Pub Date : 2021-06-01DOI: 10.7546/nifs.2021.27.1.1-4
J. Kacprzyk
Fellow, IEEE, IET, EurAI, IFIP, IFSA, SMIA Full member, Polish Academy of Sciences Member, Academia Europaea Member, European Academy of Sciences and Arts Member, International Academy for Systems and Cybernetic Sciences Foreign member, Bulgarian Academy of Sciences Foreign member, Finnish Society of Sciences and Letters Foreign member, Royal Flemish Academy of Belgium for Sciences and the Arts Foreign member, Spanish Royal Academy of Economic and Financial Sciences
{"title":"Lotfi A. Zadeh: A great researcher and scholar already before fuzzy sets/logic","authors":"J. Kacprzyk","doi":"10.7546/nifs.2021.27.1.1-4","DOIUrl":"https://doi.org/10.7546/nifs.2021.27.1.1-4","url":null,"abstract":"Fellow, IEEE, IET, EurAI, IFIP, IFSA, SMIA Full member, Polish Academy of Sciences Member, Academia Europaea Member, European Academy of Sciences and Arts Member, International Academy for Systems and Cybernetic Sciences Foreign member, Bulgarian Academy of Sciences Foreign member, Finnish Society of Sciences and Letters Foreign member, Royal Flemish Academy of Belgium for Sciences and the Arts Foreign member, Spanish Royal Academy of Economic and Financial Sciences","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115298829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-01DOI: 10.7546/nifs.2021.27.1.53-59
M. Vassilev-Missana
The inequality mu^{frac{1}{nu}} + nu^{frac{1}{mu}} leq 1 is introduced and proved, where mu and nu are real numbers, for which mu, nu in [0, 1] and mu + nu leq 1. The same inequality is valid for mu = mu_A(x), nu = nu_A(x), where mu_A and nu_A are the membership and the non-membership functions of an arbitrary intuitionistic fuzzy set A over a fixed universe E and x in E. Also, a generalization of the above inequality for arbitrary n geq 2 is proposed and proved.
引入并证明了不等式mu ^ {frac{1}{nu}} + nu ^ {frac{1}{mu}}leq 1,其中mu和nu为实数,其中mu、nuin[0,1]和mu + nuleq 1。同样的不等式也适用于mu = mu _A(x), nu = nu _A(x),其中mu _A和nu _A是任意直觉模糊集A在固定宇宙E和x in E上的隶属函数和非隶属函数。此外,对任意n geq 2提出并证明了上述不等式的推广。
{"title":"Note on one inequality and its application in intuitionistic fuzzy sets theory. Part 1","authors":"M. Vassilev-Missana","doi":"10.7546/nifs.2021.27.1.53-59","DOIUrl":"https://doi.org/10.7546/nifs.2021.27.1.53-59","url":null,"abstract":"The inequality mu^{frac{1}{nu}} + nu^{frac{1}{mu}} leq 1 is introduced and proved, where mu and nu are real numbers, for which mu, nu in [0, 1] and mu + nu leq 1. The same inequality is valid for mu = mu_A(x), nu = nu_A(x), where mu_A and nu_A are the membership and the non-membership functions of an arbitrary intuitionistic fuzzy set A over a fixed universe E and x in E. Also, a generalization of the above inequality for arbitrary n geq 2 is proposed and proved.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131364706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-01DOI: 10.7546/nifs.2021.27.1.9-23
K. Atanassov, Nora A. Angelova
In [24], G. Klir and B. Yuan named after L. Zadeh the implication p → q = max(1 − p, min(p, q)). In a series of papers, the author introduced two intuitionistic fuzzy forms of Zadeh’s implication and their basic properties have been studied. In the present paper, a new (third) intuitionistic fuzzy form of Zadeh’s implication is given and some of its properties are studied.
{"title":"Modifications of the Third Zadeh’s intuitionistic fuzzy implication","authors":"K. Atanassov, Nora A. Angelova","doi":"10.7546/nifs.2021.27.1.9-23","DOIUrl":"https://doi.org/10.7546/nifs.2021.27.1.9-23","url":null,"abstract":"In [24], G. Klir and B. Yuan named after L. Zadeh the implication p → q = max(1 − p, min(p, q)). In a series of papers, the author introduced two intuitionistic fuzzy forms of Zadeh’s implication and their basic properties have been studied. In the present paper, a new (third) intuitionistic fuzzy form of Zadeh’s implication is given and some of its properties are studied.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134346754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-01DOI: 10.7546/nifs.2021.27.1.5-8
E. Szmidt
{"title":"Lotfi Zadeh – some personal memories","authors":"E. Szmidt","doi":"10.7546/nifs.2021.27.1.5-8","DOIUrl":"https://doi.org/10.7546/nifs.2021.27.1.5-8","url":null,"abstract":"","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"108 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133310233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-01DOI: 10.7546/nifs.2021.27.1.24-52
C. Kahraman, Nurşah Alkan
The membership function of a general type-2 fuzzy set is three-dimensional in order to incorporate its vagueness through the third dimension. Similarly, Circular intuitionistic fuzzy sets (CIFSs) have been recently introduced by Atanassov (2020) as a new extension of intuitionistic fuzzy sets, which are represented by a circle representing the vagueness of the membership function. CIFSs allow decision-makers to express their judgments including this vagueness. In this study, the TOPSIS method, which is one of the most used multi-criteria decision-making methods is extended to its CIF version. The proposed CIF-TOPSIS methodology is applied to the supplier selection problem. Then, a sensitivity analysis based on criteria weights is conducted to check the robustness of the proposed approach. A comparative analysis with single-valued intuitionistic fuzzy TOPSIS method is also performed to verify the developed approach and to demonstrate its effectiveness
{"title":"Circular intuitionistic fuzzy TOPSIS method with vague membership functions: Supplier selection application context","authors":"C. Kahraman, Nurşah Alkan","doi":"10.7546/nifs.2021.27.1.24-52","DOIUrl":"https://doi.org/10.7546/nifs.2021.27.1.24-52","url":null,"abstract":"The membership function of a general type-2 fuzzy set is three-dimensional in order to incorporate its vagueness through the third dimension. Similarly, Circular intuitionistic fuzzy sets (CIFSs) have been recently introduced by Atanassov (2020) as a new extension of intuitionistic fuzzy sets, which are represented by a circle representing the vagueness of the membership function. CIFSs allow decision-makers to express their judgments including this vagueness. In this study, the TOPSIS method, which is one of the most used multi-criteria decision-making methods is extended to its CIF version. The proposed CIF-TOPSIS methodology is applied to the supplier selection problem. Then, a sensitivity analysis based on criteria weights is conducted to check the robustness of the proposed approach. A comparative analysis with single-valued intuitionistic fuzzy TOPSIS method is also performed to verify the developed approach and to demonstrate its effectiveness","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130640236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-01DOI: 10.7546/NIFS.2020.26.4.53-63
Tamanna Tasnim Prova, Md. Sahadat Hossain
In this paper, we define the notion of intuitionistic fuzzy based regular and normal spaces. We also study that classical regular and normal spaces are also intuitionistic fuzzy based regular and normal spaces but the converses are not true in general. This notion opens up a new conception of generalization of classical regular and normal spaces. The hereditary and topological properties of intuitionistic fuzzy based regular and normal spaces have been also investigated. Moreover, by setting some examples we show that every intuitionistic fuzzy based regular space as well as intuitionistic fuzzy based normal space need not be T1 spaces. Finally, it is shown that under some conditions the images and homeomorphic images are preserved in intuitionistic fuzzy based regular and normal spaces.
{"title":"Intuitionistic fuzzy based regular and normal spaces","authors":"Tamanna Tasnim Prova, Md. Sahadat Hossain","doi":"10.7546/NIFS.2020.26.4.53-63","DOIUrl":"https://doi.org/10.7546/NIFS.2020.26.4.53-63","url":null,"abstract":"In this paper, we define the notion of intuitionistic fuzzy based regular and normal spaces. We also study that classical regular and normal spaces are also intuitionistic fuzzy based regular and normal spaces but the converses are not true in general. This notion opens up a new conception of generalization of classical regular and normal spaces. The hereditary and topological properties of intuitionistic fuzzy based regular and normal spaces have been also investigated. Moreover, by setting some examples we show that every intuitionistic fuzzy based regular space as well as intuitionistic fuzzy based normal space need not be T1 spaces. Finally, it is shown that under some conditions the images and homeomorphic images are preserved in intuitionistic fuzzy based regular and normal spaces.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132362613","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-01DOI: 10.7546/NIFS.2020.26.4.71-79
Zhelyana Ivanova, Veselina Bureva
In the current research work a multimodal biometric system is investigated. It combines the palm vein authentication and palm geometry recognition methods. The system will be used to manage the access control. The apparatus of generalized nets is applied to model the biometric authentication processes. The constructed generalized net model of biometric authentication system based on palm geometry and palm vein matching using intuitionistic fuzzy evaluations can be used for simulation of the real processes. The intuitionistic fuzzy evaluations are used to compare the user traits with the templates stored in database.
{"title":"Generalized net model of a biometric authentication system based on palm geometry and palm vein matching using intuitionistic fuzzy evaluations","authors":"Zhelyana Ivanova, Veselina Bureva","doi":"10.7546/NIFS.2020.26.4.71-79","DOIUrl":"https://doi.org/10.7546/NIFS.2020.26.4.71-79","url":null,"abstract":"In the current research work a multimodal biometric system is investigated. It combines the palm vein authentication and palm geometry recognition methods. The system will be used to manage the access control. The apparatus of generalized nets is applied to model the biometric authentication processes. The constructed generalized net model of biometric authentication system based on palm geometry and palm vein matching using intuitionistic fuzzy evaluations can be used for simulation of the real processes. The intuitionistic fuzzy evaluations are used to compare the user traits with the templates stored in database.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126540691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-01DOI: 10.7546/NIFS.2020.26.4.9-52
K. Atanassov
The possibilities for using the apparatuses of generalized nets and intuitionistic fuzzy sets as means for modelling and evaluation of Data Mining processes and tools are discussed and illustrated by examples.
本文讨论并举例说明了使用广义网络和直觉模糊集作为数据挖掘过程和工具的建模和评估手段的可能性。
{"title":"Generalized nets and intuitionistic fuzziness as tools for modelling of data mining processes and tools","authors":"K. Atanassov","doi":"10.7546/NIFS.2020.26.4.9-52","DOIUrl":"https://doi.org/10.7546/NIFS.2020.26.4.9-52","url":null,"abstract":"The possibilities for using the apparatuses of generalized nets and intuitionistic fuzzy sets as means for modelling and evaluation of Data Mining processes and tools are discussed and illustrated by examples.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130730824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-01DOI: 10.7546/NIFS.2020.26.4.90-106
Veselina Bureva, Lilija Atanassova, K. Atanassov, A. Zlatarov
The concept of a temporal intuitionistic fuzzy pair is introduced. It is used for an evaluation of the results of a Game Method for Modelling applied over some areas of fire in a two-dimensional orthogonal grid of cells.
{"title":"Game method for modelling with temporal intuitionistic fuzzy evaluations for locating the wildfire ignition point","authors":"Veselina Bureva, Lilija Atanassova, K. Atanassov, A. Zlatarov","doi":"10.7546/NIFS.2020.26.4.90-106","DOIUrl":"https://doi.org/10.7546/NIFS.2020.26.4.90-106","url":null,"abstract":"The concept of a temporal intuitionistic fuzzy pair is introduced. It is used for an evaluation of the results of a Game Method for Modelling applied over some areas of fire in a two-dimensional orthogonal grid of cells.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128737515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-01DOI: 10.7546/NIFS.2020.26.4.64-70
R. K. Nivendhaa, R. Parvathi
It is usual in image processing that binary (black & white) and gray images are represented by crisp sets and fuzzy sets respectively. In this paper, an attempt has been made to represent a color image (RGB) using intuitionistic fuzzy index matrices. The objective of this representation is to apply mathematical operators on intuitionistic fuzzy index matrices in processing RGB images.
{"title":"Intuitionistic fuzzy index matrix representation of color images","authors":"R. K. Nivendhaa, R. Parvathi","doi":"10.7546/NIFS.2020.26.4.64-70","DOIUrl":"https://doi.org/10.7546/NIFS.2020.26.4.64-70","url":null,"abstract":"It is usual in image processing that binary (black & white) and gray images are represented by crisp sets and fuzzy sets respectively. In this paper, an attempt has been made to represent a color image (RGB) using intuitionistic fuzzy index matrices. The objective of this representation is to apply mathematical operators on intuitionistic fuzzy index matrices in processing RGB images.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129730781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}