Normal wiggly probabilistic hesitant fuzzy-based TODIM approach for optimal solid waste disposal method selection.

Area of Science:

• Decision Sciences
• Fuzzy Set Theory
• Operations Research

Background:

• Conventional probabilistic hesitant fuzzy sets (PHFS) capture explicit probabilistic data.
• There is a need to capture underlying details missed by traditional methods.
• Multi-criteria decision-making (MCDM) often involves uncertainty and incomplete information.

Purpose of the Study:

• To introduce a novel extension of the TODIM method using normal wiggly probabilistic hesitant fuzzy sets (NWPHFS).
• To develop new distance measures and operations for NWPHFS.
• To address MCDM problems with unknown criteria weights.

Main Methods:

• Defined subtraction and division operations for NWPHFS.
• Developed and examined properties of NWPHFS-specific distance measures.
• Established optimization models for criteria weight determination using maximizing deviation and Lagrange functions.
• Extended the TODIM method to NWPHFT for MCDM.

Main Results:

• The NWPHFT method was developed, integrating NWPHFS distance measures and weight determination models.
• The method was applied to a solid waste disposal site selection problem.
• Sensitivity analyses and comparisons demonstrated the approach's stability and effectiveness.

Conclusions:

• The proposed NWPHFT method effectively handles MCDM problems with uncertain and incomplete information.
• The novel NWPHFS framework enhances data representation in decision-making.
• The approach offers a robust and stable solution for complex selection tasks.