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To better express and handle the increasing complicated fuzzy decision making information, we firstly put forward the concept of multiple-valued picture fuzzy linguistic set (MVPFLS), which is motivated by the advantages of hesitant fuzzy set (HFS), linguistic term set (LTS), and picture fuzzy set (PFS). First, the concepts concerning MVPFLS and the multiple-valued picture fuzzy linguistic element (MVPFLE) are proposed. Second, the operating rules of MVPFLEs on account of linguistic scale functions (LSFs) are given, and the compared functions for MVPFLE are also defined. Third, the traditional generalized Heronian mean (HM) operators capturing the correlation among attributes are extended to multiple-valued picture fuzzy linguistic environment, namely, the multiple-valued picture fuzzy linguistic generalized weighted Heronian mean (MVPFLGWHM) aggregating operator and the multiple-valued picture fuzzy linguistic generalized weighted geometric Heronian mean (MVPFLGWGHM) aggregating operator are proposed, their interesting characteristics and some particular instances are also given. Fourth, the method utilizing the proposed aggregating operators to settle multiple attribute decision making (MADM) issues is provided. Eventually, a practical instance is employed to validate the powerfulness of the new approach, and the sensitivity analysis is performed along with comparative analysis.

Multiple-Valued Picture Fuzzy Linguistic Set Based on Generalized Heronian Mean Operators and Their Applications in Multiple Attribute Decision Making