A construction of a fuzzy topology from a strong fuzzy metric

[EN] After the inception of the concept of a fuzzy metric by I. Kramosil and J. Michalek, and especially after its revision by A. George and G. Veeramani, the attention of many researches was attracted to the topology induced by a fuzzy metric. In most of the works devoted to this subject the resulting topology is an ordinary, that is a crisp one. Recently some researchers showed interest in the fuzzy-type topologies induced by fuzzy metrics. In particular, in the paper  (J.J. Mi\~{n}ana, A. \v{S}ostak, {\it Fuzzifying topology induced by a strong fuzzy metric}, Fuzzy Sets and Systems,  6938 DOI information: 10.1016/j.fss.2015.11.005.) a fuzzifying topology ${\mathcal T}:2^X \to [0,1]$ induced by a fuzzy metric  $m: X\times X \times [0,\infty)$ was constructed. In this paper we extend  this construction to get the fuzzy topology ${\mathcal T}: [0,1]^X \to [0,1]$ and study some properties of this fuzzy topology.54AGrecova, S.; Sostak, A.; Uljane, I. (2016). 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Fuzzy functions: a fuzzy extension of the category SET and some related categories

[EN] In research Works where fuzzy sets are used, mostly certain usual functions are taken as morphisms. On the other hand, the aim of this paper is to fuzzify the concept of a function itself. Namely, a certain class of L-relations F : X x Y -> L is distinguished which could be considered as fuzzy functions from an L-valued set (X,Ex) to an L-valued set (Y,Ey). We study basic properties of these functions, consider some properties of the corresponding category of L-valued sets and fuzzy functions as well as briefly describe some categories related to algebra and topology with fuzzy functions in the role of morphisms.Höhle, U.; Porst, H.; Sostak, AP. (2000). Fuzzy functions: a fuzzy extension of the category SET and some related categories. Applied General Topology. 1(1):115-127. doi:10.4995/agt.2000.3028.SWORD1151271

A fuzzification of the category of M-valued L-topological spaces

[EN] A fuzzy category is a certain superstructure over an ordinary category in which ”potential” objects and ”potential” morphisms could be such to a certain degree. The aim of this paper is to introduce a fuzzy category FTOP(L,M) extending the category TOP(L,M) of M-valued L- topological spaces which in its turn is an extension of the category TOP(L) of L-fuzzy topological spaces in Kubiak-Sostak’s sense. Basic properties of the fuzzy category FTOP(L,M) and its objects are studied.Kubiak, T.; Sostak, AP. (2004). A fuzzification of the category of M-valued L-topological spaces. Applied General Topology. 5(2):137-154. doi:10.4995/agt.2004.1965.SWORD1371545

Fuzzifying topologies induced by a strong fuzzymetric

[eng] A construction of a fuzzifying topology induced by a strong fuzzy metric is presented. Properties of this fuzzifying topology, in particular, its convergence structure are studied. Our special interest is in the study of the relations between products of fuzzy metrics and the products of the induced fuzzifying topologies

National Institutes of Health Consensus Development Project on Criteria for Clinical Trials in Chronic Graft-versus-Host Disease: IV. The 2020 Highly morbid forms report

Chronic graft-versus-host disease (GVHD) can be associated with significant morbidity, in part because of nonreversible fibrosis, which impacts physical functioning (eye, skin, lung manifestations) and mortality (lung, gastrointestinal manifestations). Progress in preventing severe morbidity and mortality associated with chronic GVHD is limited by a complex and incompletely understood disease biology and a lack of prognostic biomarkers. Likewise, treatment advances for highly morbid manifestations remain hindered by the absence of effective organ-specific approaches targeting irreversible fibrotic sequelae and difficulties in conducting clinical trials in a heterogeneous disease with small patient numbers. The purpose of this document is to identify current gaps, to outline a roadmap of research goals for highly morbid forms of chronic GVHD including advanced skin sclerosis, fasciitis, lung, ocular and gastrointestinal involvement, and to propose strategies for effective trial design. The working group made the following recommendations: (1) Phenotype chronic GVHD clinically and biologically in future cohorts, to describe the incidence, prognostic factors, mechanisms of organ damage, and clinical evolution of highly morbid conditions including long-term effects in children; (2) Conduct longitudinal multicenter studies with common definitions and research sample collections; (3) Develop new approaches for early identification and treatment of highly morbid forms of chronic GVHD, especially biologically targeted treatments, with a special focus on fibrotic changes; and (4) Establish primary endpoints for clinical trials addressing each highly morbid manifestation in relationship to the time point of intervention (early versus late). Alternative endpoints, such as lack of progression and improvement in physical functioning or quality of life, may be suitable for clinical trials in patients with highly morbid manifestations. Finally, new approaches for objective response assessment and exploration of novel trial designs for small populations are required. (C) 2021 The American Society for Transplantation and Cellular Therapy. Published by Elsevier Inc. All rights reserved