2-tuple Linguistic Bonferroni Mean Operators and Their Application to Multiple Attribute Group Decision Making
Zhiming Zhang *
College of Mathematics and Computer Science, Hebei University, Baoding 071002, Hebei Province, PR China and School of Management, Harbin Institute of Technology, Harbin 150001, Heilongjiang Province, PR China.
Chong Wu
School of Management, Harbin Institute of Technology, Harbin 150001, Heilongjiang Province, PR China.
*Author to whom correspondence should be addressed.
Abstract
Aims: The aim of this paper is to develop the 2-tuple linguistic Bonferroni mean and the weighted 2-tuple linguistic Bonferroni mean.
Study Design: Some desirable properties and special cases of the developed operators are discussed. The geometric Bonferroni mean (GBM) is a generalization of the Bonferroni mean and geometric mean. In this paper, we also investigate the GBM under 2-tuple linguistic environments. We develop the 2-tuple linguistic geometric Bonferroni mean and the weighted 2-tuple linguistic geometric Bonferroni mean. We investigate some fundamental properties and special cases of them.
Place and Duration of Study: The Bonferroni Mean (BM) operator is a traditional mean type aggregation operator, which can capture the expressed interrelationship of the individual arguments and which is only suitable to aggregate crisp data.
Methodology: This paper extends the BM operator to 2-tuple linguistic environments.
Results: Based on these operators, we develop two approaches for multiple attribute group decision making with 2-tuple linguistic information.
Conclusion: Two numerical examples are provided to illustrate the effectiveness and practicality of the proposed approaches.
Keywords: Multiple attribute group decision making, 2-tuple linguistic information, 2-tuple linguistic Bonferroni mean, 2-tuple linguistic geometric Bonferroni mean