Pub Date : 2021-12-01DOI: 10.7546/nifs.2021.27.4.20-29
J. Kacprzyk, K. Čunderlíková, Nora A. Angelova, K. Atanassov
On the basis of the Goguen’s intuitionistic fuzzy implication, seven of its modifications are constructed. Some of their basic properties are studied. The negations, generated by these implications are introduced and some of their properties are also described.
{"title":"Modifications of the Goguen's intuitionistic fuzzy implication","authors":"J. Kacprzyk, K. Čunderlíková, Nora A. Angelova, K. Atanassov","doi":"10.7546/nifs.2021.27.4.20-29","DOIUrl":"https://doi.org/10.7546/nifs.2021.27.4.20-29","url":null,"abstract":"On the basis of the Goguen’s intuitionistic fuzzy implication, seven of its modifications are constructed. Some of their basic properties are studied. The negations, generated by these implications are introduced and some of their properties are also described.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"90 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124619871","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 : 2021-12-01DOI: 10.7546/nifs.2021.27.4.36-43
Sinem Tarsuslu (Yılmaz)
In this study, it is purposed to introduced the concept of quasi-interior ideal on intuitionistic fuzzy semigroups. The concept introduced is supported with examples and its basic algebraic properties are examined.
{"title":"Intuitionistic fuzzy quasi-interior ideals of semigroups","authors":"Sinem Tarsuslu (Yılmaz)","doi":"10.7546/nifs.2021.27.4.36-43","DOIUrl":"https://doi.org/10.7546/nifs.2021.27.4.36-43","url":null,"abstract":"In this study, it is purposed to introduced the concept of quasi-interior ideal on intuitionistic fuzzy semigroups. The concept introduced is supported with examples and its basic algebraic properties are examined.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122849002","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 : 2021-12-01DOI: 10.7546/nifs.2021.27.4.9-19
Lilija Atanassova, P. Dworniczak
In this paper, the Δ operation is discussed as an appropriate tool for the de-i-fuzzification procedure. Some properties of the Δ operation are presented. A known way of the correction of the unconscientious experts’ evaluations in the intuitionistic fuzzy environment is given as the result of the Δ operation.
{"title":"Operation Δ as the tool for the de-i-fuzzification procedure and for the correction of the unconscientious experts' evaluations","authors":"Lilija Atanassova, P. Dworniczak","doi":"10.7546/nifs.2021.27.4.9-19","DOIUrl":"https://doi.org/10.7546/nifs.2021.27.4.9-19","url":null,"abstract":"In this paper, the Δ operation is discussed as an appropriate tool for the de-i-fuzzification procedure. Some properties of the Δ operation are presented. A known way of the correction of the unconscientious experts’ evaluations in the intuitionistic fuzzy environment is given as the result of the Δ operation.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121417598","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 : 2021-12-01DOI: 10.7546/nifs.2021.27.4.71-77
T. Petkov, Veselina Bureva, Stanislav Popov
In this paper a method that evaluates a trained artificial neural network is presented. The learning type of an artificial neural network is supervised learning which requires labeled input training vectors. Labeled medical data is provided to train the network, where the labels can either be 1 if the person is alive, or 0 if the person has deceased. The data is divided into training and validation vectors. The validation input vectors are used to evaluate the model and the results are summarized by using intuitionistic fuzzy values.
{"title":"Intuitionistic fuzzy evaluation of artificial neural network model","authors":"T. Petkov, Veselina Bureva, Stanislav Popov","doi":"10.7546/nifs.2021.27.4.71-77","DOIUrl":"https://doi.org/10.7546/nifs.2021.27.4.71-77","url":null,"abstract":"In this paper a method that evaluates a trained artificial neural network is presented. The learning type of an artificial neural network is supervised learning which requires labeled input training vectors. Labeled medical data is provided to train the network, where the labels can either be 1 if the person is alive, or 0 if the person has deceased. The data is divided into training and validation vectors. The validation input vectors are used to evaluate the model and the results are summarized by using intuitionistic fuzzy values.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"125 23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132369737","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 : 2021-12-01DOI: 10.7546/nifs.2021.27.4.55-70
P. K. Sharma, Chandni
The category theory deals with mathematical structures and relationships between them. Categories now appear in most branches of mathematics and in some areas of theoretical computer science and mathematical physics, and acting as a unifying notion. In this paper, we study the relationship between the category of groups and the category of intuitionistic fuzzy groups. We prove that the category of groups is a subcategory of category of intuitionistic fuzzy groups and that it is not an Abelian category. We establish a function β : Hom(A, B) → [0; 1] × [0; 1] on the set of all intuitionistic fuzzy homomorphisms between intuitionistic fuzzy groups A and B of groups G and H, respectively. We prove that β is a covariant functor from the category of groups to the category of intuitionistic fuzzy groups. Further, we show that the category of intuitionistic fuzzy groups is a top category by establishing a contravariant functor from the category of intuitionistic fuzzy groups to the lattices of all intuitionistic fuzzy groups.
{"title":"Categorical properties of intuitionistic fuzzy groups","authors":"P. K. Sharma, Chandni","doi":"10.7546/nifs.2021.27.4.55-70","DOIUrl":"https://doi.org/10.7546/nifs.2021.27.4.55-70","url":null,"abstract":"The category theory deals with mathematical structures and relationships between them. Categories now appear in most branches of mathematics and in some areas of theoretical computer science and mathematical physics, and acting as a unifying notion. In this paper, we study the relationship between the category of groups and the category of intuitionistic fuzzy groups. We prove that the category of groups is a subcategory of category of intuitionistic fuzzy groups and that it is not an Abelian category. We establish a function β : Hom(A, B) → [0; 1] × [0; 1] on the set of all intuitionistic fuzzy homomorphisms between intuitionistic fuzzy groups A and B of groups G and H, respectively. We prove that β is a covariant functor from the category of groups to the category of intuitionistic fuzzy groups. Further, we show that the category of intuitionistic fuzzy groups is a top category by establishing a contravariant functor from the category of intuitionistic fuzzy groups to the lattices of all intuitionistic fuzzy groups.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130653091","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.2021.27.3.9-17
Selami Bayeğ, R. Mert
In this paper, by using alpha- and beta-cuts approach and the intuitionistic fuzzy Zadeh’s extension principle, we have proved a result which reveals that the alpha- and beta-cuts of an intuitionistic fuzzy number obtained by the intuitionistic fuzzy Zadeh’s extension principle coincide with the images of the alpha- and beta-cuts by the crisp function. Then we have given a corollary about monotonicity of the extension principle. Finally, we have extended these results to IF_N(mathbb{R}) times IF_N(mathbb{R}).
本文利用alpha -和beta -切法和直觉模糊Zadeh的可拓原理，证明了由直觉模糊Zadeh的可拓原理得到的直觉模糊数的alpha -切和beta -切与由酥函数得到的alpha -切和beta -切的图像重合的结果。然后给出了可拓原理单调性的一个推论。最后，我们将这些结果推广到IF＿N(mathbb{R}) times IF＿N(mathbb{R})。
{"title":"On intuitionistic fuzzy version of Zadeh's extension principle","authors":"Selami Bayeğ, R. Mert","doi":"10.7546/nifs.2021.27.3.9-17","DOIUrl":"https://doi.org/10.7546/nifs.2021.27.3.9-17","url":null,"abstract":"In this paper, by using alpha- and beta-cuts approach and the intuitionistic fuzzy Zadeh’s extension principle, we have proved a result which reveals that the alpha- and beta-cuts of an intuitionistic fuzzy number obtained by the intuitionistic fuzzy Zadeh’s extension principle coincide with the images of the alpha- and beta-cuts by the crisp function. Then we have given a corollary about monotonicity of the extension principle. Finally, we have extended these results to IF_N(mathbb{R}) times IF_N(mathbb{R}).","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"3 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":"114621727","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.2021.27.3.51-68
R. Rasuli
In this paper, by using norms, we define the concept of intuitionistic fuzzy equivalence relations and intuitionistic fuzzy congruence relations on ring R and we investigate some assertions. Also we define intuitionistic fuzzy ideals of ring R under norms and compare this with fuzzy equivalence relation and fuzzy congruence relation on ring R such that we define new introduced ring.
{"title":"Norms over intuitionistic fuzzy congruence relations on rings","authors":"R. Rasuli","doi":"10.7546/nifs.2021.27.3.51-68","DOIUrl":"https://doi.org/10.7546/nifs.2021.27.3.51-68","url":null,"abstract":"In this paper, by using norms, we define the concept of intuitionistic fuzzy equivalence relations and intuitionistic fuzzy congruence relations on ring R and we investigate some assertions. Also we define intuitionistic fuzzy ideals of ring R under norms and compare this with fuzzy equivalence relation and fuzzy congruence relation on ring R such that we define new introduced ring.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"3 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":"130222092","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.2021.27.3.69-82
M. S. Islam, R. Islam, M. Hossain
The purpose of this paper is to give some new inferences of intuitionistic fuzzy normal spaces based on the concept of the most studied topics as fuzzy topological spaces. After that, the authors embed an implication among these notions and show that all these conceptions are good extensions of normal spaces. Moreover, the image and the pre-image of intuitionistic fuzzy normal space are also intuitionistic fuzzy normal space.
{"title":"On а study on intuitionistic fuzzy r-normal spaces","authors":"M. S. Islam, R. Islam, M. Hossain","doi":"10.7546/nifs.2021.27.3.69-82","DOIUrl":"https://doi.org/10.7546/nifs.2021.27.3.69-82","url":null,"abstract":"The purpose of this paper is to give some new inferences of intuitionistic fuzzy normal spaces based on the concept of the most studied topics as fuzzy topological spaces. After that, the authors embed an implication among these notions and show that all these conceptions are good extensions of normal spaces. Moreover, the image and the pre-image of intuitionistic fuzzy normal space are also intuitionistic fuzzy normal space.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"9 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":"122469893","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.2021.27.3.40-50
I. M. Adamu
Environmental management is a decision making problem with a great deal of uncertainties. Intuitionistic fuzzy sets provide a model to elaborate these uncertainties and vagueness involve in decision making. This paper, proposes an application of intuitionistic fuzzy set to environmental management in order to determine the type of erosion(s) affecting some towns for an effective control measure that has to be taken using a distance function. In order to achieve this, a set of erosions and their causes are assumed, and also we assume a survey for the set of towns to determine the type of erosion approaching them for an effective control measure to be taken.
{"title":"Application of intuitionistic fuzzy sets to environmental management","authors":"I. M. Adamu","doi":"10.7546/nifs.2021.27.3.40-50","DOIUrl":"https://doi.org/10.7546/nifs.2021.27.3.40-50","url":null,"abstract":"Environmental management is a decision making problem with a great deal of uncertainties. Intuitionistic fuzzy sets provide a model to elaborate these uncertainties and vagueness involve in decision making. This paper, proposes an application of intuitionistic fuzzy set to environmental management in order to determine the type of erosion(s) affecting some towns for an effective control measure that has to be taken using a distance function. In order to achieve this, a set of erosions and their causes are assumed, and also we assume a survey for the set of towns to determine the type of erosion approaching them for an effective control measure to be taken.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"334 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":"133896318","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.2021.27.3.83-97
Zineb Belhallaj, S. Melliani, M. Elomari, L. S. Chadli
In the present paper, we use the generalized differentiability concept to study the intuitionistic fuzzy transport equation. We consider transport equation in the homogeneous and non-homogeneous cases with intuitionistic fuzzy initial condition. To illustrate the results, we will solve an advection equation using the finite difference method.
{"title":"Intuitionistic fuzzy transport equation","authors":"Zineb Belhallaj, S. Melliani, M. Elomari, L. S. Chadli","doi":"10.7546/nifs.2021.27.3.83-97","DOIUrl":"https://doi.org/10.7546/nifs.2021.27.3.83-97","url":null,"abstract":"In the present paper, we use the generalized differentiability concept to study the intuitionistic fuzzy transport equation. We consider transport equation in the homogeneous and non-homogeneous cases with intuitionistic fuzzy initial condition. To illustrate the results, we will solve an advection equation using the finite difference method.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"86 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":"128712144","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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