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Group decision making in the analytic hierarchy process by hesitant fuzzy numbers
Mahdi Ranjbar1, Sohrab Effati2,3
1Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran. m.ranjbart@gmail.com.
This study introduces a new method using hesitant fuzzy numbers (HFNs) for group decision-making. It enhances accuracy by incorporating expert opinions within a hesitant fuzzy analytic hierarchy process framework.
Area of Science:
- Decision Science
- Fuzzy Mathematics
- Operations Research
Background:
- Group decision-making faces complexity and expert evaluation ambiguity.
- Hesitant fuzzy numbers (HFNs) extend fuzzy numbers to handle multiple membership values.
- HFNs improve parameter membership determination by multiple experts.
Purpose of the Study:
- To propose a novel approach for group decision-making using hesitant fuzzy numbers.
- To integrate hesitant fuzzy numbers into the analytic hierarchy process (AHP).
- To enhance decision accuracy by preserving expert opinions in a hesitant fuzzy environment.
Main Methods:
- Utilized triangular hesitant fuzzy numbers (HFNs) within the AHP pairwise comparison matrix.
- Defined consistency for hesitant fuzzy pairwise comparison matrices.
- Applied arithmetic operations on HFNs and a new comparison method to derive hesitant fuzzy performance scores.
Main Results:
- Developed a method to calculate hesitant fuzzy performance scores.
- Introduced a score function to obtain final alternative scores.
- Demonstrated the effectiveness of the proposed method through a practical example.
Conclusions:
- The new method effectively incorporates expert opinions in decision-making.
- The approach provides a better solution by maintaining expert hesitancy.
- This framework enhances group decision-making in complex, ambiguous scenarios.
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