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Power Aggregation Operators and Similarity Measures Based on Improved Intuitionistic Hesitant Fuzzy Sets and their Applications to Multiple Attribute Decision Making 被引量:1
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作者 Tahir Mahmood Wajid Ali +1 位作者 Zeeshan Ali Ronnason Chinram 《Computer Modeling in Engineering & Sciences》 SCIE EI 2021年第3期1165-1187,共23页
Intuitionistic hesitant fuzzy set(IHFS)is amixture of two separated notions called intuitionistic fuzzy set(IFS)and hesitant fuzzy set(HFS),as an important technique to cope with uncertain and awkward information in r... Intuitionistic hesitant fuzzy set(IHFS)is amixture of two separated notions called intuitionistic fuzzy set(IFS)and hesitant fuzzy set(HFS),as an important technique to cope with uncertain and awkward information in realistic decision issues.IHFS contains the grades of truth and falsity in the formof the subset of the unit interval.The notion of IHFS was defined by many scholars with different conditions,which contain several weaknesses.Here,keeping in view the problems of already defined IHFSs,we will define IHFS in another way so that it becomes compatible with other existing notions.To examine the interrelationship between any numbers of IHFSs,we combined the notions of power averaging(PA)operators and power geometric(PG)operators with IHFSs to present the idea of intuitionistic hesitant fuzzy PA(IHFPA)operators,intuitionistic hesitant fuzzy PG(IHFPG)operators,intuitionistic hesitant fuzzy power weighted average(IHFPWA)operators,intuitionistic hesitant fuzzy power ordered weighted average(IHFPOWA)operators,intuitionistic hesitant fuzzy power ordered weighted geometric(IHFPOWG)operators,intuitionistic hesitant fuzzy power hybrid average(IHFPHA)operators,intuitionistic hesitant fuzzy power hybrid geometric(IHFPHG)operators and examined as well their fundamental properties.Some special cases of the explored work are also discovered.Additionally,the similarity measures based on IHFSs are presented and their advantages are discussed along examples.Furthermore,we initiated a new approach to multiple attribute decision making(MADM)problem applying suggested operators and a mathematical model is solved to develop an approach and to establish its common sense and adequacy.Advantages,comparative analysis,and graphical representation of the presented work are elaborated to show the reliability and effectiveness of the presented works. 展开更多
关键词 Intuitionistic fuzzy sets intuitionistic hesitant fuzzy sets power aggregation operators similarity measures multiple attribute decision making
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On similarity measures of interval-valued intuitionistic fuzzy sets and their application to pattern recognitions 被引量:29
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作者 徐泽水 《Journal of Southeast University(English Edition)》 EI CAS 2007年第1期139-143,共5页
The concept of the degree of similarity between interval-valued intuitionistic fuzzy sets (IVIFSs) is introduced, and some distance measures between IVIFSs are defined based on the Hamming distance, the normalized H... The concept of the degree of similarity between interval-valued intuitionistic fuzzy sets (IVIFSs) is introduced, and some distance measures between IVIFSs are defined based on the Hamming distance, the normalized Hamming distance, the weighted Hamming distance, the Euclidean distance, the normalized Euclidean distance, and the weighted Euclidean distance, etc. Then, by combining the Hausdorff metric with the Hamming distance, the Euclidean distance and their weighted versions, two other similarity measures between IVIFSs, i. e., the weighted Hamming distance based on the Hausdorff metric and the weighted Euclidean distance based on the Hausdorff metric, are defined, and then some of their properties are studied. Finally, based on these distance measures, some similarity measures between IVIFSs are defined, and the similarity measures are applied to pattern recognitions with interval-valued intuitionistic fuzzy information. 展开更多
关键词 interval-valued intuitionistic fuzzy set similarity pattern recognition
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A novel similarity measure between intuitionistic fuzzy sets based on the mid points of transformed triangular fuzzy numbers with applications to pattern recognition and medical diagnosis 被引量:3
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作者 J Dhivya B Sridevi 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2019年第2期229-252,共24页
Similarity measure is an essential tool to compare and determine the degree of similarity between intuitionistic fuzzy sets (IFSs). In this paper, a new similarity measure between intuitionistic fuzzy sets based on th... Similarity measure is an essential tool to compare and determine the degree of similarity between intuitionistic fuzzy sets (IFSs). In this paper, a new similarity measure between intuitionistic fuzzy sets based on the mid points of transformed triangular fuzzy numbers is proposed. The proposed similarity measure provides reasonable results not only for the sets available in the literature but also gives very reasonable results, especially for fuzzy sets as well as for most intuitionistic fuzzy sets. To provide supportive evidence, the proposed similarity measure is tested on certain sets available in literature and is also applied to pattern recognition and medical diagnosis problems. It is observed that the proposed similarity measure provides a very intuitive quantification. 展开更多
关键词 fuzzy sets (FSs) Intuitionistic fuzzy sets (IFSs) Most intuitionistic fuzzy sets (MIFSs) Simi- larity measure (SM) Transformed TRIANGULAR fuzzy NUMBERS (TTFNs)
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Novel Distance Measures on Hesitant Fuzzy Sets Based on Equal-Probability Transformation and Their Application in Decision Making on Intersection Traffic Control
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作者 Fangwei Zhang Yi Zhao +2 位作者 Jun Ye Shuhong Wang Jingyi Hu 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第5期1589-1602,共14页
The purpose of this study is to reduce the uncertainty in the calculation process on hesitant fuzzy sets(HFSs).The innovation of this study is to unify the cardinal numbers of hesitant fuzzy elements(HFEs)in a special... The purpose of this study is to reduce the uncertainty in the calculation process on hesitant fuzzy sets(HFSs).The innovation of this study is to unify the cardinal numbers of hesitant fuzzy elements(HFEs)in a special way.Firstly,a probability density function is assigned for any given HFE.Thereafter,equal-probability transformation is introduced to transform HFEs with different cardinal numbers on the condition into the same probability density function.The characteristic of this transformation is that the higher the consistency of the membership degrees in HFEs,the higher the credibility of the mentioned membership degrees is,then,the bigger the probability density values for them are.According to this transformation technique,a set of novel distance measures on HFSs is provided.Finally,an illustrative example of intersection traffic control is introduced to show the usefulness of the given distance measures.The example also shows that this study is a good complement to operation theories on HFSs. 展开更多
关键词 Hesitant fuzzy sets equal-probability mapping distance measure intersection traffic control cardinality theory
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Fuzzy description logic based on vague sets
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作者 马宗民 王海龙 +1 位作者 严丽 赵法信 《Journal of Southeast University(English Edition)》 EI CAS 2007年第3期399-402,共4页
To enable the representation and reasoning for fuzzy ontologies with expressive fuzzy knowledge on the semantic web, a new fuzzy extension of description logics called vague ALC which is based on vague sets is present... To enable the representation and reasoning for fuzzy ontologies with expressive fuzzy knowledge on the semantic web, a new fuzzy extension of description logics called vague ALC which is based on vague sets is presented. The definition of vague set is introduced and then the syntax and semantics of vague ALC are formally defined. The forms of axioms and assertions in the vague ALC knowledge bases are specified. Finally, the tableau algorithm is developed for the reasoning in the vague ALC. The vague ALC based on vague set uses two degrees of membership instead of a single membership degree in the fuzzy sets and is more accurate in representing the imprecision in the degrees of membership. The vague ALC has more expressive power than ALC and can represent fuzzy knowledge and perform reasoning tasks based on them. Therefore, the vague ALC can enable the representation and reasoning for fuzzy ontologies with expressive fuzzy knowledge on the semantic web. 展开更多
关键词 semantic web description logic fuzzy logic vague sets tableau algorithm
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On Similarity Measures and Distance Measures of Fuzzy Soft Sets 被引量:3
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作者 刘雅雅 秦克云 王玲 《Chinese Quarterly Journal of Mathematics》 2015年第3期349-357,共9页
In this paper we introduce several new similarity measures and distance measures between fuzzy soft sets, these measures are examined based on the set-theoretic approach and the matching function. Comparative studies ... In this paper we introduce several new similarity measures and distance measures between fuzzy soft sets, these measures are examined based on the set-theoretic approach and the matching function. Comparative studies of these measures are derived. By introducing two general formulas, we propose a new method to define the similarity measures and the distance measures between two fuzzy soft sets with different parameter sets. 展开更多
关键词 fuzzy SOFT SET similarity measure DISTANCE measure
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P-Indeterminate Vector Similarity Measures of Orthopair Neutrosophic Number Sets and Their Decision-MakingMethod with Indeterminate Degrees
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作者 Mailing Zhao Jun Ye 《Computer Modeling in Engineering & Sciences》 SCIE EI 2021年第9期1219-1230,共12页
In the complexity and indeterminacy of decision making(DM)environments,orthopair neutrosophic number set(ONNS)presented by Ye et al.can be described by the truth and falsity indeterminacy degrees.Then,ONNS demonstrate... In the complexity and indeterminacy of decision making(DM)environments,orthopair neutrosophic number set(ONNS)presented by Ye et al.can be described by the truth and falsity indeterminacy degrees.Then,ONNS demonstrates its advantages in the indeterminate information expression,aggregations,and DM problems with some indeterminate ranges.However,the existing research lacks some similarity measures between ONNSs.They are indispensable mathematical tools and play a crucial role in DM,pattern recognition,and clustering analysis.Thus,it is necessary to propose some similaritymeasures betweenONNSs to supplement the gap.To solve the issue,this study firstly proposes the p-indeterminate cosine measure,p-indeterminate Dice measure,p-indeterminate Jaccard measure of ONNSs(i.e.,the three parameterized indeterminate vector similarity measures of ONNSs)in vector space.Then,a DMmethod based on the parameterized indeterminate vector similarity measures of ONNSs is developed to solve indeterminate multiple attribute DM problems by choosing different indeterminate degrees of the parameter p,such as the small indeterminate degree(p=0)or the moderate indeterminate degree(p=0.5)or the big indeterminate degree(p=1).Lastly,an actual DM example on choosing a suitable logistics supplier is provided to demonstrate the flexibility and practicability of the developed DM approach in indeterminate DM problems.By comparison with existing relative DM methods,the superiority of this study is that the established DMapproach indicates its flexibility and suitability depending on decision makers’indeterminate degrees(decision risks)in ONNS setting. 展开更多
关键词 Orthopair neutrosophic number set p-indeterminate vector similarity measure p-indeterminate cosine measure p-indeterminate Dice measure p-indeterminate Jaccard measure decision making
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Cotangent Similarity Measure of Consistent Neutrosophic Sets and Application to Multiple Attribute Decision-Making Problems in Neutrosophic Multi-Valued Setting
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作者 Angyan Tu Jiancheng Chen Bing Wang 《Computer Modeling in Engineering & Sciences》 SCIE EI 2022年第11期377-387,共11页
A neutrosophic multi-valued set(NMVS)is a crucial representation for true,false,and indeterminate multivalued information.Then,a consistent single-valued neutrosophic set(CSVNS)can effectively reflect the mean and con... A neutrosophic multi-valued set(NMVS)is a crucial representation for true,false,and indeterminate multivalued information.Then,a consistent single-valued neutrosophic set(CSVNS)can effectively reflect the mean and consistency degree of true,false,and indeterminate multi-valued sequences and solve the operational issues between different multi-valued sequence lengths in NMVS.However,there has been no research on consistent single-valued neutrosophic similarity measures in the existing literature.This paper proposes cotangent similarity measures and weighted cotangent similarity measures between CSVNSs based on cotangent function in the neutrosophic multi-valued setting.The cosine similarity measures showthe cosine of the angle between two vectors projected into amultidimensional space,rather than their distance.The cotangent similaritymeasures in this study can alleviate several shortcomings of cosine similarity measures in vector space to a certain extent.Then,a decisionmaking approach is presented in viewof the established cotangent similarity measures in the case of NMVSs.Finally,the developed decision-making approach is applied to selection problems of potential cars.The proposed approach has obtained two different results,which have the same sort sequence as the compared literature.The decision results prove its validity and effectiveness.Meantime,it also provides a new manner for neutrosophic multi-valued decision-making issues. 展开更多
关键词 Neutrosophic multi-valued set consistency single-valued neutrosophic sets cotangent similarity measure multiple attribute decision-making
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Two-Sided Matching Decision Making with Multi-Attribute Probabilistic Hesitant Fuzzy Sets
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作者 Peichen Zhao Qi Yue Zhibin Deng 《Intelligent Automation & Soft Computing》 SCIE 2023年第7期849-873,共25页
In previous research on two-sided matching(TSM)decision,agents’preferences were often given in the form of exact values of ordinal numbers and linguistic phrase term sets.Nowdays,the matching agent cannot perform the... In previous research on two-sided matching(TSM)decision,agents’preferences were often given in the form of exact values of ordinal numbers and linguistic phrase term sets.Nowdays,the matching agent cannot perform the exact evaluation in the TSM situations due to the great fuzziness of human thought and the complexity of reality.Probability hesitant fuzzy sets,however,have grown in popularity due to their advantages in communicating complex information.Therefore,this paper develops a TSM decision-making approach with multi-attribute probability hesitant fuzzy sets and unknown attribute weight information.The agent attribute weight vector should be obtained by using the maximum deviation method and Hamming distance.The probabilistic hesitancy fuzzy information matrix of each agent is then arranged to determine the comprehensive evaluation of two matching agent sets.The agent satisfaction degree is calculated using the technique for order preference by similarity to ideal solution(TOPSIS).Additionally,the multi-object programming technique is used to establish a TSM method with the objective of maximizing the agent satisfaction of two-sided agents,and the matching schemes are then established by solving the built model.The study concludes by providing a real-world supply-demand scenario to illustrate the effectiveness of the proposed method.The proposed method is more flexible than prior research since it expresses evaluation information using probability hesitating fuzzy sets and can be used in scenarios when attribute weight information is unclear. 展开更多
关键词 Two-sided matching decision-making(TSMDM) probabilistic hesitant fuzzy set(PHFS) the technique for order preference by similarity to ideal solution(TOPSIS) MULTI-ATTRIBUTE
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A Knowledge Measure with Parameter of Intuitionistic Fuzzy Sets 被引量:2
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作者 Zhenhua Zhang Shenguo Yuan +3 位作者 Jing Zhang Chao Ma Jinhui Xu Xiaolong Lin 《Applied Mathematics》 2018年第7期874-889,共16页
A new knowledge measure with parameter of intuitionistic fuzzy sets (IFSs) is presented based on the membership degree and the non-membership degree of IFSs, which complies with the extended form of Szmidt-Kacprzyk ax... A new knowledge measure with parameter of intuitionistic fuzzy sets (IFSs) is presented based on the membership degree and the non-membership degree of IFSs, which complies with the extended form of Szmidt-Kacprzyk axioms for intuitionistic fuzzy entropy. And a sufficient and necessary condition of order property in the Szmidt-Kacprzyk axioms is discussed. Additionally, some numerical examples are given to illustrate the applications of the proposed knowledge measure and some conventional entropies and knowledge measures of IFSs. The experimental results show that the results of the parametric model proposed in this paper are more accurate than those of most of the classic models. 展开更多
关键词 Intuitionistic fuzzy sets KNOWLEDGE measure ENTROPY Uncertainty Order PROPERTY
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Rough similarity degree and rough close degree in rough fuzzy sets and the applications
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作者 Li Jian Xu Xiaojing Shi Kaiquan 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2008年第5期945-951,共7页
Based on rough similarity degree of rough sets and close degree of fuzzy sets, the definitions of rough similarity degree and rough close degree of rough fuzzy sets are given, which can be used to measure the similar ... Based on rough similarity degree of rough sets and close degree of fuzzy sets, the definitions of rough similarity degree and rough close degree of rough fuzzy sets are given, which can be used to measure the similar degree between two rough fuzzy sets. The properties and theorems are listed. Using the two new measures, the method of clustering in the rough fuzzy system can be obtained. After clustering, the new fuzzy sample can be recognized by the principle of maximal similarity degree. 展开更多
关键词 rough fuzzy set rough similarity degree rough close degree CLUSTERING recognition of rough pattern maximal similarity degree principle.
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On some new fuzzy entropy measure of Pythagorean fuzzy sets for decision-making based on an extended TOPSIS approach
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作者 H.D.Arora Anjali Naithani 《Journal of Management Analytics》 EI 2024年第1期87-109,共23页
Fuzzy entropy measures are valuable tools in decision-making when dealing with uncertain or imprecise information.There exist many entropy measures for Pythagorean Fuzzy Sets(PFS)in the literature that fail to deal wi... Fuzzy entropy measures are valuable tools in decision-making when dealing with uncertain or imprecise information.There exist many entropy measures for Pythagorean Fuzzy Sets(PFS)in the literature that fail to deal with the problem of providing reasonable or consistent results to the decision-makers.To deal with the shortcomings of the existing measures,this paper proposes a robust fuzzy entropy measure for PFS to facilitate decision-making under uncertainty.The usefulness of the measure is illustrated through an illustration of decision-making in a supplier selection problem and compared with existing fuzzy entropy measures.The Technique for Order Performance by Similarity to Ideal Solution(TOPSIS)approach is also explored to solve the decision-making problem.The results demonstrate that the proposed measure can effectively capture the degree of uncertainty in the decision-making process,leading to more accurate decision outcomes by providing a reliable and robust ranking of alternatives. 展开更多
关键词 Pythagorean fuzzy sets entropy measures multi criteria decision analysis TOPSIS method supplier selection
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Optimal Route Selection Method Based on Vague Sets
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作者 郭瑞 杜利敏 王淳 《Chinese Quarterly Journal of Mathematics》 2015年第1期130-136,共7页
Optimal route selection is an important function of vehicle trac flow guidance system. Its core is to determine the index weight for measuring the route merits and to determine the evaluation method for selecting rout... Optimal route selection is an important function of vehicle trac flow guidance system. Its core is to determine the index weight for measuring the route merits and to determine the evaluation method for selecting route. In this paper, subjective weighting method which relies on driver preference is used to determine the weight and the paper proposes the multi-criteria weighted decision method based on vague sets for selecting the optimal route. Examples show that, the usage of vague sets to describe route index value can provide more decision-making information for route selection. 展开更多
关键词 trafflc guidance optimal route selection vague sets multi-criteria fuzzy decision-making
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Introduce a Novel PCA Method for Intuitionistic Fuzzy Sets Based on Cross Entropy 被引量:1
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作者 Sonia Darvishi Adel Fatemi Pouya Faroughi 《Applied Mathematics》 2015年第6期990-995,共6页
In this paper, a new method for Principal Component Analysis in intuitionistic fuzzy situations has been proposed. This approach is based on cross entropy as an information index. This new method is a useful method fo... In this paper, a new method for Principal Component Analysis in intuitionistic fuzzy situations has been proposed. This approach is based on cross entropy as an information index. This new method is a useful method for data reduction for situations in which data are not exact. The inexactness in the situations assumed here is due to fuzziness and missing data information, so that we have two functions (membership and non-membership). Thus, method proposed here is suitable for Atanasov’s Intuitionistic Fuzzy Sets (A-IFSs) in which we have an uncertainty due to a mixture of fuzziness and missing data information. For the demonstration of the application of the method, we have used an example and have presented a conclusion. 展开更多
关键词 PCA Cross ENTROPY Intuitionistic fuzzy sets DISCRIMINATION Information measure A-IFSs
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Discussion about similarity measures in pattern recognition of fuzzy information
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作者 GUO Zhang-lin TIAN Jing 《通讯和计算机(中英文版)》 2008年第6期10-15,共6页
关键词 相似形 测量方法 信息技术 模糊理论
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Rough Sets Model Based on Random Fuzzy Sets and Fuzzy Logic Operators
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作者 Jialu Zhang Guojun Wang 《通讯和计算机(中英文版)》 2006年第3期11-18,24,共9页
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Entropy and Similarity Measure for T2SVNSs and Its Application
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作者 GENG Juan-juan YE Wan-hong +1 位作者 ZHANG Ju Xu Dong-sheng 《Chinese Quarterly Journal of Mathematics》 2021年第2期160-175,共16页
The objective of this paper is to present a new approach for solving the multicriteria group decision-making(MCGDM)problems in type-2 single valued neutrosophic set(T2SVNS)environment.Firstly,we give the concepts SVNS... The objective of this paper is to present a new approach for solving the multicriteria group decision-making(MCGDM)problems in type-2 single valued neutrosophic set(T2SVNS)environment.Firstly,we give the concepts SVNS,T2SVNS and tangent similarity measure with T2SVN information.Secondly,we define a new entropy function for determining unknown attribute weights.In addition,a MCGDM method is developed based on entropy and tangent similarity measure of T2SVNSs.Finally,an illustrative example and comparative analysis are given to confirm the rationality and feasibility of the proposed method. 展开更多
关键词 Type-2 single valued neutrosophic set ENTROPY Tangent function similarity measure MCGDM
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The Rough Method for Spatial Data Subzone Similarity Measurement
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作者 Weihua Liao 《Journal of Geographic Information System》 2012年第1期37-45,共9页
There are two methods for GIS similarity measurement problem, one is cross-coefficient for GIS attribute similarity measurement, and the other is spatial autocorrelation that is based on spatial location. These method... There are two methods for GIS similarity measurement problem, one is cross-coefficient for GIS attribute similarity measurement, and the other is spatial autocorrelation that is based on spatial location. These methods can not calculate subzone similarity problem based on universal background. The rough measurement based on membership function solved this problem well. In this paper, we used rough sets to measure the similarity of GIS subzone discrete data, and used neighborhood rough sets to calculate continuous data’s upper and lower approximation. We used neighborhood particle to calculate membership function of continuous attribute, then to solve continuous attribute’s subzone similarity measurement problem. 展开更多
关键词 SUBZONE ROUGH sets NEIGHBORHOOD ROUGH sets similarity measureMENT
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Study of Similarity Measures with Linear Discriminant Analysis for Face Recognition
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作者 Mohamed A. El-Sayed Kadry Hamed 《Journal of Software Engineering and Applications》 2015年第9期478-488,共11页
Face recognition systems have been in the active research in the area of image processing for quite a long time. Evaluating the face recognition system was carried out with various types of algorithms used for extract... Face recognition systems have been in the active research in the area of image processing for quite a long time. Evaluating the face recognition system was carried out with various types of algorithms used for extracting the features, their classification and matching. Similarity measure or distance measure is also an important factor in assessing the quality of a face recognition system. There are various distance measures in literature which are widely used in this area. In this work, a new class of similarity measure based on the Lp metric between fuzzy sets is proposed which gives better results when compared to the existing distance measures in the area with Linear Discriminant Analysis (LDA). The result points to a positive direction that with the existing feature extraction methods itself the results can be improved if the similarity measure in the matching part is efficient. 展开更多
关键词 fuzzy sets similarity measure Distance measure LDA FACE Recognition
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Similarity Measures of Satellite Images Using an Adaptive Feature Contrast Model
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作者 Hong Tang Adu Gong +2 位作者 Shaodan Li Wenbin Yi Chuanfu Yang 《International Journal of Geosciences》 2013年第2期329-343,共15页
Similarity measurement is one of key operations to retrieve “desired” images from an image database. As a famous psychological similarity measure approach, the Feature Contrast (FC) model is defined as a linear comb... Similarity measurement is one of key operations to retrieve “desired” images from an image database. As a famous psychological similarity measure approach, the Feature Contrast (FC) model is defined as a linear combination of both common and distinct features. In this paper, an adaptive feature contrast (AdaFC) model is proposed to measure similarity between satellite images for image retrieval. In the AdaFC, an adaptive function is used to model a variable role of distinct features in the similarity measurement. Specifically, given some distinct features in a satellite image, e.g., a COAST image, they might play a significant role when the image is compared with an image including different semantics, e.g., a SEA image, and might be trivial when it is compared with a third image including same semantics, e.g., another COAST image. Experimental results on satellite images show that the proposed model can consistently improve similarity retrieval effectiveness of satellite images including multiple geo-objects, for example COAST images. 展开更多
关键词 similarity measurement FEATURE CONTRAST Model Set-Theoretic similarity Image RETRIEVAL
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