Pub Date : 2023-03-01DOI: 10.7546/nifs.2023.29.1.46-55
Lilija Atanassova
A new – the 207-th – intuitionistic fuzzy implication is introduced over intuitionistic fuzzy sets. Over its basis, new intuitionistic fuzzy negation, conjunctions and disjunctions are constructed. For the first time, it is shown that all three conjunctions generated by the same implication coincide, whence their respective disjunctions are different. Some properties of the newly constructed operations are studied.
{"title":"A new intuitionistic fuzzy implication and the negation, conjunctions and disjunctions generated by it","authors":"Lilija Atanassova","doi":"10.7546/nifs.2023.29.1.46-55","DOIUrl":"https://doi.org/10.7546/nifs.2023.29.1.46-55","url":null,"abstract":"A new – the 207-th – intuitionistic fuzzy implication is introduced over intuitionistic fuzzy sets. Over its basis, new intuitionistic fuzzy negation, conjunctions and disjunctions are constructed. For the first time, it is shown that all three conjunctions generated by the same implication coincide, whence their respective disjunctions are different. Some properties of the newly constructed operations are studied.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132501876","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 : 2022-12-12DOI: 10.7546/nifs.2022.28.4.457-463
K. Atanassov
Two new Intuitionistic Fuzzy Modal Feeble Topological Structures (IFMFTSs) are introduced of fifth and sixth types. Examples for these structures are given.
介绍了两种新的直觉模糊模态弱拓扑结构(IFMFTSs)的第五类和第六类。给出了这些结构的例子。
{"title":"On intuitionistic fuzzy modal topological structures with modal operator of second type","authors":"K. Atanassov","doi":"10.7546/nifs.2022.28.4.457-463","DOIUrl":"https://doi.org/10.7546/nifs.2022.28.4.457-463","url":null,"abstract":"Two new Intuitionistic Fuzzy Modal Feeble Topological Structures (IFMFTSs) are introduced of fifth and sixth types. Examples for these structures are given.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124082391","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 : 2022-12-12DOI: 10.7546/nifs.2022.28.4.475-490
S. Geetha, R. Parvathi
Krassimir T. Atanassov’s intuitionistic fuzzy sets (IFS), one of the extensions of fuzzy sets, have shown to be one of the most effective ways to handle ambiguity. John N. Mordeson and Davender S. Malik developed the idea of a fuzzy finite state machine. Intuitionistic fuzzy finite state machines were created by Jun as a generalisation of fuzzy finite state machines. In order to increase the uncertainty and lower the periodic functions in intuitionistic fuzzy finite state automata, new membership and non-membership functions based on transitions were introduced in this study. Also, temporal intuitionistic fuzzy automata (TIFA) were defined and used to model a pattern.
Krassimir T. Atanassov的直觉模糊集(IFS)是模糊集的扩展之一，已被证明是处理模糊性的最有效方法之一。John N. Mordeson和Davender S. Malik发展了模糊有限状态机的概念。直觉模糊有限状态机是由Jun作为模糊有限状态机的推广而创建的。为了增加直觉模糊有限状态自动机的不确定性，降低周期函数，引入了基于过渡的隶属函数和非隶属函数。同时，定义了时间直觉模糊自动机(TIFA)，并将其用于模式建模。
{"title":"A mathematical model using temporal intuitionistic fuzzy sets","authors":"S. Geetha, R. Parvathi","doi":"10.7546/nifs.2022.28.4.475-490","DOIUrl":"https://doi.org/10.7546/nifs.2022.28.4.475-490","url":null,"abstract":"Krassimir T. Atanassov’s intuitionistic fuzzy sets (IFS), one of the extensions of fuzzy sets, have shown to be one of the most effective ways to handle ambiguity. John N. Mordeson and Davender S. Malik developed the idea of a fuzzy finite state machine. Intuitionistic fuzzy finite state machines were created by Jun as a generalisation of fuzzy finite state machines. In order to increase the uncertainty and lower the periodic functions in intuitionistic fuzzy finite state automata, new membership and non-membership functions based on transitions were introduced in this study. Also, temporal intuitionistic fuzzy automata (TIFA) were defined and used to model a pattern.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123655872","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 : 2022-12-12DOI: 10.7546/nifs.2022.28.4.413-427
V. Kobza
The basic study of fuzzy sets theory was introduced by Lotfi Zadeh in 1965. Many authors investigated possibilities how two fuzzy sets can be compared and the most common kind of measures used in the mathematical literature are dissimilarity measures. The previous approach to the dissimilarities is too restrictive, because the third axiom in the definition of dissimilarity measure assumes the inclusion relation between fuzzy sets. While there exist many pairs of fuzzy sets, which are incomparable to each other with respect to the inclusion relation. Therefore we need some new concept for measuring a difference between fuzzy sets so that it could be applied for arbitrary fuzzy sets. We focus on the special class of so called local divergences. In the next part we discuss the divergences defined on more general objects, namely intuitionistic fuzzy sets. In this case we define the local property modified to this object. We discuss also the relation of usual divergences between fuzzy sets to the divergences between intuitionistic fuzzy sets.
{"title":"Divergence measures on intuitionistic fuzzy sets","authors":"V. Kobza","doi":"10.7546/nifs.2022.28.4.413-427","DOIUrl":"https://doi.org/10.7546/nifs.2022.28.4.413-427","url":null,"abstract":"The basic study of fuzzy sets theory was introduced by Lotfi Zadeh in 1965. Many authors investigated possibilities how two fuzzy sets can be compared and the most common kind of measures used in the mathematical literature are dissimilarity measures. The previous approach to the dissimilarities is too restrictive, because the third axiom in the definition of dissimilarity measure assumes the inclusion relation between fuzzy sets. While there exist many pairs of fuzzy sets, which are incomparable to each other with respect to the inclusion relation. Therefore we need some new concept for measuring a difference between fuzzy sets so that it could be applied for arbitrary fuzzy sets. We focus on the special class of so called local divergences. In the next part we discuss the divergences defined on more general objects, namely intuitionistic fuzzy sets. In this case we define the local property modified to this object. We discuss also the relation of usual divergences between fuzzy sets to the divergences between intuitionistic fuzzy sets.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127028469","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 : 2022-12-12DOI: 10.7546/nifs.2022.28.4.442-456
Nour Abed Alhaleem, A. Ahmad
In this paper, we generalize direct product of finite intuitionistic anti fuzzy normal subrings over normed rings. In particular, we discuss the relation between intuitionistic anti characteristic function and direct product of finite intuitionistic anti fuzzy normed normal subrings. Finally, we give characterizations of direct product of finite intuitionistic anti fuzzy normed normal subrings and some relevant properties are presented.
{"title":"Direct product of finite intuitionistic anti fuzzy normed normal subrings","authors":"Nour Abed Alhaleem, A. Ahmad","doi":"10.7546/nifs.2022.28.4.442-456","DOIUrl":"https://doi.org/10.7546/nifs.2022.28.4.442-456","url":null,"abstract":"In this paper, we generalize direct product of finite intuitionistic anti fuzzy normal subrings over normed rings. In particular, we discuss the relation between intuitionistic anti characteristic function and direct product of finite intuitionistic anti fuzzy normed normal subrings. Finally, we give characterizations of direct product of finite intuitionistic anti fuzzy normed normal subrings and some relevant properties are presented.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"391 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122784036","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 : 2022-12-12DOI: 10.7546/nifs.2022.28.4.375-380
Ü. Deniz
In this paper we give the definitions of t-lower level set (Lt(A)) and t-upper level set (Ut(A)) of an Intuitionistic fuzzy set. [1] A t-lower level set is defined by giving a lower boundary on μA(x) + νA(x). A t-upper level set is defined by giving an upper boundary on μA(x) + νA(x). If A is an Intuitionistic fuzzy set of X, then Lt(A) and Ut(A) are subsets of X. In this paper we give some theorems by using t-lower level sets and t-upper level sets and prove them.
{"title":"t-Lower level set and t-upper level set of an intuitionistic fuzzy set","authors":"Ü. Deniz","doi":"10.7546/nifs.2022.28.4.375-380","DOIUrl":"https://doi.org/10.7546/nifs.2022.28.4.375-380","url":null,"abstract":"In this paper we give the definitions of t-lower level set (Lt(A)) and t-upper level set (Ut(A)) of an Intuitionistic fuzzy set. [1] A t-lower level set is defined by giving a lower boundary on μA(x) + νA(x). A t-upper level set is defined by giving an upper boundary on μA(x) + νA(x). If A is an Intuitionistic fuzzy set of X, then Lt(A) and Ut(A) are subsets of X. In this paper we give some theorems by using t-lower level sets and t-upper level sets and prove them.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122918947","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 : 2022-12-12DOI: 10.7546/nifs.2022.28.4.397-412
R. Parvathi, C. Yuvapriya
This paper is devoted to develop the theory of temporal intuitionistic fuzzy sets. The matrix representation of a TIFS is also introduced for easy symbolization. In addition to a few basic operations, length of a TIFS and its properties are discussed. Morphological operations on temporal intuitionistic fuzzy sets are defined using (i) mathematical operations, (ii) structuring element, (iii) inclusion indicators, and (iv) temporal intuitionistic fuzzy divergence and verified with suitable examples.
{"title":"Morphological operations on temporal intuitionistic fuzzy sets","authors":"R. Parvathi, C. Yuvapriya","doi":"10.7546/nifs.2022.28.4.397-412","DOIUrl":"https://doi.org/10.7546/nifs.2022.28.4.397-412","url":null,"abstract":"This paper is devoted to develop the theory of temporal intuitionistic fuzzy sets. The matrix representation of a TIFS is also introduced for easy symbolization. In addition to a few basic operations, length of a TIFS and its properties are discussed. Morphological operations on temporal intuitionistic fuzzy sets are defined using (i) mathematical operations, (ii) structuring element, (iii) inclusion indicators, and (iv) temporal intuitionistic fuzzy divergence and verified with suitable examples.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114585117","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 : 2022-12-12DOI: 10.7546/nifs.2022.28.4.464-474
Veselina Bureva, Petar R. Petrov, Vassia Atanassova, Ivo Umlenski
In the paper, the intuitionistic fuzzy sets based InterCriteria Analysis (ICA) and big data systems are applied to the 2021 dataset of the National Statistical Institute with respect to the Bulgarian system of higher education. The results are produced using the Big Data platform Hortonworks and the ICA software ICrAData. Discussion is presented on the discovered relationships regarding tendencies between enrolled and graduated students, and teaching staff.
{"title":"InterCriteria Analysis as a tool for analyzing Big Data datasets: Case study of 2021 national statistics of Bulgarian system of higher education","authors":"Veselina Bureva, Petar R. Petrov, Vassia Atanassova, Ivo Umlenski","doi":"10.7546/nifs.2022.28.4.464-474","DOIUrl":"https://doi.org/10.7546/nifs.2022.28.4.464-474","url":null,"abstract":"In the paper, the intuitionistic fuzzy sets based InterCriteria Analysis (ICA) and big data systems are applied to the 2021 dataset of the National Statistical Institute with respect to the Bulgarian system of higher education. The results are produced using the Big Data platform Hortonworks and the ICA software ICrAData. Discussion is presented on the discovered relationships regarding tendencies between enrolled and graduated students, and teaching staff.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124088125","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 : 2022-12-12DOI: 10.7546/nifs.2022.28.4.428-435
Nora A. Angelova, K. Čunderlíková, E. Szmidt, K. Atanassov
One of the essential formulas of the classical mathematical logic is (A → B) → ((¬A → B) → B). In the present paper, its intuitionistic fuzzy interpretation is introduced, and lists of all defined intuitionistic fuzzy implications that satisfy it as a tautology and an intuitionistic fuzzy tautology are given.
{"title":"Intuitionistic fuzzy interpretations of formula (A → B) → ((¬A → B) → B)","authors":"Nora A. Angelova, K. Čunderlíková, E. Szmidt, K. Atanassov","doi":"10.7546/nifs.2022.28.4.428-435","DOIUrl":"https://doi.org/10.7546/nifs.2022.28.4.428-435","url":null,"abstract":"One of the essential formulas of the classical mathematical logic is (A → B) → ((¬A → B) → B). In the present paper, its intuitionistic fuzzy interpretation is introduced, and lists of all defined intuitionistic fuzzy implications that satisfy it as a tautology and an intuitionistic fuzzy tautology are given.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130958835","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 : 2022-12-12DOI: 10.7546/nifs.2022.28.4.436-441
Velin Andonov, S. Zadrożny, Lilija Atanassova
The basic study of fuzzy sets theory was introduced by Lotfi Zadeh in 1965. Many authors investigated possibilities how two fuzzy sets can be compared and the most common kind of measures used in the mathematical literature are dissimilarity measures. The previous approach to the dissimilarities is too restrictive, because the third axiom in the definition of dissimilarity measure assumes the inclusion relation between fuzzy sets. While there exist many pairs of fuzzy sets, which are incomparable to each other with respect to the inclusion relation. Therefore we need some new concept for measuring a difference between fuzzy sets so that it could be applied for arbitrary fuzzy sets. We focus on the special class of so called local divergences. In the next part we discuss the divergences defined on more general objects, namely intuitionistic fuzzy sets. In this case we define the local property modified to this object. We discuss also the relation of usual divergences between fuzzy sets to the divergences between intuitionistic fuzzy sets.
{"title":"A new operation over intuitionistic fuzzy pairs","authors":"Velin Andonov, S. Zadrożny, Lilija Atanassova","doi":"10.7546/nifs.2022.28.4.436-441","DOIUrl":"https://doi.org/10.7546/nifs.2022.28.4.436-441","url":null,"abstract":"The basic study of fuzzy sets theory was introduced by Lotfi Zadeh in 1965. Many authors investigated possibilities how two fuzzy sets can be compared and the most common kind of measures used in the mathematical literature are dissimilarity measures. The previous approach to the dissimilarities is too restrictive, because the third axiom in the definition of dissimilarity measure assumes the inclusion relation between fuzzy sets. While there exist many pairs of fuzzy sets, which are incomparable to each other with respect to the inclusion relation. Therefore we need some new concept for measuring a difference between fuzzy sets so that it could be applied for arbitrary fuzzy sets. We focus on the special class of so called local divergences. In the next part we discuss the divergences defined on more general objects, namely intuitionistic fuzzy sets. In this case we define the local property modified to this object. We discuss also the relation of usual divergences between fuzzy sets to the divergences between intuitionistic fuzzy sets.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125925225","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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