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Recently, bipolar fuzzy sets have been studied and applied a bit enthusiastically and a bit increasingly. In this paper we prove that bipolar fuzzy sets and [0,1]2-sets (which have been deeply studied) are actually cryptomorphic mathematical notions. Since researches or modelings on real world problems often involve multi-agent, multi-attribute, multi-object, multi-index, multi-polar information, uncertainty, or/and limit process, we put forward (or highlight) the notion of m-polar fuzzy set (actually, [0,1]m-set which can be seen as a generalization of bipolar fuzzy set, where m is an arbitrary ordinal number) and illustrate how many concepts have been defined based on bipolar fuzzy sets and many results which are related to these concepts can be generalized to the case of m-polar fuzzy sets. We also give examples to show how to apply m-polar fuzzy sets in real world problems.

No abstract

Immune checkpoint inhibitors (ICIs), such as PD-1/PD-L1 antibodies (Abs) and anti-cytotoxic T lymphocyte antigen 4 (CTLA-4) Abs, are effective for patients with various cancers. However, low response rates to ICI monotherapies and even hyperprogressive disease (HPD) have limited the clinical application of ICIs. HPD is a novel pattern of progression, with an unexpected and fast progression in tumor volume and rate, poor survival of patients and early fatality. Considering the limitations of ICI due to HPD incidence, valid biomarkers are urgently needed to predict the occurrence of HPD and the efficacy of ICI. Here, we reviewed and summarized the known biomarkers of HPD, including tumor cell biomarkers, tumor microenvironment biomarkers, laboratory biomarkers and clinical indicators, which provide a potential effective approach for selecting patients sensitive to ICI cancer treatments.