Pub Date : 2023-12-01DOI: 10.7546/nifs.2023.29.4.411-417
Veselina Bureva, K. Atanassov
In the present research paper, the data partitioning operations are investigated. Their functionalities are discussed. n-Dimensional intuitionistic fuzzy index matrix is used to represent the multidimensional data partitioning. Attributes selection and values selection by predicates is presented.
{"title":"n-Dimensional intuitionistic fuzzy index matrix representation of multidimensional data partitioning methods","authors":"Veselina Bureva, K. Atanassov","doi":"10.7546/nifs.2023.29.4.411-417","DOIUrl":"https://doi.org/10.7546/nifs.2023.29.4.411-417","url":null,"abstract":"In the present research paper, the data partitioning operations are investigated. Their functionalities are discussed. n-Dimensional intuitionistic fuzzy index matrix is used to represent the multidimensional data partitioning. Attributes selection and values selection by predicates is presented.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"358 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139022966","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 : 2023-12-01DOI: 10.7546/nifs.2023.29.4.418-424
Vassia Atanassova, Ivo Umlenski
The present short note aims to propose a new, alternative, way to interpret the results of the intuitionistic fuzzy sets-based method for multicriteria decision support named InterCriteria Analysis. Given an m times n dataset of multiple (''m'') objects evaluated numerically against multiple (''n'') criteria, the ICA method generates an n times n table of intuitionistic fuzzy pairs langle mu_{i,j}, nu_{i,j} rangle, i, j in {1, 2, ldots, n} where the given pair indicates the extent of relation between the corresponding pair of criteria C_i, C_j. Traditionally, the interpretation of these intuitionistic fuzzy pairs regarding the extent of positive or negative dependence between two criteria (or, respectively, the lack of such) requires that two threshold values, both in the [0,1] interval too, are used. Now we propose to use only one such threshold value belonging to the [0,1] interval, for instance a minimal threshold of the degree of membership, while the other threshold {would} be essentially related to the size of the subset of intercriteria pairs being shortlisted for interpretation, rather than their degree of non-membership. We justify that the proposed approach, inspired by the Pareto Principle, in certain cases yields better results than the traditionally used one..
本短文旨在提出一种新的、替代性的方法来解释基于直觉模糊集的多标准决策支持方法（名为 "标准间分析"）的结果。给定一个由多个（''m''）对象组成的 m 次 n 数据集，根据多个（''n''）标准进行数值评估，ICA 方法会生成一个 n 次 n 表，其中包含直觉模糊对 langle mu_{i,j}, nu_{i,j} 和 rangle mu_{i,j}, nu_{i,j} 。其中给定的对表示相应的一对标准 C_i, C_j 之间的关系程度。传统上，要解释这些关于两个标准之间正或负依赖程度（或分别表示缺乏这种依赖）的直觉模糊对，需要使用两个阈值，这两个阈值也都在 [0,1] 区间内。现在，我们建议只使用一个属于 [0,1] 区间的阈值，例如成员度的最小阈值，而另一个阈值{将}基本上与入围解释的标准间对子集的大小有关，而不是与它们的非成员度有关。我们证明，受帕累托原则启发而提出的方法在某些情况下会比传统方法产生更好的结果。
{"title":"Interpreting the results of InterCriteria Analysis: Pareto principle at work","authors":"Vassia Atanassova, Ivo Umlenski","doi":"10.7546/nifs.2023.29.4.418-424","DOIUrl":"https://doi.org/10.7546/nifs.2023.29.4.418-424","url":null,"abstract":"The present short note aims to propose a new, alternative, way to interpret the results of the intuitionistic fuzzy sets-based method for multicriteria decision support named InterCriteria Analysis. Given an m times n dataset of multiple (''m'') objects evaluated numerically against multiple (''n'') criteria, the ICA method generates an n times n table of intuitionistic fuzzy pairs langle mu_{i,j}, nu_{i,j} rangle, i, j in {1, 2, ldots, n} where the given pair indicates the extent of relation between the corresponding pair of criteria C_i, C_j. Traditionally, the interpretation of these intuitionistic fuzzy pairs regarding the extent of positive or negative dependence between two criteria (or, respectively, the lack of such) requires that two threshold values, both in the [0,1] interval too, are used. Now we propose to use only one such threshold value belonging to the [0,1] interval, for instance a minimal threshold of the degree of membership, while the other threshold {would} be essentially related to the size of the subset of intercriteria pairs being shortlisted for interpretation, rather than their degree of non-membership. We justify that the proposed approach, inspired by the Pareto Principle, in certain cases yields better results than the traditionally used one..","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"65 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139014092","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 : 2023-08-01DOI: 10.7546/nifs.2023.29.2.157-165
K. Atanassov, D. Mavrov, Vassia Atanassova
The idea of the InterCriteria Analysis (ICA) was generated by the authors in 2014. For the next (already 9) years, ICA has been an object of intensive research and applications. In the present paper, an extension of the ICA is introduced. In it, the criteria or the objects have their own weight coefficients, or priorities. In the particular case, when these coefficients are equal to 1, the standard ICA appears.
{"title":"InterCriteria Analysis with weight coefficients of objects or criteria","authors":"K. Atanassov, D. Mavrov, Vassia Atanassova","doi":"10.7546/nifs.2023.29.2.157-165","DOIUrl":"https://doi.org/10.7546/nifs.2023.29.2.157-165","url":null,"abstract":"The idea of the InterCriteria Analysis (ICA) was generated by the authors in 2014. For the next (already 9) years, ICA has been an object of intensive research and applications. In the present paper, an extension of the ICA is introduced. In it, the criteria or the objects have their own weight coefficients, or priorities. In the particular case, when these coefficients are equal to 1, the standard ICA appears.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115138807","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 : 2023-08-01DOI: 10.7546/nifs.2023.29.2.178-196
D. Mavrov, Stanislav Popov, V. Nenov, D. Stratiev
In this paper, we will apply InterCriteria Analysis to evaluate the performance of two catalysts and two feedstocks in the fluid catalytic cracking process. For the purposes of this analysis, each object is given a weight coefficient which affects the final evaluation between every pair of criteria. After presenting our results, we discuss their implications.
{"title":"Evaluating the performance of catalyst and feedstocks in the fluid catalytic cracking process: Application of InterCriteria Analysis with weight coefficients of the criteria","authors":"D. Mavrov, Stanislav Popov, V. Nenov, D. Stratiev","doi":"10.7546/nifs.2023.29.2.178-196","DOIUrl":"https://doi.org/10.7546/nifs.2023.29.2.178-196","url":null,"abstract":"In this paper, we will apply InterCriteria Analysis to evaluate the performance of two catalysts and two feedstocks in the fluid catalytic cracking process. For the purposes of this analysis, each object is given a weight coefficient which affects the final evaluation between every pair of criteria. After presenting our results, we discuss their implications.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126327694","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 : 2023-08-01DOI: 10.7546/nifs.2023.29.2.218-230
R. Parvathi, R. K. Nivedhaa, Vassia Atanassova
In this paper, an attempt has been made to define contrast intensification operator on intuitionistic fuzzy index matrices, which is useful for enhancing color images. Further, an algorithm is designed and developed for image preprocessing. The validity is verified by using a few real RGB images.
{"title":"The role of operations over intuitionistic fuzzy index matrices in color image analysis","authors":"R. Parvathi, R. K. Nivedhaa, Vassia Atanassova","doi":"10.7546/nifs.2023.29.2.218-230","DOIUrl":"https://doi.org/10.7546/nifs.2023.29.2.218-230","url":null,"abstract":"In this paper, an attempt has been made to define contrast intensification operator on intuitionistic fuzzy index matrices, which is useful for enhancing color images. Further, an algorithm is designed and developed for image preprocessing. The validity is verified by using a few real RGB images.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"168 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134514428","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 : 2023-08-01DOI: 10.7546/nifs.2023.29.2.197-207
Veselina Bureva, Cengiz Kahraman, S. Sotirov
In the current investigation Turkish university rankings are analyzed. The dataset for overall ranking of universities for 2021-2022 is used. The information is downloaded from the University Ranking by Academic Performance website. Dependencies and independencies between Turkish universities are analyzed. The relationship between university rankings indicators are investigated.
{"title":"Investigation of the Turkish university rankings using InterCriteria Analysis","authors":"Veselina Bureva, Cengiz Kahraman, S. Sotirov","doi":"10.7546/nifs.2023.29.2.197-207","DOIUrl":"https://doi.org/10.7546/nifs.2023.29.2.197-207","url":null,"abstract":"In the current investigation Turkish university rankings are analyzed. The dataset for overall ranking of universities for 2021-2022 is used. The information is downloaded from the University Ranking by Academic Performance website. Dependencies and independencies between Turkish universities are analyzed. The relationship between university rankings indicators are investigated.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129915132","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 : 2023-08-01DOI: 10.7546/nifs.2023.29.2.231-238
S. Sotirov, M. Krawczak, Diana Petkova, K. Atanassov
Biological neurons and their connection in neural networks have motivated the creation of the architecture of artificial neural networks. In the previously considered cases, the description of the neural networks and their connections are described with standard matrices where the values for the weighting coefficients and biases are placed. By recalculating them, the artificial neural network is trained. The paper presents an approach for describing multilayer neural networks with Intuitionistic Fuzzy Index Matrix (IFIM). The neural network input was described in IFIM form, then the weight coefficients of the connections between the nodes of the input vector, and then activation functions of the neurons. The use of IFIM extends the understanding and description as well as the structure and use of multilayer neural networks.
{"title":"Intuitionistic fuzzy neural network with filtering functions. An index matrix interpretation","authors":"S. Sotirov, M. Krawczak, Diana Petkova, K. Atanassov","doi":"10.7546/nifs.2023.29.2.231-238","DOIUrl":"https://doi.org/10.7546/nifs.2023.29.2.231-238","url":null,"abstract":"Biological neurons and their connection in neural networks have motivated the creation of the architecture of artificial neural networks. In the previously considered cases, the description of the neural networks and their connections are described with standard matrices where the values for the weighting coefficients and biases are placed. By recalculating them, the artificial neural network is trained. The paper presents an approach for describing multilayer neural networks with Intuitionistic Fuzzy Index Matrix (IFIM). The neural network input was described in IFIM form, then the weight coefficients of the connections between the nodes of the input vector, and then activation functions of the neurons. The use of IFIM extends the understanding and description as well as the structure and use of multilayer neural networks.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"482 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125985864","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 : 2023-08-01DOI: 10.7546/nifs.2023.29.2.208-217
Veselina Bureva, I. Stamova, Zlatko Yordanov, E. Sotirova
In the current investigation the health problems in Bulgaria through the years 2008, 2014 and 2019 are observed. The datasets for self-reported chronic morbidity datasets by Eurostat data browser are used. InterCriteria Analysis (ICA) is applied to estimate the relationships between the health problems in different countries. The outcomes will present tendencies of chronic diseases appearance in the selected countries. The prevalence of health problems by countries and years is observed.
{"title":"InterCriteria Analysis applied to the health problems declared by individuals in Bulgaria","authors":"Veselina Bureva, I. Stamova, Zlatko Yordanov, E. Sotirova","doi":"10.7546/nifs.2023.29.2.208-217","DOIUrl":"https://doi.org/10.7546/nifs.2023.29.2.208-217","url":null,"abstract":"In the current investigation the health problems in Bulgaria through the years 2008, 2014 and 2019 are observed. The datasets for self-reported chronic morbidity datasets by Eurostat data browser are used. InterCriteria Analysis (ICA) is applied to estimate the relationships between the health problems in different countries. The outcomes will present tendencies of chronic diseases appearance in the selected countries. The prevalence of health problems by countries and years is observed.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128821223","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 : 2023-08-01DOI: 10.7546/nifs.2023.29.2.166-177
Veselina Bureva, K. Atanassov, Yana Mersinkova, D. Stratiev
In the current investigation an evaluation of the performance of catalyst and feedstocks in the fluid catalytic cracking process is proposed. An application of the newly modified method of InterCriteria Analysis—with weight coefficients of the objects—is performed. The obtained results are discussed in the light of a comparison with the standard ICrA.
{"title":"Evaluating the performance of catalyst and feedstocks in the fluid catalytic cracking process: Application of InterCriteria Analysis with weight coefficients of the objects","authors":"Veselina Bureva, K. Atanassov, Yana Mersinkova, D. Stratiev","doi":"10.7546/nifs.2023.29.2.166-177","DOIUrl":"https://doi.org/10.7546/nifs.2023.29.2.166-177","url":null,"abstract":"In the current investigation an evaluation of the performance of catalyst and feedstocks in the fluid catalytic cracking process is proposed. An application of the newly modified method of InterCriteria Analysis—with weight coefficients of the objects—is performed. The obtained results are discussed in the light of a comparison with the standard ICrA.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128197483","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 : 2023-07-01DOI: 10.7546/nifs.2023.29.2.144-156
E. Szmidt, J. Kacprzyk, Paweł Bujnowski
Dimension reduction of the models, i.e., pointing out only the necessary number of input variables (attributes, features) is an important task enabling the efficient performance of different algorithms. This paper is a continuation of our previous works on a new method of selection of the attributes in the models making use of Atanassov's intuitionistic fuzzy sets. We consider classification problems trying to point out the reduced number of the attributes and still obtain satisfactory results. We investigate the previously proposed method in more details comparing its performance with a well-known method of extraction parameters, namely Principal Component Analysis (PCA), and with a well-known method of selecting the attributes in which the so-called Gain Ratio is used. We illustrate our considerations using benchmark data from UCI Machine Learning Repository.
{"title":"Identification of a sufficient number of the best attributes in the intuitionistic fuzzy models","authors":"E. Szmidt, J. Kacprzyk, Paweł Bujnowski","doi":"10.7546/nifs.2023.29.2.144-156","DOIUrl":"https://doi.org/10.7546/nifs.2023.29.2.144-156","url":null,"abstract":"Dimension reduction of the models, i.e., pointing out only the necessary number of input variables (attributes, features) is an important task enabling the efficient performance of different algorithms. This paper is a continuation of our previous works on a new method of selection of the attributes in the models making use of Atanassov's intuitionistic fuzzy sets. We consider classification problems trying to point out the reduced number of the attributes and still obtain satisfactory results. We investigate the previously proposed method in more details comparing its performance with a well-known method of extraction parameters, namely Principal Component Analysis (PCA), and with a well-known method of selecting the attributes in which the so-called Gain Ratio is used. We illustrate our considerations using benchmark data from UCI Machine Learning Repository.","PeriodicalId":433687,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"83 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115231516","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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