As an effective way of expressing information,Z-number can well describe the natural language with uncertain information. But most research on Z-number relies on evenly distributed linguistic term sets,and the aggregation operators used to aggregate Z-number information rarely take into account the relationships between attributes.Therefore,a non-uniform distribution language scale function was proposed,then the situation of the probability language Z-number under unbalanced semantics was discussed,and a new type of defined operator was used to aggregate the probability language Z-number.At the same time,the relevant operations and score function was defined.Then,a multi-objective linear optimization model was build to determine the optimal investment ratio.Finally,the feasibility and effectiveness of the proposed method are illustrated by examples,and sensitivity analysis is performed.

β-Galactosidase (β-gal) is the gold standard marker of cellular senescence, which is linked with various age-related diseases. Therefore, it is essential to develop more excellent probes that can real-time monitor β-gal activity in cellular senescence in vivo. Fluorescent/photoacoustic (FL/PA) dual-modal imaging possesses excellent sensitivity and spatial resolution. To our knowledge, there has been no tumor-targeted FL/PA probe to image cellular senescence by monitoring the activity of β-gal in vivo. Therefore, we developed a tumor-targeted FL/PA probe (Gal-HCy-Biotin) for β-gal-activatable imaging of tumor senescence. Gal-HCy without tumor-targeted biotin is used as a control probe. Gal-HCy-Biotin is superior to Gal-HCy due to the higher kinetic parameter of Gal-HCy-Biotin than Gal-HCy in vitro. Moreover, biotin could help Gal-HCy-Biotin enter and accumulate in tumor cells with higher FL/PA signal. In detail, Gal-HCy-Biotin or Gal-HCy could image senescent tumor cells with 4.6-fold or 3.5-fold FL enhancement and 4.1-fold or 3.3-fold PA enhancement. Gal-HCy-Biotin or Gal-HCy could image tumor senescence with 2.9-fold or 1.7-fold FL enhancement and 3.8-fold or 1.3-fold PA enhancement. We envision that Gal-HCy-Biotin will be applied for FL/PA imaging of tumor senescence in clinic.

Caspase-3 is an essential executor in apoptosis, andits activationhas been regarded as a biomarker of cell apoptosis. The developmentof Caspase-3-responsive multimodal probes is a promising researchprospect. Fluorescent/photoacoustic (FL/PA) imaging has attractedconsiderable attention due to the high sensitivity of FL as well asthe high spatial resolution and penetration depth of PA. To our knowledge,there has been no tumor-targeted FL/PA probe to monitor the activityof Caspase-3 in vivo. Therefore, we developed a tumor-targetedFL/PA probe (Bio-DEVD-HCy) for Caspase-3-responsive imagingof tumor apoptosis. Ac-DEVD-HCy without tumor-targetedbiotin is used as a control probe. In vitro experimentsindicated that Bio-DEVD-HCy is superior to Ac-DEVD-HCy because of the higher kinetic parameter of Bio-DEVD-HCy in comparison to Ac-DEVD-HCy. Cell and tumor imagingresults suggested that Bio-DEVD-HCy could enter and accumulatein tumor cells with higher FL/PA signal with the help of tumor-targetedbiotin. In detail, Bio-DEVD-HCy or Ac-DEVD-HCy could image apoptotic tumor cells with 4.3-fold or 3.5-fold FL enhancementand 3.4-fold or 1.5-fold PA enhancement. Bio-DEVD-HCy or Ac-DEVD-HCy could image tumor apoptosis with 2.5-foldor 1.6-fold FL enhancement and 4.1-fold or 1.9-fold PA enhancement.We envision that Bio-DEVD-HCy will be applied for FL/PAimaging of tumor apoptosis in clinical settings.