Interval Type 2 Fuzzy Analytic Hierarchy Process Synthesizing with Ordered Weighted Average Variation of Bonferroni Mean Operator

Abstract

In multiple criteria decision making (MCDM), analytic hierarchy process (AHP) is one of the widely used methodologies. The synthesis of the local weighted rates to the global rates is a critical stage. AHP assumes that the decision criteria are independent. However, most real MCDM problems involve the set of criteria that are interrelated each other. Bonferroni mean (BM) can express the interrelationship of the input arguments. The BM is a mean type aggregator in decision making with different combinations of indexes. In this paper, based on Yager's ordered weighted average (OWA), the crisp BM operator is extended to the models with interval type 2 fuzzy sets (IT2FS) decision input judgments. The IT2FS aggregation models with BM OWA weights and linguistic quantifier guided OWA weights associated with orness levels are developed. The traditional AHP is extended with the developed IT2FS OWA variation of BM aggregation models in the AHP synthesizing stage. Such IT2FS AHP models can deal with even more realistic decision making problems. A warehouse location MCDM problem with interrelated attributes is examined for illustrating the proposed IT2FS AHP synthesis models.