Multi-criteria decision making with interval type 2 fuzzy Bonferroni mean.

• The interval type 2 fuzzy Bonferroni mean Ordered Weighted Averaging is developed. • Seven Bonferroni mean quantifier Ordered Weighted Averaging models are formulated. • The optimal weights are solved from the mixed integer linear programming models. • The models are applied to various linguistic decision making aggregation schemes. In this paper, the new aggregation models for the interrelated multi-criteria decision making (MCDM) problems based on the quantifier guided ordered weighted averaging (QGOWA) and Bonferroni mean (BM) operator with interval type 2 fuzzy sets (IT2FS) are developed. In most MCDM problems, the decision criteria might not be totally independent. For some MCDM methodologies that are not considering the interrelationship of the criteria, the decision results suggested are meaningless. The BM operator can express the interrelationship of the input arguments, which serves as a mean type aggregator. Yager introduced the OWA operator which is associated with the orness level (attitudinal character) by means of the quantifiers. Different quantifier functions are associated with the respective different orness levels. This is referred to as the QGOWA operator. Besides, the real world MCDM problems are mostly under uncertain environments. To address such MCDM problems, the linguistic criteria weights and the alternative rates are better characterized by IT2FS. The major contributions of this paper are to propose the interrelation MCDM aggregation models with various extensions, to construct the mixed integer linear programming models for obtaining the optimal QGOWA BM IT2FS weights, and to formulate a new interrelation MCDM paradigm. The developed aggregation models are: (1). Ordinary MCDM aggregation; (2). BM with OWA weights; (3). BM with OWA weights and personal importance; (4). BM with QGOWA weights; (5). BM with QGOWA weights and personal importance; (6). BM with QGOWA weights and attitudinal characters; (7). BM with QGOWA weights, attitudinal characters and personal importance. A new MCDM aggregation methodology with application based on the developed models is introduced. The application results from the MCDM aggregation methodology demonstrate that the final decision prioritization are actually affected by the various orness levels predetermined by the decision experts. [ABSTRACT FROM AUTHOR]