Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Picture Fuzzy Interactional Aggregation Operators via Strict Triangular
  Norms and Applications to Multi-Criteria Decision Making   The picture fuzzy set, characterized by three membership degrees, is a
helpful tool for multi-criteria decision making (MCDM). This paper investigates
the structure of the closed operational laws in the picture fuzzy numbers
(PFNs) and proposes efficient picture fuzzy MCDM methods. We first introduce an
admissible order for PFNs and prove that all PFNs form a complete lattice under
this order. Then, we give some specific examples to show the non-closeness of
some existing picture fuzzy aggregation operators. To ensure the closeness of
the operational laws in PFNs, we construct a new class of picture fuzzy
operators based on strict triangular norms, which consider the interaction
between the positive degrees (negative degrees) and the neutral degrees. Based
on these new operators, we obtain the picture fuzzy interactional weighted
average (PFIWA) operator and the picture fuzzy interactional weighted geometric
(PFIWG) operator. They are proved to be monotonous, idempotent, bounded,
shift-invariant, and homogeneous. We also establish a novel MCDM method under
the picture fuzzy environment applying PFIWA and PFIWG operators. Furthermore,
we present an illustrative example for a clear understanding of our method. We
also give the comparative analysis among the operators induced by six classes
of famous triangular norms.

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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn