<p>Understanding bipolar information is crucial as it enables individuals to make informed decisions that consider both extremes of a spectrum, leading to more balanced and effective outcomes. Interval-valued bipolar fuzzy set (IVBFS) has already been introduced in the literature as a great decision-making tool that can capture interval-valued bipolar information to properly address uncertainty. In this article, we introduce a hybrid of Interval-valued bipolar fuzzy set (IVBFS) and bipolar hypersoft sets (BHSS) called interval-valued bipolar fuzzy hypersoft set <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((IVBF_{HSS})\)</EquationSource> </InlineEquation>, which merges the capabilities of IVBFS and BHSS. The rationale behind the design of the presented data structure is to manipulate and process information in decision-making scenarios when the data is bipolar, has multiple attributes that need to be addressed up to a sub-attributive level to get a proper representation of the data provided, and needs to be presented in the form of intervals. In <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((IVBF_{HSS})\)</EquationSource> </InlineEquation>, two hyper soft sets (HSSs) are used, one providing positive interval-valued membership information and the other providing negative interval-valued membership information. We outline the essential features and basic operations of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\((IVBF_{HSS})\)</EquationSource> </InlineEquation> in this paper, examining its commutative, associative, distributive, and De Morgan laws to ensure a comprehensive analysis. To demonstrate the significance of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\((IVBF_{HSS})\)</EquationSource> </InlineEquation>, we develop a preferential decision support algorithm for selecting the best alternative in e-learning, such as identifying the most suitable instructional method, which can effectively be formulated as a Multi-Attribute Decision-Making (MADM) problem. This approach allows for the systematic evaluation of various alternatives based on multiple parameters and sub-parameters, enabling a rational and well-informed decision. This algorithm helps select the best alternative from a given set of options, leveraging the versatile nature of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\((IVBF_{HSS})\)</EquationSource> </InlineEquation>. The presented study conducts both computation-based and structural comparisons to evaluate the adaptability and reliability of the proposed framework.</p>

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

A robust E learning recommendation system based on novel interval valued bipolar fuzzy hypersoft set theory

  • Muhammad Imran Harl,
  • Muhammad Saeed,
  • Muhammad Haris Saeed,
  • Muhammad Salman Habib,
  • Mehran Ullah

摘要

Understanding bipolar information is crucial as it enables individuals to make informed decisions that consider both extremes of a spectrum, leading to more balanced and effective outcomes. Interval-valued bipolar fuzzy set (IVBFS) has already been introduced in the literature as a great decision-making tool that can capture interval-valued bipolar information to properly address uncertainty. In this article, we introduce a hybrid of Interval-valued bipolar fuzzy set (IVBFS) and bipolar hypersoft sets (BHSS) called interval-valued bipolar fuzzy hypersoft set \((IVBF_{HSS})\) , which merges the capabilities of IVBFS and BHSS. The rationale behind the design of the presented data structure is to manipulate and process information in decision-making scenarios when the data is bipolar, has multiple attributes that need to be addressed up to a sub-attributive level to get a proper representation of the data provided, and needs to be presented in the form of intervals. In \((IVBF_{HSS})\) , two hyper soft sets (HSSs) are used, one providing positive interval-valued membership information and the other providing negative interval-valued membership information. We outline the essential features and basic operations of \((IVBF_{HSS})\) in this paper, examining its commutative, associative, distributive, and De Morgan laws to ensure a comprehensive analysis. To demonstrate the significance of \((IVBF_{HSS})\) , we develop a preferential decision support algorithm for selecting the best alternative in e-learning, such as identifying the most suitable instructional method, which can effectively be formulated as a Multi-Attribute Decision-Making (MADM) problem. This approach allows for the systematic evaluation of various alternatives based on multiple parameters and sub-parameters, enabling a rational and well-informed decision. This algorithm helps select the best alternative from a given set of options, leveraging the versatile nature of \((IVBF_{HSS})\) . The presented study conducts both computation-based and structural comparisons to evaluate the adaptability and reliability of the proposed framework.