Fuzzy Implications: Some Recently Solved Problems

In this chapter we discuss some open problems related to fuzzy implications, which have either been completely solved or those for which partial answers are known. In fact, this chapter also contains the answer for one of the open problems, which is hitherto unpublished. The recently solved problems are so chosen to reflect the importance of the problem or the significance of the solution. Finally, some other problems that still remain unsolved are stated for quick reference

Advances in the geometrical study of rotation-invariant t-norms

T-norm properties for left-continuous, increasing [0, 1](2)-> [0, 1.] functions can be fully described in terms of contour lines. For a left-continuous t-norm T, the rotation-invariance property comes down to the continuity of its contour line C-o. However, contour lines are inadequate to investigate the geometrical structure of these rotation-invariant t-norms. Enforced with the companion and zooms it is possible to totally reconstruct T by means of its contour line CO and its beta-zoom, with beta the unique fixpoint of C-o

Dysregulation of type 2 innate lymphoid cells and TH2 cells impairs pollutant-induced allergic airway responses

Background: Although the prominent role of TH2 cells in type 2 immune responses is well established, the newly identified type 2 innate lymphoid cells (ILC2s) can also contribute to orchestration of allergic responses. Several experimental and epidemiologic studies have provided evidence that allergen-induced airway responses can be further enhanced on exposure to environmental pollutants, such as diesel exhaust particles (DEPs). However, the components and pathways responsible remain incompletely known. Objective: We sought to investigate the relative contribution of ILC2 and adaptive TH2 cell responses in a murine model of DEP-enhanced allergic airway inflammation. Methods: Wild-type, Gata-3+/nlslacZ (Gata-3-haploinsufficient), RAR-related orphan receptor α (RORα)fl/flIL7RCre (ILC2-deficient), and recombination-activating gene (Rag) 2-/- mice were challenged with saline, DEPs, or house dust mite (HDM) or DEP+HDM. Airway hyperresponsiveness, as well as inflammation, and intracellular cytokine expression in ILC2s and TH2 cells in the bronchoalveolar lavage fluid and lung tissue were assessed. Results: Concomitant DEP+HDM exposure significantly enhanced allergic airway inflammation, as characterized by increased airway eosinophilia, goblet cell metaplasia, accumulation of ILC2s and TH2 cells, type 2 cytokine production, and airway hyperresponsiveness compared with sole DEPs or HDM. Reduced Gata-3 expression decreased the number of functional ILC2s and TH2 cells in DEP+HDM-exposed mice, resulting in an impaired DEP-enhanced allergic airway inflammation. Interestingly, although the DEP-enhanced allergic inflammation was marginally reduced in ILC2-deficient mice that received combined DEP+HDM, it was abolished in DEP+HDM-exposed Rag2-/- mice. Conclusion: These data indicate that dysregulation of ILC2s and TH2 cells attenuates DEP-enhanced allergic airway inflammation. In addition, a crucial role for the adaptive immune system was shown on concomitant DEP+HDM exposure