Pub Date : 2022-12-12DOI: 10.7546/nifs.2022.28.4.381-396
K. Čunderlíková
The aim of this contribution is to define a convergence in distribution, a convergence in measure and an almost everywhere convergence with respect to an intuitionistic fuzzy probability. We prove a version of Central limit theorem, a version of Weak law of large numbers and a version of Strong law of large numbers for intuitionistic fuzzy observables with respect to the intuitionistic fuzzy probability. We study a connection between convergence of intuitionistic fuzzy observables with respect to the intuitionistic fuzzy probability and a convergence of random variables, too.
{"title":"Intuitionistic fuzzy probability and convergence of intuitionistic fuzzy observables","authors":"K. Čunderlíková","doi":"10.7546/nifs.2022.28.4.381-396","DOIUrl":"https://doi.org/10.7546/nifs.2022.28.4.381-396","url":null,"abstract":"The aim of this contribution is to define a convergence in distribution, a convergence in measure and an almost everywhere convergence with respect to an intuitionistic fuzzy probability. We prove a version of Central limit theorem, a version of Weak law of large numbers and a version of Strong law of large numbers for intuitionistic fuzzy observables with respect to the intuitionistic fuzzy probability. We study a connection between convergence of intuitionistic fuzzy observables with respect to the intuitionistic fuzzy probability and a convergence of random variables, too.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"18 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":"115250192","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 : 2022-09-08DOI: 10.7546/nifs.2022.28.3.334-342
Başar Öztayşi, Sezi Cevik Onar, C. Kahraman, S. Çebi
Digital transformation necessitates fundamental changes in business processes, business models, and even cultures of the companies. DT projects provide a substantial value to the business competition and effect their market shares. In order to reach these results, digital transformation projects should be carefully analyzed and evaluated. In this paper, we focus on digital transformation project prioritization problem under multiple criteria. Just like many other technology related decisions, digital transformation problems are inherently uncertain, which leads researchers to employ the fuzzy set theory. Interval Valued Type-2 Intuitionistic Fuzzy Sets (IVT2IFS) are a relatively new extension of fuzzy sets which take into account membership and non-membership values as an interval. In this paper, we utilize Interval Valued Type-2 Intuitionistic Fuzzy TOPSIS method for a digital transformation project prioritization problem and apply the model to a real-world example.
{"title":"Digital transformation project selection using Interval Valued Type-2 Intuitionistic Fuzzy TOPSIS","authors":"Başar Öztayşi, Sezi Cevik Onar, C. Kahraman, S. Çebi","doi":"10.7546/nifs.2022.28.3.334-342","DOIUrl":"https://doi.org/10.7546/nifs.2022.28.3.334-342","url":null,"abstract":"Digital transformation necessitates fundamental changes in business processes, business models, and even cultures of the companies. DT projects provide a substantial value to the business competition and effect their market shares. In order to reach these results, digital transformation projects should be carefully analyzed and evaluated. In this paper, we focus on digital transformation project prioritization problem under multiple criteria. Just like many other technology related decisions, digital transformation problems are inherently uncertain, which leads researchers to employ the fuzzy set theory. Interval Valued Type-2 Intuitionistic Fuzzy Sets (IVT2IFS) are a relatively new extension of fuzzy sets which take into account membership and non-membership values as an interval. In this paper, we utilize Interval Valued Type-2 Intuitionistic Fuzzy TOPSIS method for a digital transformation project prioritization problem and apply the model to a real-world example.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"112 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132854853","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}
The Tchebychev distance on fuzzy sets (FSs) has been proposed to construct a measure of proximity between two modalities in a two-dimensional statistical description. The parameterized symmetric difference operations and cardinality for intuitionistic fuzzy sets (IFSs) has been proposed. This paper extends to intuitionistic fuzzy set the Tchebychev distance and possibility measure on fuzzy sets. More precisely, we firstly use the parameterized symmetric difference operations and the cardinality on IFSs to propose a Tchebychev distance measure for IFSs. From these, we then deduce two examples of metrics. Secondly, we introduce an intuitionistic fuzzy mapping that preserves the properties of the fuzzy mapping. We use this mapping to propose a Tchebychev possibility measure based on IF-cardinality. This leads to define a proximity measure between two modalities of a given character in a two-dimensional intuitionistic fuzzy statistical description.
{"title":"On some classes of Tchebychev distance based on intuitionistic fuzzy cardinality and intuitionistic fuzzy statistical description","authors":"Romuald Thierry Dzati Kamga, Bertrand Mbama Engoulou, Siméon Fotso, L. Fono","doi":"10.7546/nifs.2022.28.3.238-258","DOIUrl":"https://doi.org/10.7546/nifs.2022.28.3.238-258","url":null,"abstract":"The Tchebychev distance on fuzzy sets (FSs) has been proposed to construct a measure of proximity between two modalities in a two-dimensional statistical description. The parameterized symmetric difference operations and cardinality for intuitionistic fuzzy sets (IFSs) has been proposed. This paper extends to intuitionistic fuzzy set the Tchebychev distance and possibility measure on fuzzy sets. More precisely, we firstly use the parameterized symmetric difference operations and the cardinality on IFSs to propose a Tchebychev distance measure for IFSs. From these, we then deduce two examples of metrics. Secondly, we introduce an intuitionistic fuzzy mapping that preserves the properties of the fuzzy mapping. We use this mapping to propose a Tchebychev possibility measure based on IF-cardinality. This leads to define a proximity measure between two modalities of a given character in a two-dimensional intuitionistic fuzzy statistical description.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114062695","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 : 2022-09-08DOI: 10.7546/nifs.2022.28.3.343-352
Georgy Urumov, P. Chountas
Clustering involves gathering a collection of objects into homogeneous groups or clusters, such that objects in the same cluster are more similar when compared to objects present in other groups. Clustering algorithms that generate a tree of clusters called dendrogram which can be either divisive or agglomerative. The partitional clustering gives a single partition of objects, with a predefined K number of clusters. The most popular partition clustering approaches are: k-means and fuzzy C-means (FCM). In k-means clustering, data are divided into a number of clusters where data elements belong to exactly one cluster. The k-means clustering works well when data elements are well separable. To overcome the problem of non-separability, FCM and IFCM clustering algorithm were proposed. Here we review the use of FCM/IFCM with reference to the problem of market volatility.
{"title":"Clustering stock price volatility using intuitionistic fuzzy sets","authors":"Georgy Urumov, P. Chountas","doi":"10.7546/nifs.2022.28.3.343-352","DOIUrl":"https://doi.org/10.7546/nifs.2022.28.3.343-352","url":null,"abstract":"Clustering involves gathering a collection of objects into homogeneous groups or clusters, such that objects in the same cluster are more similar when compared to objects present in other groups. Clustering algorithms that generate a tree of clusters called dendrogram which can be either divisive or agglomerative. The partitional clustering gives a single partition of objects, with a predefined K number of clusters. The most popular partition clustering approaches are: k-means and fuzzy C-means (FCM). In k-means clustering, data are divided into a number of clusters where data elements belong to exactly one cluster. The k-means clustering works well when data elements are well separable. To overcome the problem of non-separability, FCM and IFCM clustering algorithm were proposed. Here we review the use of FCM/IFCM with reference to the problem of market volatility.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"1991 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125520206","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 : 2022-09-08DOI: 10.7546/nifs.2022.28.3.203-210
O. Kosheleva, V. Kreinovich
While modern computers are fast, there are still many important practical situations in which we need even faster computations. It turns out that, due to the fact that the speed of all communications is limited by the speed of light, the only way to make computers drastically faster is to drastically decrease the size of computer’s components. When we decrease their size to sizes comparable with micro-sizes of individual molecules, it becomes necessary to take into account specific physics of the micro-world – known as quantum physics. Traditional approach to designing quantum computers – i.e., computers that take effect of quantum physics into account – was based on using quantum analogies of bits (2-state systems). However, it has recently been shown that the use of multi-state quantum systems – called qudits – can make quantum computers even more efficient. When processing data, it is important to take into account that in practice, data always comes with uncertainty. In this paper, we analyze how to represent different types of uncertainty by qudits.
{"title":"How to represent uncertainty via qudits: Probability distributions, regular, intuitionistic and picture fuzzy sets, F-transforms, etc.","authors":"O. Kosheleva, V. Kreinovich","doi":"10.7546/nifs.2022.28.3.203-210","DOIUrl":"https://doi.org/10.7546/nifs.2022.28.3.203-210","url":null,"abstract":"While modern computers are fast, there are still many important practical situations in which we need even faster computations. It turns out that, due to the fact that the speed of all communications is limited by the speed of light, the only way to make computers drastically faster is to drastically decrease the size of computer’s components. When we decrease their size to sizes comparable with micro-sizes of individual molecules, it becomes necessary to take into account specific physics of the micro-world – known as quantum physics. Traditional approach to designing quantum computers – i.e., computers that take effect of quantum physics into account – was based on using quantum analogies of bits (2-state systems). However, it has recently been shown that the use of multi-state quantum systems – called qudits – can make quantum computers even more efficient. When processing data, it is important to take into account that in practice, data always comes with uncertainty. In this paper, we analyze how to represent different types of uncertainty by qudits.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124195959","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 : 2022-09-08DOI: 10.7546/nifs.2022.28.3.306-318
A. Michalíková
The research presented in this paper is motivated by possibilities of using fuzzy equivalence relations to classify the data into the specific classes. We try to improve these results with the use of intuitionistic fuzzy equivalence relations. We define the basic structures and their properties, which are used in the paper. Then we present the data which we decided to classify and the methods of processing these data. At the end of the paper we discus obtained results and problems which occurred during the processing of the selected data.
{"title":"Some notes on intuitionistic fuzzy equivalence relations and their use on real data","authors":"A. Michalíková","doi":"10.7546/nifs.2022.28.3.306-318","DOIUrl":"https://doi.org/10.7546/nifs.2022.28.3.306-318","url":null,"abstract":"The research presented in this paper is motivated by possibilities of using fuzzy equivalence relations to classify the data into the specific classes. We try to improve these results with the use of intuitionistic fuzzy equivalence relations. We define the basic structures and their properties, which are used in the paper. Then we present the data which we decided to classify and the methods of processing these data. At the end of the paper we discus obtained results and problems which occurred during the processing of the selected data.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122424207","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 : 2022-09-08DOI: 10.7546/nifs.2022.28.3.353-360
S. Sotirov, Valentin Stoyanov, M. Krawczak, E. Sotirova, S. Ribagin
In this investigation the level of burnout among the medical employees was analyzed. Тhe InterCriteria Analysis (ICA) approach is used to find the dependences between different parameters characterizing the 139 medical employees from 6 medical centers. The aim is to analyze the correlations between the health indicators, by surveying with a developed questionnaire. The obtained data from the InterCriteria Analysis were clustered using an adaptive neural network.
{"title":"An application of the InterCriteria Analysis and clusterization approach over a burnout dataset","authors":"S. Sotirov, Valentin Stoyanov, M. Krawczak, E. Sotirova, S. Ribagin","doi":"10.7546/nifs.2022.28.3.353-360","DOIUrl":"https://doi.org/10.7546/nifs.2022.28.3.353-360","url":null,"abstract":"In this investigation the level of burnout among the medical employees was analyzed. Тhe InterCriteria Analysis (ICA) approach is used to find the dependences between different parameters characterizing the 139 medical employees from 6 medical centers. The aim is to analyze the correlations between the health indicators, by surveying with a developed questionnaire. The obtained data from the InterCriteria Analysis were clustered using an adaptive neural network.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129512091","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 : 2022-09-08DOI: 10.7546/nifs.2022.28.3.228-237
K. Čunderlíková, Dušana Babicová
The aim of this paper is to define a convergence in measure m, where m is an intuitionistic fuzzy state. We prove a version of weak law of large numbers for a sequence of independent intuitionistic fuzzy observables, too.
{"title":"Convergence in measure of intuitionistic fuzzy observables","authors":"K. Čunderlíková, Dušana Babicová","doi":"10.7546/nifs.2022.28.3.228-237","DOIUrl":"https://doi.org/10.7546/nifs.2022.28.3.228-237","url":null,"abstract":"The aim of this paper is to define a convergence in measure m, where m is an intuitionistic fuzzy state. We prove a version of weak law of large numbers for a sequence of independent intuitionistic fuzzy observables, too.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128392683","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 : 2022-09-08DOI: 10.7546/nifs.2022.28.3.271-279
Nora A. Angelova, J. Kacprzyk, A. Michalíková, K. Atanassov
25 years ago, in [7], it was proved that the Hauber's law is an intuitionistic fuzzy tautology. In this case, the used implication was the standard intuitionistic fuzzy one. In the present paper, we check which intuitionistic fuzzy implications, defined during these 25 years, satisfy the Hauber's law as a tautology and which if them – as an intuitionistic fuzzy tautology.
{"title":"The Hauber's law with intuitionistic fuzzy implications","authors":"Nora A. Angelova, J. Kacprzyk, A. Michalíková, K. Atanassov","doi":"10.7546/nifs.2022.28.3.271-279","DOIUrl":"https://doi.org/10.7546/nifs.2022.28.3.271-279","url":null,"abstract":"25 years ago, in [7], it was proved that the Hauber's law is an intuitionistic fuzzy tautology. In this case, the used implication was the standard intuitionistic fuzzy one. In the present paper, we check which intuitionistic fuzzy implications, defined during these 25 years, satisfy the Hauber's law as a tautology and which if them – as an intuitionistic fuzzy tautology.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"120 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124028884","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 : 2022-09-08DOI: 10.7546/nifs.2022.28.3.211-222
K. Atanassov
In the paper, for the first time, ideas for intuitionistic fuzzy modal feeble topological structures (of two types) are introduced, and some of their properties are discussed. These topologies are based on the intuitionistic fuzzy operation @, intuitionistic fuzzy operator W, on the two intuitionistic fuzzy modal operators □, ◊ and of simplest intuitionistic fuzzy extended Dα.
{"title":"On the intuitionistic fuzzy modal feeble topological structures","authors":"K. Atanassov","doi":"10.7546/nifs.2022.28.3.211-222","DOIUrl":"https://doi.org/10.7546/nifs.2022.28.3.211-222","url":null,"abstract":"In the paper, for the first time, ideas for intuitionistic fuzzy modal feeble topological structures (of two types) are introduced, and some of their properties are discussed. These topologies are based on the intuitionistic fuzzy operation @, intuitionistic fuzzy operator W, on the two intuitionistic fuzzy modal operators □, ◊ and of simplest intuitionistic fuzzy extended Dα.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133358453","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}