-criteria decision making. Soft comput 2022. [DOI: 10.1007/s00500-022-07361-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
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2
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Multiple attribute group decision-making based on novel probabilistic ordered weighted cosine similarity operators with Pythagorean fuzzy information. GRANULAR COMPUTING 2022. [DOI: 10.1007/s41066-022-00318-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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3
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Wang Z, Xiao F, Ding W. Interval-valued intuitionistic fuzzy jenson-shannon divergence and its application in multi-attribute decision making. APPL INTELL 2022. [DOI: 10.1007/s10489-022-03347-0] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
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4
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A generalized soft likelihood function in combining multi-source belief distribution functions. APPL INTELL 2022. [DOI: 10.1007/s10489-021-02366-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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5
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Ali S, Kousar M, Xin Q, Pamučar D, Hameed MS, Fayyaz R. Belief and Possibility Belief Interval-Valued N-Soft Set and Their Applications in Multi-Attribute Decision-Making Problems. ENTROPY 2021; 23:e23111498. [PMID: 34828200 PMCID: PMC8617945 DOI: 10.3390/e23111498] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/11/2021] [Revised: 11/08/2021] [Accepted: 11/09/2021] [Indexed: 11/16/2022]
Abstract
In this research article, we motivate and introduce the concept of possibility belief interval-valued N-soft sets. It has a great significance for enhancing the performance of decision-making procedures in many theories of uncertainty. The N-soft set theory is arising as an effective mathematical tool for dealing with precision and uncertainties more than the soft set theory. In this regard, we extend the concept of belief interval-valued soft set to possibility belief interval-valued N-soft set (by accumulating possibility and belief interval with N-soft set), and we also explain its practical calculations. To this objective, we defined related theoretical notions, for example, belief interval-valued N-soft set, possibility belief interval-valued N-soft set, their algebraic operations, and examined some of their fundamental properties. Furthermore, we developed two algorithms by using max-AND and min-OR operations of possibility belief interval-valued N-soft set for decision-making problems and also justify its applicability with numerical examples.
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Affiliation(s)
- Shahbaz Ali
- Department of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan 64200, Pakistan; (S.A.); (M.K.); (M.S.H.)
| | - Muneeba Kousar
- Department of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan 64200, Pakistan; (S.A.); (M.K.); (M.S.H.)
| | - Qin Xin
- Faculty of Science and Technology, University of the Faroe Islands, Vestarabryggja 15, FO 100 Torshavn, Faroe Islands, Denmark;
| | - Dragan Pamučar
- Department of Logistics, Military Academy, University of Defence in Belgrade, 11000 Belgrade, Serbia
- Correspondence:
| | - Muhammad Shazib Hameed
- Department of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan 64200, Pakistan; (S.A.); (M.K.); (M.S.H.)
| | - Rabia Fayyaz
- Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan;
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6
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Negation of BPA: a belief interval approach and its application in medical pattern recognition. APPL INTELL 2021. [DOI: 10.1007/s10489-021-02641-7] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
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7
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Mi X, Tian Y, Kang B. MADA problem: A new scheme based on D numbers and aggregation functions. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2021. [DOI: 10.3233/jifs-202413] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Describing and processing complex as well as ambiguous and uncertain information has always been an inescapable and challenging topic in multi-attribute decision analysis (MADA) problems. As an extension of Dempster-Shafer (D-S) evidence theory, D numbers breaks through the constraints of the constraint framework and is a new way of expressing uncertainty. The soft likelihood function based on POWA operator is one of the most useful tools recently developed for dealing with uncertain information, since it provides a more excellent performance for the aggregation of multiple compatible evidence. Recently, a new MADA model based on D numbers has been proposed, called DMADA. In this paper, inspired by the above mentioned theories, based on soft likelihood functions, POWA aggregation and D numbers we design a novel model to improve the performance of representing and processing uncertain information in MADA problems as an improvement of the DMADA approach. In contrast, our advantages include mainly the following. Firstly, the proposed method considers the reliability characteristics of each initial D number information. Secondly, the proposed method empowers decision makers with the possibility to express their perceptions through attitudinal features. In addition, an interesting finding is that the preference parameter in the proposed method can clearly distinguish the variability between candidates by adjusting the space values between adjacent alternatives, making the decision results clearer. Finally, the effectiveness and superiority of this model are proved through analysis and testing.
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Affiliation(s)
- Xiangjun Mi
- College of Information Engineering, Northwest A&F University, Yangling, Shaanxi, China
| | - Ye Tian
- College of Information Engineering, Northwest A&F University, Yangling, Shaanxi, China
| | - Bingyi Kang
- College of Information Engineering, Northwest A&F University, Yangling, Shaanxi, China
- Key Laboratory of Agricultural Internet of Things, Ministry of Agriculture and Rural Affairs, Yangling, Shaanxi, China
- Shaanxi Key Laboratory of Agricultural Information Perception and Intelligent Service, Yangling, Shaanxi, China
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Pȩkala B, Bentkowska U, Kosior D, Takáč Z, Castillo A, Sesma‐Sara M, Fernandez J, Lafuente J, Bustince H. Interval‐valued equivalence measures respecting uncertainty in image processing. INT J INTELL SYST 2021. [DOI: 10.1002/int.22401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Barbara Pȩkala
- Institute of Computer Science University of Rzeszów Rzeszów Poland
- Department of Artificial Intelligence University of Information Technology and Management Rzeszów Poland
| | | | - Dawid Kosior
- Institute of Computer Science University of Rzeszów Rzeszów Poland
| | - Zdenko Takáč
- Institute of Information Engineering, Automation, and Mathematics Slovak University of Technology in Bratislava Bratislava Slovakia
| | - Aitor Castillo
- Department of Statistics, Informatics, and Mathematics Public University of Navarra Pamplona Spain
| | - Mikel Sesma‐Sara
- Department of Statistics, Informatics, and Mathematics Public University of Navarra Pamplona Spain
| | - Javier Fernandez
- Department of Statistics, Informatics, and Mathematics Public University of Navarra Pamplona Spain
| | - Julio Lafuente
- Department of Statistics, Informatics, and Mathematics Public University of Navarra Pamplona Spain
| | - Humberto Bustince
- Department of Statistics, Informatics, and Mathematics Public University of Navarra Pamplona Spain
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Mi X, Lv T, Tian Y, Kang B. Multi-sensor data fusion based on soft likelihood functions and OWA aggregation and its application in target recognition system. ISA TRANSACTIONS 2021; 112:137-149. [PMID: 33349453 DOI: 10.1016/j.isatra.2020.12.009] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2020] [Revised: 12/02/2020] [Accepted: 12/02/2020] [Indexed: 06/12/2023]
Abstract
Multi-sensor data fusion plays an irreplaceable role in actual production and application. Dempster-Shafer theory (DST) is widely used in numerous fields of information modeling and information fusion due to the flexibility and effectiveness of processing uncertain information and dealing with uncertain information without prior probabilities. However, when highly contradictory evidence is combined, it may produce results that are inconsistent with human intuition. In order to solve this problem, a hybrid method for combining belief functions based on soft likelihood functions (SLFs) and ordered weighted averaging (OWA) operators is proposed. More specifically, a soft likelihood function based on OWA operators is used to provide the possibility to fuse uncertain information compatible with each other. It can characterize the degree to which the probability information of compatible propositions in the collected evidence is affected by unknown uncertain factors. This makes the results of using the Dempster's combination rule to fuse uncertain information from multiple sources more comprehensive and credible. Experimental results manifest that this method is reliable. Example and application show that this method has obvious advantages in solving the problem of conflict evidence fusion in multi-sensor. In particular, in target recognition, when three pieces of evidence are fused, the target recognition rate is 96.92%, etc.
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Affiliation(s)
- Xiangjun Mi
- College of Information Engineering, Northwest A&F University, Yangling, Shaanxi, 712100, China
| | - Tongxuan Lv
- College of Information Engineering, Northwest A&F University, Yangling, Shaanxi, 712100, China
| | - Ye Tian
- College of Information Engineering, Northwest A&F University, Yangling, Shaanxi, 712100, China
| | - Bingyi Kang
- College of Information Engineering, Northwest A&F University, Yangling, Shaanxi, 712100, China; Key Laboratory of Agricultural Internet of Things, Ministry of Agriculture and Rural Affairs, Yangling, Shaanxi 712100, China; Shaanxi Key Laboratory of Agricultural Information Perception and Intelligent Service, Yangling, Shaanxi 712100, China.
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10
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Tao R, Xiao F. A GMCDM approach with linguistic Z-numbers based on TOPSIS and Choquet integral considering risk preference. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2020. [DOI: 10.3233/jifs-200318] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
Abstract
Group multi-criteria decision-making (GMCDM) is an important part of decision theory, which is aimed to assess alternatives according to multiple criteria by collecting the wisdom of experts. However, in the process of evaluating, because of the limitation of human knowledge and the complexity of problems, an efficient GMCDM approach under uncertain environment still need to be further explored. Thus, in this paper, a novel GMCDM approach with linguistic Z-numbers based on TOPSIS and Choquet integral is proposed. Firstly, since linguistic Z-numbers performs better in coping with uncertain information, it is used to express the evaluation information. Secondly, TOPSIS, one of the most useful and systematic multi-criteria decision-making (MCDM) method, is adopted as the framework of the proposed approach. Thirdly, frequently it exists interaction between criteria, so Choquet integral is introduced to capture this kind of influence. What’s more, viewing that decision makers (DMs) show different preferences for uncertainty, the risk preference is regarded as a vital parameter when calculating the score of linguistic Z-numbers. An application in supplier selection is illustrated to demonstrate the effectiveness of the proposed approach. Finally, a further comparison and discussion of the proposed GMCDM method is given.
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Affiliation(s)
- Ran Tao
- School of Computer and Information Science, Southwest University, Chongqing, China
| | - Fuyuan Xiao
- School of Computer and Information Science, Southwest University, Chongqing, China
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11
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12
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13
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Mi X, Tian Y, Kang B. A modified soft‐likelihood function based on POWA operator. INT J INTELL SYST 2020. [DOI: 10.1002/int.22228] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Xiangjun Mi
- College of Information EngineeringNorthwest A&F University Yangling Shaanxi China
| | - Ye Tian
- College of Information EngineeringNorthwest A&F University Yangling Shaanxi China
| | - Bingyi Kang
- College of Information EngineeringNorthwest A&F University Yangling Shaanxi China
- Key Laboratory of Agricultural Internet of ThingsMinistry of Agriculture and Rural Affairs Yangling Shaanxi China
- Shaanxi Key Laboratory of Agricultural Information Perception and Intelligent Service Yangling, Shaanxi China
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15
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A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis. MATHEMATICS 2020. [DOI: 10.3390/math8010142] [Citation(s) in RCA: 68] [Impact Index Per Article: 17.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Abstract
As the extension of the fuzzy sets (FSs) theory, the intuitionistic fuzzy sets (IFSs) play an important role in handling the uncertainty under the uncertain environments. The Pythagoreanfuzzy sets (PFSs) proposed by Yager in 2013 can deal with more uncertain situations than intuitionistic fuzzy sets because of its larger range of describing the membership grades. How to measure the distance of Pythagorean fuzzy sets is still an open issue. Jensen–Shannon divergence is a useful distance measure in the probability distribution space. In order to efficiently deal with uncertainty in practical applications, this paper proposes a new divergence measure of Pythagorean fuzzy sets, which is based on the belief function in Dempster–Shafer evidence theory, and is called PFSDM distance. It describes the Pythagorean fuzzy sets in the form of basic probability assignments (BPAs) and calculates the divergence of BPAs to get the divergence of PFSs, which is the step in establishing a link between the PFSs and BPAs. Since the proposed method combines the characters of belief function and divergence, it has a more powerful resolution than other existing methods. Additionally, an improved algorithm using PFSDM distance is proposed in medical diagnosis, which can avoid producing counter-intuitive results especially when a data conflict exists. The proposed method and the magnified algorithm are both demonstrated to be rational and practical in applications.
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Fei L, Feng Y, Liu L. On Pythagorean fuzzy decision making using soft likelihood functions. INT J INTELL SYST 2019. [DOI: 10.1002/int.22199] [Citation(s) in RCA: 37] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Affiliation(s)
- Liguo Fei
- Department of Management Science and Engineering, School of ManagementHarbin Institute of Technology Harbin China
| | - Yuqiang Feng
- Department of Management Science and Engineering, School of ManagementHarbin Institute of Technology Harbin China
| | - Luning Liu
- Department of Management Science and Engineering, School of ManagementHarbin Institute of Technology Harbin China
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17
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Li P, Fei L. On combination rule in Dempster–Shafer theory using OWA‐based soft likelihood functions and its applications in environmental impact assessment. INT J INTELL SYST 2019. [DOI: 10.1002/int.22189] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Affiliation(s)
- Peilin Li
- School of Geographical ScienceHarbin Normal University Harbin China
| | - Liguo Fei
- School of ManagementHarbin Institute of Technology Harbin China
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18
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Song Y, Deng Y. A new soft likelihood function based on power ordered weighted average operator. INT J INTELL SYST 2019. [DOI: 10.1002/int.22182] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Affiliation(s)
- Yutong Song
- Glasgow CollegeUniversity of Electronic Science and Technology of China Chengdu China
- Institute of Fundamental and Frontier ScienceUniversity of Electronic Science and Technology of China Chengdu China
| | - Yong Deng
- Glasgow CollegeUniversity of Electronic Science and Technology of China Chengdu China
- Institute of Fundamental and Frontier ScienceUniversity of Electronic Science and Technology of China Chengdu China
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20
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Fei L, Feng Y, Liu L, Mao W. On intuitionistic fuzzy decision‐making using soft likelihood functions. INT J INTELL SYST 2019. [DOI: 10.1002/int.22141] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Affiliation(s)
- Liguo Fei
- Management Science and Engineering, School of ManagementHarbin Institute of TechnologyHarbin China
| | - Yuqiang Feng
- Management Science and Engineering, School of ManagementHarbin Institute of TechnologyHarbin China
| | - Luning Liu
- Management Science and Engineering, School of ManagementHarbin Institute of TechnologyHarbin China
| | - Weicheng Mao
- Management Science and Engineering, School of ManagementHarbin Institute of TechnologyHarbin China
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21
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Fei L, Feng Y, Liu L. Evidence combination using OWA‐based soft likelihood functions. INT J INTELL SYST 2019. [DOI: 10.1002/int.22166] [Citation(s) in RCA: 48] [Impact Index Per Article: 9.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Liguo Fei
- School of ManagementHarbin Institute of TechnologyHarbin China
| | - Yuqiang Feng
- School of ManagementHarbin Institute of TechnologyHarbin China
| | - Luning Liu
- School of ManagementHarbin Institute of TechnologyHarbin China
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