[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125980-en":3,"doc-seo-125980-105":31,"detail-sidebar-cat-0-en-105":93},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},125980,687207024478,"Liam","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","Analysis of Power Aggregation Operators through Circular Intuitionistic Fuzzy Information and Their Applications in Machine Learning Analysis","The study investigates power aggregation operators based on circular intuitionistic fuzzy (C-IF) information and demonstrates their use in machine learning-oriented decision support. The work employs the circular intuitionistic fuzzy set as a flexible framework to model incomplete and redundant expert opinions. Four operator families are explored: C-IF power weighted averaging, ordered averaging, geometric, and ordered geometric operators. Core properties are established, followed by a multi-attribute decision-making (MADM) procedure and numerical comparisons with existing methods to validate effectiveness and reliability.","Engineering Review, DOI: 10.30765/er.2571 141  \nANALYSIS OF POWER AGGREGATION OPERATORS THROUGH CIRCULAR INTUITIONISTIC FUZZY INFORMATION AND THEIR APPLICATIONS IN MACHINE  \nLEARNING ANALYSIS  \nMaleha Rukhsar1 – Kifayat Ullah1 􀀍 – Zeeshan Ali2 – Abrar Hussain1*  \n1Department of Mathematics, Riphah International University (Lahore Campus), Lahore, Pakistan  \n2Department of Information Management, National Yunlin University of Science and Technology Douliu, Yunlin, Taiwan  \n\n| ARTICLE INFO | Abstract: |\n| --- | --- |\n\nArticle history:  \nReceived: 01.08.2024.  \nReceived in revised form: 08.11.2024.  \nAccepted: 04.12.2024.  \nKeywords:  \nCircular intuitionistic fuzzy sets Power aggregation operators Machine learning algorithms Decision-making procedures  \nDOI: 10.30765/er.2571  \nMachine learning language is very valuable for depicting different problems, especially computer language, data mining, data sciences, and machine language. The circular intuitionistic fuzzy set (C-IFS) is a flexible approach to fuzzy sets and intuitionistic fuzzy sets. Keep in mind the flexibility of C-IFS, decision-maker used C-IFS to cope with incomplete and redundant human opinions accurately. Furthermore, power operators are used for depicting or aggregating the collection of data into a singleton set. In this manuscript, we explore the power operators for circular intuitionistic fuzzy (C-IF) information, such as C-IF power weighted averaging (C-IFPWA) operator, C-IF power weighted ordered averaging (C-IFPWOA) operator, C-IF power weighted geometric (C-IFPWG) operator, and C-IF power weighted ordered geometric (C-IFPWOG) operator. Some properties of the above information are also stated. Additionally, we evaluate the procedure of the multi-attribute decision-making (MADM) technique for resolving the utilization of the most suitable part of machine learning in complicated scenarios. Finally, we illustrate some numerical examples for addressing the comparison between proposed techniques and existing methods to show the  effectiveness and reliability of the presented operators.   \n1 Introduction  \nMachine learning algorithms and machine language are two different techniques that are the subpart of artificial intelligence that concentrate on the occurrence or development of algorithms and techniques that enable machines to learn from decisions and predictions. These algorithms are very reliable, and many scholars have employed them in many fields in the consideration of classical set theory. Because of these reasons, experts have faced a lot of problems due to limited opinions. To enhance or modify the range of the decision, Zadeh [1] exposed the fuzzy set theory (FST), where FST has only one function, called truth or positive or membership grade such as: 􀟤஺ : 􀜺 → [0,1], where 􀟤஺ (􀝔) ∈ [0,1] . Some applications of the Zadeh’s principle are stated, for instance, extended form of fuzzy sets, called fuzzy superior Mandelbrot set [2], PROMETHEE techniques [3], (a,b)-fuzzy soft sets [4], fuzzy N-soft sets (FNSSs) [5], multi-fuzzy N-soft sets [6], fuzzy parameterized soft sets [7], fuzzy systems [8], multi-person decision-making techniques [9], and fuzzy decision support systems [10] .  \nFST is very strong and effective because FST has only to cope with those problems that cover the onedimension problems, but in many cases, we face negative information about people, things, and objects. To cope with this kind of situation, Atanassov [11], [12], [13] explored the intuitionistic FST (IFST), where IFST  \n􀀍 Corresponding authors:  \nE-mail address: [kifayat.khan.dr@gmail.com](kifayat.khan.dr@gmail.com); [abrar353eb@gmail.com](abrar353eb@gmail.com)  \nM. Rukhsar et al.: Analysis ofpower aggregation operators… 142  \n________________________________________________________________________________________________________________________  \ntalked about the positive and negative grades with the characteristic that the sum of the pair will be contained in a unit interval. IF","cbCaikfAln7qPacJ","https://ap.wps.com/l/cbCaikfAln7qPacJ","pdf",1052269,5,1,19,"English","en",105,"# Introduction\n## Fuzzy set theory and intuitionistic fuzzy sets\n## Circular intuitionistic fuzzy sets (C-IFS)\n## Power aggregation operators in classical and fuzzy contexts","[{\"question\":\"What role does circular intuitionistic fuzzy information play in the proposed operators?\",\"answer\":\"Circular intuitionistic fuzzy sets provide a flexible way to represent incomplete and redundant human opinions using circular-structured intuitionistic fuzzy information.\"},{\"question\":\"Which power aggregation operators are analyzed in this manuscript?\",\"answer\":\"The manuscript studies C-IF power weighted averaging (C-IFPWA), C-IF power weighted ordered averaging (C-IFPWOA), C-IF power weighted geometric (C-IFPWG), and C-IF power weighted ordered geometric (C-IFPWOG) operators.\"},{\"question\":\"How is machine learning used in the evaluation of these operators?\",\"answer\":\"The operators are applied within a multi-attribute decision-making (MADM) procedure to determine the most suitable choice in complex scenarios, supported by numerical examples comparing with existing methods.\"}]","Analysis of Power Aggregation Operators through Circular Intuitionistic Fuzzy Information and Their Applications in Machine Learning Analysis | 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role does circular intuitionistic fuzzy information play in the proposed operators?","Question",{"text":77,"@type":78},"Circular intuitionistic fuzzy sets provide a flexible way to represent incomplete and redundant human opinions using circular-structured intuitionistic fuzzy information.","Answer",{"name":80,"@type":75,"acceptedAnswer":81},"Which power aggregation operators are analyzed in this manuscript?",{"text":82,"@type":78},"The manuscript studies C-IF power weighted averaging (C-IFPWA), C-IF power weighted ordered averaging (C-IFPWOA), C-IF power weighted geometric (C-IFPWG), and C-IF power weighted ordered geometric (C-IFPWOG) operators.",{"name":84,"@type":75,"acceptedAnswer":85},"How is machine learning used in the evaluation of these operators?",{"text":86,"@type":78},"The operators are applied within a multi-attribute decision-making (MADM) procedure to determine the most suitable choice in complex scenarios, supported by numerical examples comparing with existing 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