Pub Date : 2021-10-01DOI: 10.7546/nifs.2021.27.3.18-31
Nora A. Angelova, K. Atanassov
In the theories of intuitionistic fuzzy sets and intuitionistic fuzzy logics, there are 54 different negations. Here, we check the relationship between every two of them.
在直觉模糊集理论和直觉模糊逻辑理论中，有54种不同的否定。这里，我们检查每两个元素之间的关系。
{"title":"Research on intuitionistic fuzzy negations","authors":"Nora A. Angelova, K. Atanassov","doi":"10.7546/nifs.2021.27.3.18-31","DOIUrl":"https://doi.org/10.7546/nifs.2021.27.3.18-31","url":null,"abstract":"In the theories of intuitionistic fuzzy sets and intuitionistic fuzzy logics, there are 54 different negations. Here, we check the relationship between every two of them.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130956818","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 : 2021-10-01DOI: 10.7546/nifs.2021.27.3.1-8
K. Atanassov
In 2021, we celebrate the 100th anniversary of the birth of Prof. Lotfi Zadeh. On this occasion, in this short note, I will share memories from my brief meetings with one of the few persons whose endless enthusiasm, hard work, purposefulness and capacity to innovate I have always admired.
{"title":"My meetings with Prof. Lotfi Zadeh","authors":"K. Atanassov","doi":"10.7546/nifs.2021.27.3.1-8","DOIUrl":"https://doi.org/10.7546/nifs.2021.27.3.1-8","url":null,"abstract":"In 2021, we celebrate the 100th anniversary of the birth of Prof. Lotfi Zadeh. On this occasion, in this short note, I will share memories from my brief meetings with one of the few persons whose endless enthusiasm, hard work, purposefulness and capacity to innovate I have always admired.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124779174","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 : 2021-10-01DOI: 10.7546/nifs.2021.27.3.32-39
A. Michalíková, E. Szmidt, P. Vassilev
In [6], G. Klir and B. Yuan named after J. Łukasiewicz the implication p rightarrow q = min(1, p+q). In a series of papers, 198 different intuitionistic fuzzy implications have been introduced, and their basic properties have been studied. Here we introduce six new implications which are modifications of Łukasiewicz’s intuitionistic fuzzy implication, and we describe and prove some of their properties.
{"title":"Modifications of Łukasiewicz’s intuitionistic fuzzy implication","authors":"A. Michalíková, E. Szmidt, P. Vassilev","doi":"10.7546/nifs.2021.27.3.32-39","DOIUrl":"https://doi.org/10.7546/nifs.2021.27.3.32-39","url":null,"abstract":"In [6], G. Klir and B. Yuan named after J. Łukasiewicz the implication p rightarrow q = min(1, p+q). In a series of papers, 198 different intuitionistic fuzzy implications have been introduced, and their basic properties have been studied. Here we introduce six new implications which are modifications of Łukasiewicz’s intuitionistic fuzzy implication, and we describe and prove some of their properties.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129071007","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 : 2021-08-01DOI: 10.7546/nifs.2021.27.2.94-102
K. Čunderlíková
The aim of this contribution is to show a representation of a conditional intuitionistic fuzzy mean value of intuitionistic fuzzy observables by a conditional mean value of random variables. We formulate a martingale convergence theorem for a conditional intuitionistic fuzzy mean value, too.
{"title":"Martingale convergence theorem for a conditional intuitionistic fuzzy mean value","authors":"K. Čunderlíková","doi":"10.7546/nifs.2021.27.2.94-102","DOIUrl":"https://doi.org/10.7546/nifs.2021.27.2.94-102","url":null,"abstract":"The aim of this contribution is to show a representation of a conditional intuitionistic fuzzy mean value of intuitionistic fuzzy observables by a conditional mean value of random variables. We formulate a martingale convergence theorem for a conditional intuitionistic fuzzy mean value, too.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128558597","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 : 2021-08-01DOI: 10.7546/nifs.2021.27.2.1-10
O. Castillo, P. Melin
We provide in this article a short review of the research work that has been done in Mexico on developing new methods and theory for designing intelligent systems utilizing type-2 fuzzy systems in combination with soft computing techniques. Soft Computing (SC) is an area formed by intelligent paradigms, like fuzzy systems, neural networks, and bio-inspired and swarm algorithms, which may be utilized to build high performance hybrid systems. The combination of type-2 fuzzy systems with SC enables the constructing of efficient intelligent systems for solving complex problems in a wide diversity of areas, such as control, pattern recognition, medical diagnosis and others. We also recall some of the main moments and memories of encounters and meetings with the father of fuzzy logic (Prof. L. Zadeh), which were very positive and motivated us to continue his work and legacy.
{"title":"Fuzzy logic research work in Mexico motivated by Lotfi Zadeh","authors":"O. Castillo, P. Melin","doi":"10.7546/nifs.2021.27.2.1-10","DOIUrl":"https://doi.org/10.7546/nifs.2021.27.2.1-10","url":null,"abstract":"We provide in this article a short review of the research work that has been done in Mexico on developing new methods and theory for designing intelligent systems utilizing type-2 fuzzy systems in combination with soft computing techniques. Soft Computing (SC) is an area formed by intelligent paradigms, like fuzzy systems, neural networks, and bio-inspired and swarm algorithms, which may be utilized to build high performance hybrid systems. The combination of type-2 fuzzy systems with SC enables the constructing of efficient intelligent systems for solving complex problems in a wide diversity of areas, such as control, pattern recognition, medical diagnosis and others. We also recall some of the main moments and memories of encounters and meetings with the father of fuzzy logic (Prof. L. Zadeh), which were very positive and motivated us to continue his work and legacy.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127766370","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 : 2021-08-01DOI: 10.7546/nifs.2021.27.2.11-19
Lilija Atanassova, P. Dworniczak
In this paper, a new weak intuitionistic fuzzy implication is introduced. Fulfillment of some axioms and properties, together with the Modus Ponens and Modus Tollens inference rules are investigated. Negation induced by the newly proposed implication is presented.
{"title":"On the weak intuitionistic fuzzy implication based on △ operation","authors":"Lilija Atanassova, P. Dworniczak","doi":"10.7546/nifs.2021.27.2.11-19","DOIUrl":"https://doi.org/10.7546/nifs.2021.27.2.11-19","url":null,"abstract":"In this paper, a new weak intuitionistic fuzzy implication is introduced. Fulfillment of some axioms and properties, together with the Modus Ponens and Modus Tollens inference rules are investigated. Negation induced by the newly proposed implication is presented.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115989599","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 : 2021-08-01DOI: 10.7546/nifs.2021.27.2.20-93
Nora A. Angelova, K. Atanassov
Currently in the theories of intuitionistic fuzzy sets, logics and pairs, there are 198 different implications. Here, we check the relationships between every two of them.
目前在直觉模糊集、逻辑和对的理论中，有198种不同的含义。这里，我们检查每两个元素之间的关系。
{"title":"Research on intuitionistic fuzzy implications","authors":"Nora A. Angelova, K. Atanassov","doi":"10.7546/nifs.2021.27.2.20-93","DOIUrl":"https://doi.org/10.7546/nifs.2021.27.2.20-93","url":null,"abstract":"Currently in the theories of intuitionistic fuzzy sets, logics and pairs, there are 198 different implications. Here, we check the relationships between every two of them.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129950766","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.2021.27.1.83-100
S. Melliani, Ali El Mfadel, L. S. Chadli, M. Elomari
In this paper, we study the existence and uniqueness results of solution for the intuitionistic fuzzy nonlinear fractional differential equations involving the Caputo concepts of fractional derivative. In addition, we establish essentially the Mittag-Leffler stability result for the intuitionistic fuzzy nonlinear fractional differential equations by giving some sufficient criteria to guarantee the stability of the zero solution. Finally, some examples are presented to illustrate the proposed stability theorem.
{"title":"Stability of intuitionistic fuzzy nonlinear fractional differential equations","authors":"S. Melliani, Ali El Mfadel, L. S. Chadli, M. Elomari","doi":"10.7546/nifs.2021.27.1.83-100","DOIUrl":"https://doi.org/10.7546/nifs.2021.27.1.83-100","url":null,"abstract":"In this paper, we study the existence and uniqueness results of solution for the intuitionistic fuzzy nonlinear fractional differential equations involving the Caputo concepts of fractional derivative. In addition, we establish essentially the Mittag-Leffler stability result for the intuitionistic fuzzy nonlinear fractional differential equations by giving some sufficient criteria to guarantee the stability of the zero solution. Finally, some examples are presented to illustrate the proposed stability theorem.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"14 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":"123322341","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.2021.27.1.60-71
N. A. Alhaleem, A. Ahmad
In this paper, we introduce the notion of intuitionistic anti fuzzy normed subrings and intuitionistic anti fuzzy normed ideals and various properties of intuitionistic anti fuzzy normal subrings and ideals are examined. Also, we prove that the intersection of two intuitionistic anti fuzzy normed ideals is also an intuitionistic anti fuzzy normed ideal. Besides, we define the anti level subsets and identify the relationship between these sets and intuitionistic anti fuzzy normed ideals. In addition, we define the anti-image of intuitionistic anti fuzzy normed ideals and discuss the inverse image and anti-image for intuitionistic anti fuzzy normed ideals under epimorphism mapping.
{"title":"Intuitionistic anti fuzzy normed ideals","authors":"N. A. Alhaleem, A. Ahmad","doi":"10.7546/nifs.2021.27.1.60-71","DOIUrl":"https://doi.org/10.7546/nifs.2021.27.1.60-71","url":null,"abstract":"In this paper, we introduce the notion of intuitionistic anti fuzzy normed subrings and intuitionistic anti fuzzy normed ideals and various properties of intuitionistic anti fuzzy normal subrings and ideals are examined. Also, we prove that the intersection of two intuitionistic anti fuzzy normed ideals is also an intuitionistic anti fuzzy normed ideal. Besides, we define the anti level subsets and identify the relationship between these sets and intuitionistic anti fuzzy normed ideals. In addition, we define the anti-image of intuitionistic anti fuzzy normed ideals and discuss the inverse image and anti-image for intuitionistic anti fuzzy normed ideals under epimorphism mapping.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"14 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":"125861644","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.2021.27.1.72-82
Md. Aman Mahbub, Md. Sahadat Hossain, M. A. Hossain
The purpose of this paper is to establish the connectedness in intuitionistic fuzzy topological space. In this paper we give six notions of separatedness, connectedness and total connectedness and one notion of T1-space in intuitionistic fuzzy topological space. Also, we find a relation between classical topology and intuitionistic fuzzy topology. Further, we show that connectedness in intuitionistic fuzzy topological spaces are productive and we demonstrate some of its features.
{"title":"Connectedness concept in intuitionistic fuzzy topological spaces","authors":"Md. Aman Mahbub, Md. Sahadat Hossain, M. A. Hossain","doi":"10.7546/nifs.2021.27.1.72-82","DOIUrl":"https://doi.org/10.7546/nifs.2021.27.1.72-82","url":null,"abstract":"The purpose of this paper is to establish the connectedness in intuitionistic fuzzy topological space. In this paper we give six notions of separatedness, connectedness and total connectedness and one notion of T1-space in intuitionistic fuzzy topological space. Also, we find a relation between classical topology and intuitionistic fuzzy topology. Further, we show that connectedness in intuitionistic fuzzy topological spaces are productive and we demonstrate some of its features.","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":"130505418","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}
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