Linguistic Hypersoft Set with Application to Multi-Criteria Decision-Making to Enhance Rural Health Services

Abstract: Language, as an abstract system and a creative act, possesses inherent complexity due to its contextual nature and the variability of its meaning. The context of language is shaped by an individual's empirical knowledge, derived from observation and experience. Decision-making challenges related to language encompass both quantitative and qualitative factors, which further contribute to the intricacy of the process. Decision-making challenges may involve both quantitative and qualitative aspects of further subdivided attributes. However, linguistic knowledge cannot be easily quantified by existing methods. Therefore, current methods are ineffective in handling linguistic knowledge. Using mathematical values, such as fuzzy, intuitionistic, and neutrosophic, in decision-making problems without following linguistic knowledge rules can result in vagueness and imprecision. To address these issues, this paper presents a comprehensive generic model. The model introduces the linguistic set structure of the hypersoft set (LHSS) as a solution for decision-making problems. The definition of fundamental operations, including AND, NOT, OR complement, and negation, is proposed alongside illustrative examples and their respective properties. Additionally, operational laws for the linguistic hypersoft set are introduced to effectively address decision-making challenges. By implementing the proposed aggregate operators and operational laws, linguistic quantifiers can be converted into numerical values, thereby enhancing the accuracy and precision of the hypersoft set structure in decision-making scenarios.