This paper focuses on multi-attribute group decision-making (MAGDM) course in which attributes are evaluated in terms of interval-valued intuitionistic fuzzy (IVIF) information. More explicitly, this paper introduces new aggregation operators for IVIF information and further proposes a new IVIF MAGDM method. The power average (PA) operator and the Muirhead mean (MM) are two powerful and effective information aggregation technologies. The most attractive advantage of the PA operator is its power to combat the adverse effects of ultra-evaluation values on the information aggregation results. The prominent characteristic of the MM operator is that it is flexible to capture the interrelationship among any numbers of arguments, making it more powerful than Bonferroni mean (BM), Heronian mean (HM), and Maclaurin symmetric mean (MSM). To absorb the virtues of both PA and MM, it is necessary to combine them to aggregate IVIF information and propose IVIF power Muirhead mean (IVIFPMM) operator and the IVIF weighted power Muirhead mean (IVIFWPMM) operator. We investigate their properties to show the strongness and flexibility. Furthermore, a novel approach to MAGDM problems with IVIF decision-making information is introduced. Finally, a numerical example is provided to show the performance of the proposed method.
The linguistic Pythagorean fuzzy sets (LPFSs), which employ linguistic terms to express membership and non-membership degrees, can effectively deal with decision makers’ complicated evaluation values in the process of multiple attribute group decision-making (MAGDM). To improve the ability of LPFSs in depicting fuzzy information, this paper generalized LPFSs to cubic LPFSs (CLPFSs) and studied CLPFSs-based MAGDM method. First, the definition, operational rules, comparison method and distance measure of CLPFSs are investigated. The CLPFSs fully adsorb the advantages of LPFSs and cubic fuzzy sets and hence they are suitable and flexible to depict attribute values in fuzzy and complicated decision-making environments. Second, based on the extension of power Hamy mean operator in CLPFSs, the cubic linguistic Pythagorean fuzzy power average operator, the cubic linguistic Pythagorean fuzzy power Hamy mean operator as well as their weighted forms were introduced. These aggregation operators can effectively and comprehensively aggregate attribute values in MAGDM problems. Besides, some important properties of these operators were studied. Finally, we presented a new MAGDM method based on CLPFSs and their aggregation operators. Illustrative examples and comparative analysis are provided to show the effectiveness and advantages of our proposed decision-making method.
The interval-valued q-rung dual hesitant fuzzy sets (IVq-RDHFSs) effectively model decision makers' (DMs') evaluation information as well as their high hesitancy in complicated multi-attribute decision-making (MADM) situations. Note that the IVq-RDHFSs only depict DMs' evaluation values quantificationally but overlook their qualitative decision information. To improve the performance of IVq-RDHFSs in dealing with fuzzy information, we incorporate the concept of uncertain linguistic variables (ULVs) into them and propose a new tool, called interval-valued q-rung dual hesitant uncertain linguistic sets (IVq-RDHULSs). Then we investigate MADM approach with interval-valued q-rung dual hesitant uncertain linguistic (IVq-RDHUL) information. Afterwards, the concept of IVq-RDHULSs as well as their operations and ranking method are proposed. Further, we propose a set of IVq-RDHUL aggregation operators (AOs) on the basis of the powerful Muirhead mean, i.e., the IVq-RDHUL Muirhead mean operator, the IVq-RDHUL weighted Muirhead mean operator, the IVq-RDHUL dual Muirhead mean operator, and the IVq-RDHUL weighted dual Muirhead mean operator. The significant properties of the proposed AOs are also discussed in detail. Lastly, we try to introduce a new method to MADM issues in IVq-RDHUL context based on the newly developed AOs. INDEX TERMS Interval-valued q-rung dual hesitant fuzzy sets, interval-valued q-rung dual hesitant uncertain linguistic sets, Muirhead mean, multi-attribute decision-making.
This paper investigates multi-attribute group decision-making (MAGDM) problems based on interval-valued Pythagorean fuzzy linguistic sets (IVPFLSs). The IVPFLSs are regarded as an efficient tool to describe decision makers' (DMs') evaluation information from both quantitative and qualitative aspects. However, existing IVPFLSs based MAGDM methods are still insufficient and inadequate to deal with complicated practical situations. This paper aims to propose a novel MAGDM method and the main contributions of the present work are threefold. First, we propose new operations of interval-valued Pythagorean fuzzy linguistic numbers (IVPFLNs) based on linguistic scale function. Second, we propose new aggregation operators (AOs) of IVPFLNs based on power average operator and Muirhead mean. The proposed AOs take the interrelationship among any numbers of attributes into account and eliminate the bad influence of DMs' unreasonable evaluation values on the final decision results. Third, based on the new operations and AOs of IVPFLNs, we introduce a novel approach to MAGDM and present its main steps. Finally, we discuss the effectiveness of the proposed approach and investigates their advantages through numerical examples. INDEX TERMS; interval-valued Pythagorean fuzzy linguistic sets; interval-valued Pythagorean fuzzy linguistic power Muirhead mean; linguistic scale function; multiple attribute group decision-making
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