The trapezoid fuzzy linguistic Bonferroni mean operators and their application to multiple attribute decision making

Abstract

The Bonferroni Mean (BM) operator is a traditional mean type aggregation operator which can capture the expressed interrelationship of the individual arguments, and is only suitable to aggregate crisp data. In this paper, we develop some Bonferroni mean operators based on trapezoid fuzzy linguistic variables, such as a Trapezoid Fuzzy Linguistic Bonferroni Mean (TFLBM) operator, a Trapezoid Fuzzy Linguistic Weighted Bonferroni Mean (TFLWBM) operator, a Trapezoid Fuzzy Linguistic Bonferroni OWA (TFLBOWA) operator and a Trapezoid Fuzzy Linguistic Weighted Bonferroni OWA (TFLWBOWA) operator. Furthermore, some desirable properties of these operators are studied. At the same time, some special cases in these operators are analyzed. Based on these operators, methods of multiple attribute decision making with trapezoid fuzzy linguistic information are proposed. Finally, an illustrative example is given to verify the developed approaches and to demonstrate their practicality and effectiveness.