Linguistic interval-valued intuitionistic fuzzy sets, as an extension of interval-valued intuitionistic fuzzy sets, have strong practical value in the management of complex uncertainty system with qualitative evaluation information. This study focuses on the development of several linguistic interval-valued intuitionistic fuzzy Hamacher (LIVIFH) aggregation operators based on the extended Hamacher t-norm and s-norm. First, the extended Hamacher t-norm and s-norm, which are applicable to linguistic information environment, are applied to define the linguistic interval-valued intuitionistic fuzzy Hamacher operational laws. Second, based on the proposed operational laws, this study defines the linguistic interval-valued intuitionistic fuzzy Hamacher weighted average (LIVIFHWA) operator and the linguistic interval-valued intuitionistic fuzzy Hamacher weighted geometric (LIVIFHWG) operator, and then investigates their properties. Furthermore, the degeneracy and monotonicity of the proposed operators with respect to the adjustable parameter are explored. Finally, a multiple attribute group decision-making (MAGDM) approach is developed based on the proposed LIVIFH aggregation operators, and then this approach is applied to a supplier selection problem. Parameter analysis indicates that the adjustable parameter in the proposed LIVIFH aggregation operators could reflect the attitudes of decision makers. The LIVIFHWA operator would be more appropriate to optimistic decision makers, and the LIVIFHWG operator to pessimistic decision makers. In addition, as the adjustable parameter increasing, both attitudes tend to be neutral. The proposed method is also compared with two other approaches to show its feasibility and efficiency.Keywords: extended Hamacher t-norm and s-norm; linguistic interval-valued intuitionistic fuzzy set; linguistic interval-valued intuitionistic fuzzy Hamacher operators; multi-attribute group decision-making
A binocular full-color holographic three-dimensional near eye display system using a single spatial light modulator (SLM) is proposed. In the display system, the frequency spectrum shifting operation and color spectrum shifting operation are adopted to realize the frequency division multiplexing (FDM) and frequency superposition multiplexing (FSM) by manipulating the frequency spectrums of each color- and view-channel sub-holograms. The FDM combined with polarization multiplexing will be used to implement binocular display using a single SLM, and the FSM working with a bandpass filter for each view-channel will be used to achieve full-color display from single frame hologram. The optical analysis and experiments with 3D color objects confirm the feasibility of the proposed system in the practical application.
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