1
|
Roszkowska E, Filipowicz-Chomko M, Kusterka-Jefmańska M, Jefmański B. The Impact of the Intuitionistic Fuzzy Entropy-Based Weights on the Results of Subjective Quality of Life Measurement Using Intuitionistic Fuzzy Synthetic Measure. ENTROPY (BASEL, SWITZERLAND) 2023; 25:961. [PMID: 37509908 PMCID: PMC10378645 DOI: 10.3390/e25070961] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2023] [Revised: 06/05/2023] [Accepted: 06/13/2023] [Indexed: 07/30/2023]
Abstract
In this paper, an extended Intuitionistic Fuzzy Synthetic Measure (IFSM) with intuitionistic fuzzy (IF) entropy-based weights is presented. This method can be implemented in a ranking problem where the assessments of the criteria are expressed in the form of intuitionistic fuzzy values and the information about the importance criteria is unknown. One example of such a problem is measuring the subjective quality of life in cities. We join the debate on the determination of weights for the analysis of the quality of life problem using multi-criteria methods. To handle this problem, four different IF entropy-based weight methods were applied. Their performances were compared and analyzed based on the questionnaires from the survey concerning the quality of life in European cities. The studies show very similar weighting systems obtained by different IF entropy-based approaches, resulting in almost the same city rankings acquired through IFSM by using those weights. The differences in rankings obtained through the IFSM measure (and only by one position) concern the six cities included in the analysis. Our results support the assumption of the equal importance of the criteria in measuring this complex phenomenon.
Collapse
Affiliation(s)
- Ewa Roszkowska
- Faculty of Computer Science, Bialystok University of Technology, Wiejska 45A, 15-351 Bialystok, Poland
| | - Marzena Filipowicz-Chomko
- Faculty of Computer Science, Bialystok University of Technology, Wiejska 45A, 15-351 Bialystok, Poland
| | - Marta Kusterka-Jefmańska
- Department of Quality and Environmental Management, Wroclaw University of Economics and Business, 53-345 Wrocław, Poland
| | - Bartłomiej Jefmański
- Department of Econometrics and Computer Science, Wroclaw University of Economics and Business, 53-345 Wrocław, Poland
| |
Collapse
|
2
|
A novel intuitionistic fuzzy similarity measure with applications in decision-making, pattern recognition, and clustering problems. GRANULAR COMPUTING 2023. [DOI: 10.1007/s41066-023-00366-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/24/2023]
|
3
|
An Application of the Pythagorean Fuzzy Sets in the Fault Diagnosis. JOURNAL OF KONBIN 2022. [DOI: 10.2478/jok-2022-0041] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
Abstract
In this paper, a comprehensive review and critical analyses of methods based on the ordinary fuzzy set, Atanassov’s intuitionistic fuzzy set, and its extensions have been conducted to show their limitations and defects. Then, a novel similarity measure based on the generalized score function has been introduced that incorporates the significance (importance) of information, making it more intuitive to compare them. The proposed method is employed for the fault diagnosis of steam turbine generator unit under Pythagorean fuzzy environment. Ten fault types of rotating machines are established as failure patterns in nine different vibration frequency ranges, expressed in terms of Pythagorean fuzzy numbers. The superiority of the proposed method in dealing with uncertain and vague information is shown by comparing it with some existing measures in numerical examples.
Collapse
|
4
|
Singh K, Singh S. On a dual proximity measure based on intuitionistic fuzzy sets. Neural Comput Appl 2022. [DOI: 10.1007/s00521-022-07946-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
|
5
|
Roszkowska E, Jefmański B, Kusterka-Jefmańska M. On Some Extension of Intuitionistic Fuzzy Synthetic Measures for Two Reference Points and Entropy Weights. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1081. [PMID: 36010745 PMCID: PMC9407115 DOI: 10.3390/e24081081] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/13/2022] [Revised: 08/02/2022] [Accepted: 08/02/2022] [Indexed: 06/15/2023]
Abstract
In this paper, a novel Double Intuitionistic Fuzzy Synthetic Measure (DIFSM), based on intuitionistic fuzzy values for handling multi-criteria decision-making problems used to rank alternatives, is presented. In the studies, intuitionistic fuzzy sets (IFSs) represented uncertain, imprecise information or human judgment. The intuitionistic fuzzy sets can also reflect the approval, rejection, and hesitation of decision-makers. The degrees of satisfiability and non-satisfiability and uncertainty of each alternative with respect to a set of criteria are described by membership functions, non-membership functions, and hesitancy indexes, respectively. The aggregation algorithm DIFSM is inspired by Hellwig's method based on two reference points: ideal point (pattern) and anti-ideal point (anti-pattern), measuring distances between the alternative and ideal point and distance between the ideal and anti-ideal point. The proposed methods take into consideration the entropy-based weights of criteria. An illustrative example is given to demonstrate the practicality and effectiveness of the proposed approach. Additionally, the comparative analysis results, using the DIFSM and the Intuitionistic Fuzzy TOPSIS-based framework, are presented.
Collapse
Affiliation(s)
- Ewa Roszkowska
- Faculty of Computer Science, Bialystok University of Technology, Wiejska 45A, 15-351 Bialystok, Poland
| | - Bartłomiej Jefmański
- Department of Econometrics and Computer Science, Wroclaw University of Economics and Business, 53-345 Wrocław, Poland
| | - Marta Kusterka-Jefmańska
- Department of Quality and Environmental Management, Wroclaw University of Economics and Business, 53-345 Wrocław, Poland
| |
Collapse
|
6
|
Ganie AH. Some t-conorm-based distance measures and knowledge measures for Pythagorean fuzzy sets with their application in decision-making. COMPLEX INTELL SYST 2022. [DOI: 10.1007/s40747-022-00804-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
Abstract
AbstractThe Pythagorean fuzzy sets are more robust than fuzzy sets and intuitionistic fuzzy sets in dealing with the problems involving uncertainty. To compare two Pythagorean fuzzy sets, distance measures play a crucial role. In this paper, we have proposed some novel distance measures for Pythagorean fuzzy sets using t-conorms. We have also discussed their various desirable properties. With the help of suggested distance measures, we have introduced some new knowledge measures for Pythagorean fuzzy sets. Through numerical comparison and linguistic hedges, we have established the effectiveness of the suggested distance measures and knowledge measures, respectively, over the existing measures in the Pythagorean fuzzy setting. At last, we have demonstrated the application of the suggested measures in pattern analysis and multi-attribute decision-making.
Collapse
|
7
|
Interval-valued intuitionistic fuzzy multi-attribute group decision-making method considering risk preference of decision-makers and its application. Sci Rep 2022; 12:11597. [PMID: 35804077 PMCID: PMC9270440 DOI: 10.1038/s41598-022-15815-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2022] [Accepted: 06/29/2022] [Indexed: 11/09/2022] Open
Abstract
An improved interval-valued intuitionistic fuzzy multi-attribute group decision-making method considering the risk preference of decision-makers is proposed to solve the multi-attribute group decision-making problem with interval-valued intuitionistic fuzzy numbers and the condition that the attribute weight information is completely unknown. Firstly, the decision-maker weight of each attribute is determined by combining similarity and proximity. In order to consider the influence of the decision-maker's risk preference on the decision result and avoid the asymptotic behavior of interval-valued intuitionistic fuzzy matrix, the risk aversion coefficient of the decision-maker is introduced and combined with the determined decision-maker's weight aggregation to form a group decision matrix. Then, the information of group decision matrix is mined, and the interval-valued intuitionistic fuzzy entropy is used to determine the attribute weight and relative weight. Based on the interval-valued intuitionistic fuzzy distance measure formula and the TODIM method, the overall superiority of each scheme relative to other schemes is obtained by calculating the superiority between schemes, and the optimal scheme is determined by comparing and sequencing. Finally, the rationality and effectiveness of the proposed method are verified by an example of mechanical assembly supplier selection decision.
Collapse
|
8
|
An extended interval-valued Pythagorean fuzzy WASPAS method based on new similarity measures to evaluate the renewable energy sources. Appl Soft Comput 2022. [DOI: 10.1016/j.asoc.2022.108689] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
9
|
A Decision-Making Approach Based on New Aggregation Operators under Fermatean Fuzzy Linguistic Information Environment. AXIOMS 2021. [DOI: 10.3390/axioms10020113] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Fermatean fuzzy linguistic (FFL) set theory provides an efficient tool for modeling a higher level of uncertain and imprecise information, which cannot be represented using intuitionistic fuzzy linguistic (IFL)/Pythagorean fuzzy linguistic (PFL) sets. On the other hand, the linguistic scale function (LSF) is the better way to consider the semantics of the linguistic terms during the evaluation process. It is worth noting that the existing operational laws and aggregation operators (AOs) for Fermatean fuzzy linguistic numbers (FFLNs) are not valid in many situations, which can generate errors in real-life applications. The present study aims to define new robust operational laws and AOs under Fermatean fuzzy linguistic environment. To do so, first, we define some new modified operational laws for FFLNs based on LSF and prove some important mathematical properties of them. Next, the work defines several new AOs, namely, the FFL-weighted averaging (FFLWA) operator, the FFL-weighted geometric (FFLWG) operator, the FFL-ordered weighted averaging (FFLOWA) operator, the FFL-ordered weighted geometric (FFLOWG) operator, the FFL-hybrid averaging (FFLHA) operator and the FFL-hybrid geometric (FFLHG) operator under Fermatean fuzzy linguistic environment. Several properties of these AOs are investigated in detail. Further, based on the proposed AOs, a new decision-making approach with Fermatean fuzzy linguistic information is developed to solve group decision-making problems with multiple attributes. Finally, to illustrate the effectiveness of the present approach, a real-life supplier selection problem is presented where the evaluation information of the alternatives is given in terms of FFLNs. Compared to the existing methods, the salient features of the developed approach are (1) it can solve decision-making problems with qualitative information data using FFLNs; (2) It can consider the attitudinal character of the decision-makers during the solution process; (3) It has a solid ability to distinguish the optimal alternative.
Collapse
|
10
|
Some Information Measures Based on Centroid, Orthocenter, Circumcenter and Incenter Points of Transformed Triangular Fuzzy Numbers and their Applications. Cognit Comput 2021. [DOI: 10.1007/s12559-021-09842-9] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
|
11
|
Huang J, Jin X, Lee SJ, Huang S, Jiang Q. An effective similarity/distance measure between intuitionistic fuzzy sets based on the areas of transformed isosceles right triangle and its applications. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2021. [DOI: 10.3233/jifs-201763] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Since the intuitionistic fuzzy set (IFS) was proposed by Atanassov, many explorations of this particular fuzzy set were conducted. One of the most important areas is the study of similarity and distance between IFSs, which can measure the degree of deviation of objects with uncertain and vague features, and this technique has great value and potential to solve the fuzzy and uncertain problems in the real world. Based on our previous similarity/distance measure model DJJ (α, β), a new method is proposed for improving the performance of similarity/distance measure model of IFSs, which is derived from the sum of the areas of two triangles constructed by the transformed isosceles triangles of two IFSs. A great effort is made to prove the validity of the proposed method by mathematical derivation. In order to further demonstrate the performance of the proposed method, we apply this method to solve some practical problems such as pattern recognition, medical diagnosis, and cluster analysis. In addition, we also list a series of the existing methods which are used to compare with the proposed method to prove the effectiveness and superiority. The experimental results confirm that the performance of the proposed method exceeds most of the existing methods.
Collapse
Affiliation(s)
- Jinfang Huang
- School of Software, Yunnan University, Kunming, China
- Engineering Research Center of Cyberspace, Yunnan University, Kunming, China
| | - Xin Jin
- School of Software, Yunnan University, Kunming, China
- Engineering Research Center of Cyberspace, Yunnan University, Kunming, China
| | - Shin-Jye Lee
- Institute of Technology Management, National Chiao Tung University, Hsinchu, Taiwan
| | - Shanshan Huang
- School of Software, Yunnan University, Kunming, China
- Engineering Research Center of Cyberspace, Yunnan University, Kunming, China
| | - Qian Jiang
- School of Software, Yunnan University, Kunming, China
- Engineering Research Center of Cyberspace, Yunnan University, Kunming, China
| |
Collapse
|
12
|
Singh S, Sharma S. On a generalized entropy and dissimilarity measure in intuitionistic fuzzy environment with applications. Soft comput 2021. [DOI: 10.1007/s00500-021-05709-1] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
|
13
|
A novel intuitionistic Renyi’s–Tsallis discriminant information measure and its applications in decision-making. GRANULAR COMPUTING 2020. [DOI: 10.1007/s41066-020-00237-z] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
|
14
|
|
15
|
Ashraf Z, Khan MS, Lohani QD. New bounded variation based similarity measures between Atanassov intuitionistic fuzzy sets for clustering and pattern recognition. Appl Soft Comput 2019. [DOI: 10.1016/j.asoc.2019.105529] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
|
16
|
Liu Y, Jiang W. A new distance measure of interval-valued intuitionistic fuzzy sets and its application in decision making. Soft comput 2019. [DOI: 10.1007/s00500-019-04332-5] [Citation(s) in RCA: 37] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
|
17
|
Shi ZH, Zhang DH. A novel similarity degree of intuitionistic fuzzy sets induced by triangular norm and its application in pattern recognition. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2019. [DOI: 10.3233/jifs-190102] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Zhan-Hong Shi
- Center for Quantitative Biology, College of Science, Gansu Agricultural University, Lanzhou, P.R. China
| | - Ding-Hai Zhang
- Center for Quantitative Biology, College of Science, Gansu Agricultural University, Lanzhou, P.R. China
| |
Collapse
|
18
|
Liu D, Peng D, Liu Z. The distance measures between q‐rung orthopair hesitant fuzzy sets and their application in multiple criteria decision making. INT J INTELL SYST 2019. [DOI: 10.1002/int.22133] [Citation(s) in RCA: 38] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Donghai Liu
- Department of MathematicsHunan University of Science and TechnologyXiangtan P.R. China
| | - Dan Peng
- Department of MathematicsHunan University of Science and TechnologyXiangtan P.R. China
| | - Zaiming Liu
- Department of Mathematics and StatisticsCentral South UniversityChangsha P.R. China
| |
Collapse
|
19
|
Abstract
Complex fuzzy set (CFS) is a recent development in the field of fuzzy set (FS) theory. The significance of CFS lies in the fact that CFS assigned membership grades from a unit circle in the complex plane, i.e., in the form of a complex number whose amplitude term belongs to a [ 0 , 1 ] interval. The interval-valued complex fuzzy set (IVCFS) is one of the extensions of the CFS in which the amplitude term is extended from the real numbers to the interval-valued numbers. The novelty of IVCFS lies in its larger range comparative to CFS. We often use fuzzy distance measures to solve some problems in our daily life. Hence, this paper develops some series of distance measures between IVCFSs by using Hamming and Euclidean metrics. The boundaries of these distance measures for IVCFSs are obtained. Finally, we study two geometric properties include rotational invariance and reflectional invariance of these distance measures.
Collapse
|
20
|
Counterintuitive Test Problems for Transformed Fuzzy Number-Based Similarity Measures between Intuitionistic Fuzzy Sets. Symmetry (Basel) 2019. [DOI: 10.3390/sym11050612] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
This paper analyzes the counterintuitive behaviors of transformed fuzzy number (FN)- based similarity measures between intuitionistic fuzzy sets (IFSs). Among these transformed FN-based similarity measures, Chen and Chang’s similarity measure (2015) is a novel one. An algorithm of computing Chen and Chang’s similarity measure is proposed. We analyze the counterintuitive behaviors of Chen and Chang’s similarity measure for seven general test problems and four test problems with three inclusive IFSs. The results indicate that there are six counterintuitive test problems for Chen and Chang’s similarity measure.
Collapse
|
21
|
Kong D, Chang T, Pan J, Hao N, Xu K, Zhang L, Yang G. A decision variable-based combinatorial optimization approach for interval-valued intuitionistic fuzzy MAGDM. Inf Sci (N Y) 2019. [DOI: 10.1016/j.ins.2019.01.016] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
|
22
|
He X, Li Y, Qin K, Meng D. Distance measures on intuitionistic fuzzy sets based on intuitionistic fuzzy dissimilarity functions. Soft comput 2019. [DOI: 10.1007/s00500-019-03932-5] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
|
23
|
A shape similarity-based ranking method of hesitant fuzzy linguistic preference relations using discrete fuzzy number for group decision making. Soft comput 2019. [DOI: 10.1007/s00500-019-03895-7] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
|
24
|
You X, Yang Q. An aggregating method to big group decision-making problem for the public participation problem under the Chinese situation1. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2019. [DOI: 10.3233/jifs-18615] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Xinshang You
- College of Economics and Management, Shandong University of Science and Technology, Qingdao, China
| | - Qing Yang
- Faculty of Accounting, Shanxi University of Finance and Economics, Taiyuan, China
| |
Collapse
|
25
|
Qi M, Yang Z, Ren W, Wang H. Lorentzian knowledge measures for atanassov’s intuitionistic fuzzy sets. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2019. [DOI: 10.3233/jifs-18265] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Min Qi
- Department of Basic Teaching, Beijing College of Finance and Commerce, Beijing, PR China
| | - Zhanpeng Yang
- Key Laboratory of Technology in Geo-spatial Information Processing and Application System, Institute of Electronics, Chinese Academy of Sciences, Beijing, PR China
| | - Wenjuan Ren
- Key Laboratory of Technology in Geo-spatial Information Processing and Application System, Institute of Electronics, Chinese Academy of Sciences, Beijing, PR China
| | - Hongqi Wang
- Key Laboratory of Technology in Geo-spatial Information Processing and Application System, Institute of Electronics, Chinese Academy of Sciences, Beijing, PR China
| |
Collapse
|
26
|
A Novel Similarity Measure for Interval-Valued Intuitionistic Fuzzy Sets and Its Applications. Symmetry (Basel) 2018. [DOI: 10.3390/sym10100441] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
In this paper, a novel similarity measure for interval-valued intuitionistic fuzzy sets is introduced, which is based on the transformed interval-valued intuitionistic triangle fuzzy numbers. Its superiority is shown by comparing the proposed similarity measure with some existing similarity measures by some numerical examples. Furthermore, the proposed similarity measure is applied to deal with pattern recognition and medical diagnosis problems.
Collapse
|
27
|
New Distance Measure for Atanassov’s Intuitionistic Fuzzy Sets and Its Application in Decision Making. Symmetry (Basel) 2018. [DOI: 10.3390/sym10100429] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
The intuitionistic fuzzy set introduced by Atanassov has greater ability in depicting and handling uncertainty. Intuitionistic fuzzy measure is an important research area of intuitionistic fuzzy set theory. Distance measure and similarity measure are two complementary concepts quantifying the difference and closeness of intuitionistic fuzzy sets. This paper addresses the definition of an effective distance measure with concise form and specific meaning for Atanassov’s intuitionistic fuzzy sets (AIFSs). A new distance measure for AIFSs is defined based on a distance measure of interval values and the transformation from AIFSs to interval valued fuzzy sets. The axiomatic properties of the new distance measure are mathematically investigated. Comparative analysis based in numerical examples indicates that the new distance measure is competent to quantify the difference between AIFSs. The application of the new distance measure is also discussed. A new method for multi-attribute decision making (MADM) is developed based on the technique for order preference by similarity to an ideal solution method and the new distance measure. Numerical applications indicate that the developed MADM method can obtain reasonable preference orders. This shows that the new distance measure is effective and rational from both mathematical and practical points of view.
Collapse
|
28
|
Multi-criteria assessment of cellular mobile telephone service providers using intuitionistic fuzzy WASPAS method with similarity measures. GRANULAR COMPUTING 2018. [DOI: 10.1007/s41066-018-0114-5] [Citation(s) in RCA: 40] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
|
29
|
Intuitionistic Fuzzy Multiple Attribute Decision-Making Model Based on Weighted Induced Distance Measure and Its Application to Investment Selection. Symmetry (Basel) 2018. [DOI: 10.3390/sym10070261] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
|
30
|
A distance measure between intuitionistic fuzzy sets and its application in medical diagnosis. Artif Intell Med 2018; 89:34-39. [PMID: 29891424 DOI: 10.1016/j.artmed.2018.05.002] [Citation(s) in RCA: 60] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2018] [Revised: 05/14/2018] [Accepted: 05/20/2018] [Indexed: 11/22/2022]
Abstract
The intuitionistic fuzzy set, as a generation of fuzzy set, can express and process uncertainty much better. Distance measures between intuitionistic fuzzy sets are used to indicate the difference degree between the information carried by intuitionistic fuzzy sets. Although some distance measures have been proposed in previous studies, they can not satisfy the axioms of distance measure, or exist counter-intuitive cases. In this paper, we give a new distance measure between intuitionistic fuzzy sets, which is based on a matrix norm and a strictly increasing (or decreasing) binary function. The new distance measure not only satisfies the axiomatic definition of distance measure, but also overcomes the counter-intuitive cases. It is proved that the new distance measure is reasonable by numerical examples. Moreover, we give the algorithms for pattern recognition and use it to solve medical diagnosis problems.
Collapse
|
31
|
An extended intuitionistic fuzzy TOPSIS method based on a new distance measure with an application to credit risk evaluation. Inf Sci (N Y) 2018. [DOI: 10.1016/j.ins.2017.10.045] [Citation(s) in RCA: 140] [Impact Index Per Article: 23.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
|
32
|
Luo X, Li W, Zhao W. Intuitive distance for intuitionistic fuzzy sets with applications in pattern recognition. APPL INTELL 2017. [DOI: 10.1007/s10489-017-1091-0] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
|
33
|
|
34
|
Algorithms for interval-valued fuzzy soft sets in stochastic multi-criteria decision making based on regret theory and prospect theory with combined weight. Appl Soft Comput 2017. [DOI: 10.1016/j.asoc.2016.06.036] [Citation(s) in RCA: 148] [Impact Index Per Article: 21.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
|
35
|
Xue W, Xian S, Dong Y. A Novel Intuitionistic Fuzzy Induced Ordered Weighted Euclidean Distance Operator and Its Application for Group Decision Making. INT J INTELL SYST 2016. [DOI: 10.1002/int.21874] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Wenting Xue
- School of Science; Chongqing University of Posts and Telecommunications; Chongqing 400065 People's Republic of China
| | - Sidong Xian
- School of Science; Chongqing University of Posts and Telecommunications; Chongqing 400065 People's Republic of China
| | - Yafen Dong
- School of Science; Chongqing University of Posts and Telecommunications; Chongqing 400065 People's Republic of China
| |
Collapse
|
36
|
A novel similarity measure between intuitionistic fuzzy sets based on the centroid points of transformed fuzzy numbers with applications to pattern recognition. Inf Sci (N Y) 2016. [DOI: 10.1016/j.ins.2016.01.040] [Citation(s) in RCA: 127] [Impact Index Per Article: 15.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
|
37
|
He X, Wu Y, Yu D. Intuitionistic fuzzy multi-criteria decision making with application to job hunting: A comparative perspective. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2016. [DOI: 10.3233/ifs-151904] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Xiaorong He
- School of Economics and Management, Southeast University, Nanjing, Jiangsu, China
| | - Yingyu Wu
- School of Economics and Management, Southeast University, Nanjing, Jiangsu, China
| | - Dejian Yu
- School of Information, Zhejiang University of Finance and Economics, Hangzhou, Zhejiang, China
| |
Collapse
|
38
|
Li J, Zeng W. A new dissimilarity measure between intuitionistic fuzzy sets and its application in multiple attribute decision making1. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2015. [DOI: 10.3233/ifs-141440] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Junhong Li
- College of Information Science and Technology, Beijing Normal University, Beijing, PR China
- College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, Hebei, PR China
| | - Wenyi Zeng
- College of Information Science and Technology, Beijing Normal University, Beijing, PR China
| |
Collapse
|
39
|
A new similarity measure between intuitionistic fuzzy sets and the positive definiteness of the similarity matrix. Pattern Anal Appl 2015. [DOI: 10.1007/s10044-015-0490-2] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
|
40
|
A novel similarity measure between Atanassov’s intuitionistic fuzzy sets based on transformation techniques with applications to pattern recognition. Inf Sci (N Y) 2015. [DOI: 10.1016/j.ins.2014.07.033] [Citation(s) in RCA: 172] [Impact Index Per Article: 19.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
|
41
|
HEIDARZADE ARMAGHAN, MAHDAVI-AMIRI NEZAM, MAHDAVI IRAJ. A NEW DISTANCE FOR INTERVAL TYPE-2 FUZZY SETS WITH AN APPLICATION TO CLUSTERING. INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE AND APPLICATIONS 2014. [DOI: 10.1142/s1469026814500205] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
Type-2 fuzzy sets are generalizations of ordinary fuzzy sets, in which membership grades are characterized by fuzzy membership functions. Here, a problem of finding distance between two interval type-2 fuzzy sets (IT2-FSs) was considered. Based on a new definition of centroid for an IT2-FS, a formulation for calculation of the distance between two IT2-FSs was introduced, and an algorithm was explained to obtain it. The proposed distance formula was incorporated in Yang and Shih's clustering algorithm to reach a clustering method for interval type-2 fuzzy data sets. The applicability of the proposed distance formula was evaluated using two artificial and real data sets, and reasonable results were obtained.
Collapse
Affiliation(s)
- ARMAGHAN HEIDARZADE
- Department of Industrial Engineering, Mazandaran University of Science and Technology, P. O. Box 734, Babol, Iran
| | - NEZAM MAHDAVI-AMIRI
- Faculty of Mathematical Sciences, Sharif University of Technology, Tehran, Iran
| | - IRAJ MAHDAVI
- Department of Industrial Engineering, Mazandaran University of Science and Technology, P. O. Box 734, Babol, Iran
| |
Collapse
|
42
|
Some new entropy measures for interval-valued intuitionistic fuzzy sets based on distances and their relationships with similarity and inclusion measures. Inf Sci (N Y) 2014. [DOI: 10.1016/j.ins.2014.06.012] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
|
43
|
Song Y, Wang X, Lei L, Xue A. A novel similarity measure on intuitionistic fuzzy sets with its applications. APPL INTELL 2014. [DOI: 10.1007/s10489-014-0596-z] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
|
44
|
|
45
|
Du WS, Hu BQ. Approximate distribution reducts in inconsistent interval-valued ordered decision tables. Inf Sci (N Y) 2014. [DOI: 10.1016/j.ins.2014.02.070] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
|
46
|
Tapia-Rosero A, Bronselaer A, De Tré G. A method based on shape-similarity for detecting similar opinions in group decision-making. Inf Sci (N Y) 2014. [DOI: 10.1016/j.ins.2013.09.029] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
|