Pub Date : 2024-07-01DOI: 10.7546/nifs.2024.30.1.92-100
P. Vassilev, Vassia Atanassova
In the present work we introduce a family of geometrically inspired operators over intuitionistic fuzzy sets. In essence, if we consider the interpretational triangle as a billiards table with certain properties and each point of an intuitionistic fuzzy set as a ball propelled with a predetermined initial force, then its image after bouncing off from the boundaries of the triangle will, in general, be a new and different intuitionistic fuzzy point. The value of this image depends on the magnitude and direction of the force, which we will describe by using a parameter λ > 0 and another intuitionistic fuzzy set over the same universe.
{"title":"On a family of billiards-inspired operators over intuitionistic fuzzy sets","authors":"P. Vassilev, Vassia Atanassova","doi":"10.7546/nifs.2024.30.1.92-100","DOIUrl":"https://doi.org/10.7546/nifs.2024.30.1.92-100","url":null,"abstract":"In the present work we introduce a family of geometrically inspired operators over intuitionistic fuzzy sets. In essence, if we consider the interpretational triangle as a billiards table with certain properties and each point of an intuitionistic fuzzy set as a ball propelled with a predetermined initial force, then its image after bouncing off from the boundaries of the triangle will, in general, be a new and different intuitionistic fuzzy point. The value of this image depends on the magnitude and direction of the force, which we will describe by using a parameter λ > 0 and another intuitionistic fuzzy set over the same universe.","PeriodicalId":509276,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"9 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141711766","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 : 2024-07-01DOI: 10.7546/nifs.2024.30.1.56-65
K. Čunderlíková
The aim of this contribution is studying the almost uniform convergence on D-poset of intuitionistic fuzzy sets. We prove the connection between almost everywhere convergence of random variables in Kolmogorov probability space and almost uniform convergence of observables in the mentioned D-poset. We define a product operation on D-poset of intuitionistic fuzzy sets and prove the existence of a joint observable, too.
{"title":"A note about almost uniform convergence on D-poset of intuitionistic fuzzy sets","authors":"K. Čunderlíková","doi":"10.7546/nifs.2024.30.1.56-65","DOIUrl":"https://doi.org/10.7546/nifs.2024.30.1.56-65","url":null,"abstract":"The aim of this contribution is studying the almost uniform convergence on D-poset of intuitionistic fuzzy sets. We prove the connection between almost everywhere convergence of random variables in Kolmogorov probability space and almost uniform convergence of observables in the mentioned D-poset. We define a product operation on D-poset of intuitionistic fuzzy sets and prove the existence of a joint observable, too.","PeriodicalId":509276,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"94 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141701739","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 : 2024-07-01DOI: 10.7546/nifs.2024.30.2.142-155
G. Kaviranjanii, Rangasamy Parvathi
The authors have designed and developed algorithms for pattern recognition and clustering techniques using intuitionistic fuzzy (IF) sets, IF operators, IF logic (IFL) – shortest path in networks using IF graphs and IF hypergraphs – video processing using temporal IF sets, RGB image representation through IF index matrices, and molecular structure representation through IF directed hypergraphs. The three major steps involved in the above-said modeling processes via IFSs are (i) intuitionistic fuzzification, (ii) modification of membership and non- membership values (using IF logic/operators/rules/relations) and (iii) intuitionistic defuzzification. While developing these algorithms, parameter tuning was one of the major limitations, and hence specific values were assigned to complete the running process. To overcome this, it is necessary to introduce a toolbox in MATLAB so that the users can select the appropriate tools and parameterize them. Hence, in the long process of contributing a full-pledged intuitionistic fuzzy logic toolbox, namely IFL Toolbox in MATLAB, the membership and non-membership functions gallery has been developed initially, as one of the modules which is the foundation for any IFL control system. This module contains functions, codes, examples and figures/graphs, which will be available on the MATLAB creation page. The proposed module is compared with the existing fuzzy logic toolbox in MATLAB and verified.
作者们设计并开发了使用直觉模糊（IF）集、IF 运算符、IF 逻辑（IFL）的模式识别和聚类技术算法--使用 IF 图和 IF 超图的网络最短路径--使用时间 IF 集的视频处理、通过 IF 索引矩阵的 RGB 图像表示，以及通过 IF 有向超图的分子结构表示。通过 IFS 进行上述建模过程涉及三个主要步骤：(i) 直觉模糊化；(ii) 成员和非成员值的修改（使用 IF 逻辑/操作符/规则/关系）；(iii) 直觉去模糊化。在开发这些算法时，参数调整是主要限制之一，因此需要指定特定值来完成运行过程。为了克服这一问题，有必要在 MATLAB 中引入一个工具箱，以便用户可以选择适当的工具并对其进行参数化。因此，在开发全功能直觉模糊逻辑工具箱（即 MATLAB 中的 IFL 工具箱）的漫长过程中，首先开发了成员和非成员函数库，作为任何 IFL 控制系统的基础模块之一。该模块包含函数、代码、示例和图表，可在 MATLAB 创建页面上查看。提议的模块与 MATLAB 中现有的模糊逻辑工具箱进行了比较和验证。
{"title":"Designing and developing Intuitionistic Fuzzy Logic Toolbox in MATLAB: Membership and non-membership functions gallery","authors":"G. Kaviranjanii, Rangasamy Parvathi","doi":"10.7546/nifs.2024.30.2.142-155","DOIUrl":"https://doi.org/10.7546/nifs.2024.30.2.142-155","url":null,"abstract":"The authors have designed and developed algorithms for pattern recognition and clustering techniques using intuitionistic fuzzy (IF) sets, IF operators, IF logic (IFL) – shortest path in networks using IF graphs and IF hypergraphs – video processing using temporal IF sets, RGB image representation through IF index matrices, and molecular structure representation through IF directed hypergraphs. The three major steps involved in the above-said modeling processes via IFSs are (i) intuitionistic fuzzification, (ii) modification of membership and non- membership values (using IF logic/operators/rules/relations) and (iii) intuitionistic defuzzification. While developing these algorithms, parameter tuning was one of the major limitations, and hence specific values were assigned to complete the running process. To overcome this, it is necessary to introduce a toolbox in MATLAB so that the users can select the appropriate tools and parameterize them. Hence, in the long process of contributing a full-pledged intuitionistic fuzzy logic toolbox, namely IFL Toolbox in MATLAB, the membership and non-membership functions gallery has been developed initially, as one of the modules which is the foundation for any IFL control system. This module contains functions, codes, examples and figures/graphs, which will be available on the MATLAB creation page. The proposed module is compared with the existing fuzzy logic toolbox in MATLAB and verified.","PeriodicalId":509276,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141715091","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 : 2024-07-01DOI: 10.7546/nifs.2024.30.2.121-130
Başar Öztayşi, S. Çebi, Cengiz Kahraman, Sezi Cevik Onar
Performance measurement (PM) is a vital aspect of management, conducted periodically to assess the success or quality of a specific process or an organization. Performance encompasses both goals and relational models crucial for achieving those goals within a given time frame. From another perspective, performance measurement is about determining related performance indicators and providing a numerical summarized result which can be used for comparisons. Converting various indicators to an overall performance score can be modeled as a multi-criteria decision making problem. In this study, we focus on performance measurement of debt collection centers which are organizations specialized in collecting money from debtors. To this end, a decision model is developed and intuitionistic fuzzy Analytic Hierarchy Process is used to obtain the criteria weights. The proposed framework is shown in a real-world case study.
{"title":"Performance measurement using intuitionistic fuzzy sets: A case study from debt collection centers","authors":"Başar Öztayşi, S. Çebi, Cengiz Kahraman, Sezi Cevik Onar","doi":"10.7546/nifs.2024.30.2.121-130","DOIUrl":"https://doi.org/10.7546/nifs.2024.30.2.121-130","url":null,"abstract":"Performance measurement (PM) is a vital aspect of management, conducted periodically to assess the success or quality of a specific process or an organization. Performance encompasses both goals and relational models crucial for achieving those goals within a given time frame. From another perspective, performance measurement is about determining related performance indicators and providing a numerical summarized result which can be used for comparisons. Converting various indicators to an overall performance score can be modeled as a multi-criteria decision making problem. In this study, we focus on performance measurement of debt collection centers which are organizations specialized in collecting money from debtors. To this end, a decision model is developed and intuitionistic fuzzy Analytic Hierarchy Process is used to obtain the criteria weights. The proposed framework is shown in a real-world case study.","PeriodicalId":509276,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"2 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141717123","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 : 2024-07-01DOI: 10.7546/nifs.2024.30.2.156-164
K. Atanassov
The Intercriteria Analysis (ICA) is an decision support approach based on the apparatus of intuitionistic fuzzy sets and the relations between the evaluations of a set of given objects evaluated against a set of fixed criteria. In the present paper we discuss three new procedures for evaluation of ICA when used over objects containing elements of uncertainty.
{"title":"New results on the InterCriteria Analysis","authors":"K. Atanassov","doi":"10.7546/nifs.2024.30.2.156-164","DOIUrl":"https://doi.org/10.7546/nifs.2024.30.2.156-164","url":null,"abstract":"The Intercriteria Analysis (ICA) is an decision support approach based on the apparatus of intuitionistic fuzzy sets and the relations between the evaluations of a set of given objects evaluated against a set of fixed criteria. In the present paper we discuss three new procedures for evaluation of ICA when used over objects containing elements of uncertainty.","PeriodicalId":509276,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"45 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141697970","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}
Continuing the research from Parts 1, 2 [2, 3] where intuitionistic fuzzy implications, determined as implications with “good” properties, were investigated, here we correct the list of the implications that satisfy the Modus Ponens from Part 3, [4], and further select among them those implications that satisfy the Modus Tollens, as well. We discuss some applications of these implications and show the relationship between every two of them.
{"title":"Research on intuitionistic fuzzy implications. Part 4","authors":"Nora A. Angelova, K. Atanassov, Vassia Atanassova","doi":"10.7546/nifs.30.1.1-8","DOIUrl":"https://doi.org/10.7546/nifs.30.1.1-8","url":null,"abstract":"Continuing the research from Parts 1, 2 [2, 3] where intuitionistic fuzzy implications, determined as implications with “good” properties, were investigated, here we correct the list of the implications that satisfy the Modus Ponens from Part 3, [4], and further select among them those implications that satisfy the Modus Tollens, as well. We discuss some applications of these implications and show the relationship between every two of them.","PeriodicalId":509276,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"15 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141688756","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 : 2024-07-01DOI: 10.7546/nifs.2024.30.1.26-55
Poonam Kumar Sharma
As a generalization of the concepts of an intuitionistic fuzzy prime ideal and a prime intuitionistic fuzzy ideal, the concepts of an intuitionistic fuzzy 2-absorbing ideal and a 2-absorbing intuitionistic fuzzy ideal of a lattice are introduced. Some results on such intuitionistic fuzzy ideals are proved. It is shown that the radical of an intuitionistic fuzzy ideal of L is a 2-absorbing intuitionistic fuzzy ideal if and only if it is a 2-absorbing primary intuitionistic fuzzy ideal of L. We also introduce and study these concepts in the product of lattices.
作为对直觉模糊素理想和直觉模糊素理想概念的概括，引入了直觉模糊 2 吸收理想和网格的 2 吸收直觉模糊理想的概念。证明了关于这类直观模糊理想的一些结果。证明了当且仅当 L 的直观模糊理想的基是 L 的 2 吸直观模糊理想时，L 的直观模糊理想的基才是 2 吸直观模糊理想。
{"title":"Generalizations of prime intuitionistic fuzzy ideals of a lattice","authors":"Poonam Kumar Sharma","doi":"10.7546/nifs.2024.30.1.26-55","DOIUrl":"https://doi.org/10.7546/nifs.2024.30.1.26-55","url":null,"abstract":"As a generalization of the concepts of an intuitionistic fuzzy prime ideal and a prime intuitionistic fuzzy ideal, the concepts of an intuitionistic fuzzy 2-absorbing ideal and a 2-absorbing intuitionistic fuzzy ideal of a lattice are introduced. Some results on such intuitionistic fuzzy ideals are proved. It is shown that the radical of an intuitionistic fuzzy ideal of L is a 2-absorbing intuitionistic fuzzy ideal if and only if it is a 2-absorbing primary intuitionistic fuzzy ideal of L. We also introduce and study these concepts in the product of lattices.","PeriodicalId":509276,"journal":{"name":"Notes on Intuitionistic Fuzzy Sets","volume":"28 16","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141710139","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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