Multicriteria group decision making by using trapezoidal valued hesitant fuzzy sets

Area of Science:

• Fuzzy Set Theory
• Decision Science

Background:

• Hesitant fuzzy sets (HFS) handle uncertainty but often lack specific forms.
• Trapezoidal fuzzy numbers (TrFNs) offer a flexible representation of uncertainty.
• Integrating TrFNs into HFS provides a richer framework for uncertain information.

Purpose of the Study:

• Introduce trapezoidal valued hesitant fuzzy sets (TrVHFSet).
• Define a distance measure for TrVHFSet elements.
• Extend the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) for TrVHFSet.

Main Methods:

• Conceptualization of TrVHFSet based on hesitant fuzzy elements and trapezoidal fuzzy numbers.
• Development of a novel distance metric tailored for TrVHFSet.
• Adaptation of the TOPSIS algorithm to incorporate the new distance measure and TrVHFSet.

Main Results:

• Successful introduction and definition of TrVHFSet and its distance measure.
• Demonstration of the extended TOPSIS method's applicability.
• Validation through a multicriteria group decision-making example.

Conclusions:

• The proposed TrVHFSet and distance measure offer a robust way to model uncertainty.
• The extended TOPSIS method effectively handles group decisions with trapezoidal hesitant fuzzy information.
• This framework enhances decision-making in complex scenarios with uncertain criteria values.