Intuitionistic linguistic weighted Bonferroni mean operator and its application to multiple attribute decision making

Area of Science:

• Decision Science
• Fuzzy Mathematics
• Information Theory

Background:

• Traditional Bonferroni mean is limited to crisp numbers, hindering its application with real-world fuzzy information.
• Intuitionistic linguistic variables offer a robust framework for representing uncertainty and vagueness.
• Existing methods often fail to fully capture interrelationships between decision attributes in fuzzy environments.

Purpose of the Study:

• To extend the Bonferroni mean operator to the intuitionistic linguistic environment.
• To develop a novel multiple attribute decision making (MADM) method incorporating intuitionistic linguistic information.
• To address the limitation of processing only crisp numbers in traditional Bonferroni mean applications.

Main Methods:

• Introduction of score and accuracy functions for intuitionistic linguistic numbers.
• Development of the intuitionistic linguistic Bonferroni mean (ILBM) and intuitionistic linguistic weighted Bonferroni mean (ILWBM) operators.
• Analysis of operator characteristics and special cases concerning Bonferroni parameters (p, q).

Main Results:

• The proposed ILBM and ILWBM operators effectively aggregate intuitionistic linguistic information.
• The developed MADM method successfully considers attribute interrelationships within an intuitionistic linguistic context.
• An illustrative example validated the effectiveness and practicality of the proposed approach.

Conclusions:

• The extended Bonferroni mean provides a powerful tool for decision making with intuitionistic linguistic data.
• The new method enhances the capability of Bonferroni mean in handling complex, fuzzy, and interrelated attributes.
• This research offers a significant advancement in fuzzy decision making methodologies.