Correlation coefficients between normal wiggly hesitant fuzzy sets and their applications

Area of Science:

• Decision Sciences
• Fuzzy Logic
• Data Mining

Background:

• Multi-criteria decision-making (MCDM) requires tools to handle uncertainty.
• Hesitant fuzzy sets (HFS) capture decision-maker preferences but often miss implicit nuances.
• Traditional HFS can lead to suboptimal outcomes in complex scenarios.

Purpose of the Study:

• Introduce Normal Wiggly Hesitant Fuzzy Sets (NWHFS) to capture both explicit and implicit preferences.
• Develop novel correlation coefficients for NWHFS to quantify relationships.
• Enhance MCDM processes and clustering analysis with the new NWHFS framework.

Main Methods:

• Formulation of Normal Wiggly Hesitant Fuzzy Sets (NWHFS).
• Development of new correlation coefficients tailored for NWHFS.
• Integration of NWHFS into clustering algorithms.
• Comparative analysis against existing MCDM and fuzzy set methods.

Main Results:

• NWHFS effectively capture nuanced and implicit decision-maker preferences.
• Proposed correlation coefficients provide robust quantitative measures of relationships.
• NWHFS demonstrate superior performance in MCDM compared to traditional HFS.
• Successful application of NWHFS in clustering analysis for data classification.

Conclusions:

• NWHFS offer a more representative framework for decision-making under uncertainty.
• The developed correlation coefficients enhance understanding of variable relationships.
• NWHFS provide a significant advancement for MCDM, data mining, and resource retrieval.
• This research sets a new standard for accuracy and insight in complex decision-making.