The ambiguity and uncertainty of human cognition about actual engineering problems are very challenging and indispensable issues in the information expression and aggregation. However, existing various cubic (hesitant) concepts may not reasonably represent the hybrid information of both an interval-valued fuzzy value and a fuzzy sequence with identical and/or different fuzzy values, which commonly occurs in engineering fields. To express the hybrid information, this paper first proposes the notion of a cubic fuzzy multi-valued set as a new extension of existing cubic (hesitant) notions and defines operational relations of cubic fuzzy multi-valued elements. To obtain reasonable operations between different fuzzy sequence lengths in cubic fuzzy multi-valued elements, cubic fuzzy multi-valued elements are transformed into cubic fuzzy-consistency elements based on the average value and consistency degree/level (complement of standard deviation) of a fuzzy sequence in a cubic fuzzy multi-valued element. Next, we present operations of cubic fuzzy-consistency elements and an expected value of a cubic fuzzy-consistency element for ranking cubic fuzzy-consistency elements. Further, we propose a cubic fuzzy-consistency hybrid weighted arithmetic and geometric averaging operator, and then develop a multi-attribute group decision-making model using the cubic fuzzy-consistency hybrid weighted arithmetic and geometric averaging operator and expected value of cubic fuzzy-consistency elements to solve group decision-making problems under the cubic fuzzy multi-valued environment. To reflect the feasibility and effectiveness of the developed group decision-making model, the developed group decision-making model is utilized in an example on the selection problem of slope design schemes regarding an open pit mine in the cubic fuzzy multi-valued environment. Comparative analysis indicates the flexibility and rationality of the developed group decision-making model.
According to the production process of 20g steel(120t BOF→ LF→ CC), some system analysis are introduced to research on the content of T[O] and [N] and the type, source, composition and quantity of micro inclusions in refining process, pouring process and casting billet. The results of the study show: in billet, the main type of large inclusions is CaO-SiO2-Al2O3-MgO complex inclusion of sulfur contained. The content of large inclusions is 14.5mg/10kg in normal billet. The content of large inclusions is 33.14mg/10kg in compound casting billet which is 1.29 time than normal billet.The content of large inclusions whose particle size is more than 300μm in billet is 8.39mg/10kg, and make up 87% of the total. The content of large inclusions whose particle size is 140-300μm in billet is 2.29mg/10kg, and make up 15.79% of the total. The content of large inclusions whose particle size is 80-140μm in billet is 3.82mg/10kg, and make up 26.35% of the total. Unsteady casting plays an important role in the steel cleanliness.
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