Intuitionistic uncertain linguistic partitioned Bonferroni means and their application to multiple attribute decision-making

ABSTRACT

The Bonferroni mean (BM) was originally introduced by Bonferroni and generalised by many other researchers due to its capacity to capture the interrelationship between input arguments. Nevertheless, in many situations, interrelationships do not always exist between all of the attributes. Attributes can be partitioned into several different categories and members of intra-partition are interrelated while no interrelationship exists between attributes of different partitions. In this paper, as complements to the existing generalisations of BM, we investigate the partitioned Bonferroni mean (PBM) under intuitionistic uncertain linguistic environments and develop two linguistic aggregation operators: intuitionistic uncertain linguistic partitioned Bonferroni mean (IULPBM) and its weighted form (WIULPBM). Then, motivated by the ideal of geometric mean and PBM, we further present the partitioned geometric Bonferroni mean (PGBM) and develop two linguistic geometric aggregation operators: intuitionistic uncertain linguistic partitioned geometric Bonferroni mean (IULPGBM) and its weighted form (WIULPGBM). Some properties and special cases of these proposed operators are also investigated and discussed in detail. Based on these operators, an approach for multiple attribute decision-making problems with intuitionistic uncertain linguistic information is developed. Finally, a practical example is presented to illustrate the developed approach and comparison analyses are conducted with other representative methods to verify the effectiveness and feasibility of the developed approach.

KEYWORDS:

• Multiple attribute decision-making
• partitioned Bonferroni mean
• partitioned geometric Bonferroni mean
• intuitionistic uncertain linguistic

Acknowledgments

The authors thank the editors and anonymous reviewers for their helpful comments and suggestions that have led to an improved version of this paper.

Additional information

Funding

This paper was supported by the National Natural Science Foundation of China [grant number 71271124], [grant number 71471172], [grant number 61571272]; the Humanities and Social Sciences Research Project of Ministry of Education of China [grant number 13YJC630104]; the Shandong Provincial Natural Science Foundation [grant number ZR2013GQ011]; A Project of Shandong Province Higher Educational Science and Technology Program [grant number J15LN56], [grant number J16LN25].

Notes on contributors

Zhengmin Liu

Zhengmin Liuis currently pursuing his Ph.D. degree at the School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan, China. He is also an Associated Professor in School of Management Science and Engineering, Shandong University of Finance and Economics. His research interests include information fusion, decision-making theory and application.

Peide Liu

Peide Liu received his Ph.D. degree in information management from Beijing Jiaotong University, Beijing, China, in 2006. He is currently a Professor in School of Management Science and Engineering, Shandong University of Finance and Economics, Shandong, Chian. His research interests include aggregation operators, fuzzy logic, fuzzy decision making, and their applications.