Theory of fuzzy integrals and its applications

The research field of ferroptosis has seen exponential growth over the past few years, since the term was coined in 2012. This unique modality of cell death, driven by iron-dependent phospholipid peroxidation, is regulated by multiple cellular metabolic pathways, including redox homeostasis, iron handling, mitochondrial activity and metabolism of amino acids, lipids and sugars, in addition to various signalling pathways relevant to disease. Numerous organ injuries and degenerative pathologies are driven by ferroptosis. Intriguingly, therapy-resistant cancer cells, particularly those in the mesenchymal state and prone to metastasis, are exquisitely vulnerable to ferroptosis. As such, pharmacological modulation of ferroptosis, via both its induction and its inhibition, holds great potential for the treatment of drug-resistant cancers, ischaemic organ injuries and other degenerative diseases linked to extensive lipid peroxidation. In this Review, we provide a critical analysis of the current molecular mechanisms and regulatory networks of ferroptosis, the potential physiological functions of ferroptosis in tumour suppression and immune surveillance, and its pathological roles, together with a potential for therapeutic targeting. Importantly, as in all rapidly evolving research areas, challenges exist due to misconceptions and inappropriate experimental methods. This Review also aims to address these issues and to provide practical guidelines for enhancing reproducibility and reliability in studies of ferroptosis. Finally, we discuss important concepts and pressing questions that should be the focus of future ferroptosis research.

Ferroptosis: mechanisms, biology and role in disease.

Radiation therapy (RT) including external beam radiotherapy (EBRT) and internal radioisotope therapy (RIT) has been widely used for clinical cancer treatment. However, owing to the low radiation absorption of tumors, high doses of ionizing radiations are often needed during RT, leading to severe damages to normal tissues adjacent to tumors. Meanwhile, the RT efficacies are limited by different mechanisms, among which the tumor hypoxia-associated radiation resistance is a well-known one, as there exists hypoxia inside most solid tumors while oxygen is essential to enhance radiation-induced DNA damages. With the development in nanotechnology, there have been great interests in using nanomedicine strategies to enhance radiation responses of tumors. Nanomaterials containing high-Z elements to absorb radiation rays (e.g. X-ray) can act as radio-sensitizers to deposit radiation energy within tumors and promote treatment efficacy. Nanoscale carriers are able to deliver therapeutic radioisotopes into tumors for internal RIT, or chemotherapeutic drugs for synergistically combined chemo-radiotherapy. As uncovered in recent studies, the tumor microenvironment could be modulated by various nanomedicine approaches to overcome hypoxia-associated radiation resistance. Herein, the authors will summarize the applications of nanomedicine for RT cancer treatment, and pay particular attention to the latest development of 'advanced materials' for enhanced cancer RT.

Emerging Nanotechnology and Advanced Materials for Cancer Radiation Therapy.

Molodtsov [D. Molodtsov, Soft set theory - First results, Comput. Math. Appl. 37 (1999) 19-31] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. In this paper we apply the notion of soft sets by Molodtsov to the theory of BCK/BCI-algebras. The notion of soft BCK/BCI-algebras and soft subalgebras are introduced, and their basic properties are derived.

Soft BCK/BCI-algebras

The Metabolic Underpinnings of Ferroptosis.

A general frame for intuitionistic fuzzy rough sets

Fuzzy set theory, soft set theory and rough set theory are mathematical tools for dealing with uncertainties and are closely related. Feng et al. introduced the notions of rough soft set, soft rough set and soft rough fuzzy set by combining fuzzy set, rough set and soft set all together. This paper is devoted to the further discussion of the combinations of fuzzy set, rough set and soft set. A new soft rough set model is proposed and its properties are derived. Furthermore, fuzzy soft set is employed to granulate the universe of discourse and a more general model called soft fuzzy rough set is established. The lower and upper approximation operators are presented and their related properties are surveyed.

Soft rough fuzzy sets and soft fuzzy rough sets

On the union and intersection operations of rough sets based on various approximation spaces

Four kinds of constructive methods of rough approximation operators from existing rough sets are established, and the important conclusion is obtained: some rough sets are essentially direct applications of these constructive methods. Moreover, the new notions of non-dual multigranulation rough sets and hybrid multigranulation rough sets are introduced, and some properties are investigated.

Constructive methods of rough approximation operators and multigranulation rough sets

We introduce a new concept of ideals in BCC-algebras and describe connections between such ideals and congruences.

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Xiaohong Zhang

Papers

A general frame for intuitionistic fuzzy rough sets

Soft rough fuzzy sets and soft fuzzy rough sets

On the union and intersection operations of rough sets based on various approximation spaces

Constructive methods of rough approximation operators and multigranulation rough sets

On ideals and congruences in bcc-algebras