Distance and similarity measures of intuitionistic fuzzy hypersoft sets with application: Evaluation of air pollution in cities based on air quality index

Abstract

Decision-making in a vague, undetermined and imprecise environment has been a great issue in real-life problems. Many mathematical theories like fuzzy, intuitionistic and neutrosophic sets have been proposed to handle such kinds of environments. Intuitionistic fuzzy sets (IFSS) were formulated by Atanassov in 1986 and analyze the truth membership, which assists in evidence, along with the fictitious membership. This article describes a composition of the intuitionistic fuzzy set (IFS) with the hypersoft set, which assists in coping with multi-attributive decision-making issues. Similarity measures are the tools to determine the similarity index, which evaluates how similar two objects are. In this study, we develop some distance and similarity measures for IFHSS with the help of aggregate operators. Also, we prove some new results, theorems and axioms to check the validity of the proposed study and discuss a real-life problem. The air quality index (AQI) is one of the major factors of the environment which is affected by air pollution. Air pollution is one of the extensive worldwide problems, and now it is well acknowledged to be deleterious to human health. A decision-maker determines ϸ = region (different geographical areas) and the factors{ᵹ=human activiteis,Ϥ=humidity level,ζ=air pollution} which enhance the AQI by applying decision-making techniques. This analysis can be used to determine whether a geographical area has a good, moderate or hazardous AQI. The suggested technique may also be applied to a large number of the existing hypersoft sets. For a remarkable environment, alleviating techniques must be undertaken.

Keywords

• fuzzy set
• intuitionistic fuzzy set
• soft set
• hypersoft set
• intuitionistic fuzzy hypersoft set
• similarity measures
• distance measures
• air quality index
• air pollution