Some Notes on Monotone TSK Fuzzy Inference Systems

This article presents our recent research on monotone Takagi-Sugeno-Kang (TSK) Fuzzy inference systems (FISs). We outline a few remarks on the necessary and sufficient conditions for TSK-FIS to be monotone, building upon the Ordered Weighted Averaging (OWA) principle and the orness concept. Some remarks for constructing monotone TSK-FIS from monotone data, extended from our previous findings, are further elucidated

Monotone Interval Fuzzy Inference Systems

—In this paper, we introduce the notion of a monotone fuzzy partition, which is useful for constructing a monotone zeroorder Takagi–Sugeno–Kang Fuzzy Inference System (ZOTSKFIS). It is known that a monotone ZOTSK-FIS model can always be produced when a consistent, complete, and monotone fuzzy rule base is used. However, such an ideal situation is not always available in practice, because a fuzzy rule base is susceptible to uncertainties, e.g., inconsistency, incompleteness, and nonmonotonicity. As a result, we devise an interval method to model these uncertainties by considering the minimum interval of acceptability of a fuzzy rule, resulting in a set of monotone interval-valued fuzzy rules. This further leads to the formulation of a Monotone Interval Fuzzy Inference System (MIFIS) with a minimized uncertainty measure. The proposed MIFIS model is analyzed mathematically and evaluated empirically for the Failure Mode and Effect Analysis (FMEA) application. The results indicate that MIFIS outperforms ZOTSK-FIS, and allows effective decision making using uncertain fuzzy rules solicited from human experts in tackling real-world FMEA problems

Monotone Fuzzy Rule Interpolation for TSK-FIS-Like n-Ary Aggregation Functions

Fuzzy Rule Interpolation (FRI) is important for fuzzy inference systems modeling pertaining to a sparse fuzzy rule base system. The focus of this paper is on a specific class of FRI, i.e., monotone FRI (MFRI), for modeling monotone Takagi-Sugeno-Kang Fuzzy Inference System (TSK-FIS) in the presence of a monotone sparse fuzzy rule base. On the other hand, a function is denoted as an n-ary aggregation function for a given n-dimensional input space and an output space when both the monotone and boundary properties are satisfied. In this paper, a set of sufficient conditions derived from the principles of Ordered Weighted Averaging (OWA) and the concept of orness for TSK-FIS to obey the monotone property is firstly formulated. We show that it is necessary to have a dense fuzzy rule base, which can be obtained by interpolation of fuzzy rules in a sparse fuzzy rule base, for constructing a monotone TSK-FIS. We then devise a two-stage MFRI for establishing monotone TSK-FIS. The first stage comprises a sufficient condition, inspired from the orness concept, to generate intermediate fuzzy membership functions (FMFs). The second stage deduces the monotone consequent of each intermediate rule from the available sparse fuzzy rules. We further extend our MFRI formulation to form TSK-FIS-like n-ary aggregation functions

Multi-expert decision-making with incomplete and noisy fuzzy rules and the monotone test

The use of Fuzzy Inference System (FIS) in decision making problems has received little attention so far. This may be due to the difficulty in gathering a complete set of fuzzy rules, which is free from noise, and the complexity in constructing an FIS model that is able to satisfy a number of important properties, including the monotonicity property. Previously, we have proposed a single-input Monotone-Interval FIS (MI-FIS) model, which can handle incomplete and non-monotone fuzzy rules. Besides that, we have proposed the idea of a monotone test (MT) for a set of fuzzy rules, which give an indication pertaining to the degree of monotonicity of a fuzzy rules set. In this paper, a multi-input MI-FIS model is firstly presented. The focus of this paper is on the use of MI-FIS and MT for undertaking multi expert decision-making (MEDM) problems. A three-phase MEDM framework consists of modelling, aggregation, and exploitation phases is proposed. In the modelling phase, an MT index for each fuzzy rule base from each expert, which is potentially non-monotone and incomplete, is obtained. The provided fuzzy rule bases are also modelled as MI-FISs. In the aggregation phase, an overall collective rating score of an alternative from a number of experts is obtained through the fuzzy weighted averaging operator. We suggest including MT as part of the aggregation phase. In exploitation phase, a rank ordering procedure among the alternatives is established using a possibility method. The developed framework is evaluated with simulated information. The results show that including the MT index in the aggregation phase is able to increase the robustness of the proposed FIS-MEDM model in the presence of noisy fuzzy rule sets

Parametric Conditions for a Monotone TSK Fuzzy Inference System to be an n-Ary Aggregation Function

Despite the popularity and practical importance of the fuzzy inference system (FIS), the use of an FIS model as an n-ary aggregation function, which is characterized by both the monotonicity and boundary properties, is yet to be established. This is because research on ensuring that FIS models satisfy the monotonicity property, i.e., monotone FIS, is relatively new, not to mention the additional requirement of satisfying the boundary property. The aim of this article, therefore, is to establish the parametric conditions for the Takagi–Sugeno–Kang (TSK) FIS model to operate as an n-ary aggregation function (hereafter denoted as n-TSK-FIS) via the specifications of fuzzy membership functions and fuzzy rules. An absorption property with fuzzy rules interpretation is outlined, and the use of n-TSK-FIS as a uninorm is explained. Exploiting the established parametric conditions, a framework for which an n-TSK-FIS model can be constructed from data samples is formulated and analyzed, along with a number of remarks. Synthetic data sets and a benchmark example on education assessment are presented and discussed. To be best of the authors’ knowledge, this article serves as the first use of the TSK-FIS model as an n-ary aggregation function

Parametric Conditions for a Monotone TSK Fuzzy Inference System to be an n-Ary Aggregation Function

Despite the popularity and practical importance of the Fuzzy Inference System (FIS), the use of an FIS model as an n -ary aggregation function, which is characterized by both the monotonicity and boundary properties, is yet to be established. This is because research on ensuring that FIS models satisfy the monotonicity property, i.e., monotone FIS, is relatively new, not to mention the additional requirement of satisfying the boundary property. The aim of this paper, therefore, is to establish the parametric conditions for the Takagi-Sugeno-Kang (TSK) FIS model to operate as an n -ary aggregation function (hereafter denoted as n -TSK-FIS) via the specifications of fuzzy membership functions (FMFs) and fuzzy rules. An absorption property with fuzzy rules interpretation is outlined, and the use of n -TSK-FIS as a uni-norm is explained. Exploiting the established parametric conditions, a framework for which an n -TSK-FIS model can be constructed from data samples is formulated and analyzed, along with a number of remarks. Synthetic data sets and a benchmark example on education assessment are presented and discussed. To be best of the authors' knowledge, this study serves as the first use of the TSK-FIS model as an n -ary aggregation function

Giant X-ray circular dichroism in a time-reversal invariant altermagnet

X-ray circular dichroism, arising from the contrast in X-ray absorption between opposite photon helicities, serves as a spectroscopic tool to measure the magnetization of ferromagnetic materials and identify the handedness of chiral crystals. Antiferromagnets with crystallographic chirality typically lack X-ray magnetic circular dichroism because of time-reversal symmetry, yet exhibit weak X-ray natural circular dichroism. Here, we report the observation of giant natural circular dichroism in the Ni $L_3$-edge X-ray absorption of Ni$_3$TeO$_6$, a polar and chiral antiferromagnet with effective time-reversal symmetry. To unravel this intriguing phenomenon, we propose a phenomenological model that classifies the movement of photons in a chiral crystal within the same symmetry class as that of a magnetic field. The coupling of X-ray polarization with the induced magnetization yields giant X-ray natural circular dichroism, revealing the altermagnetism of Ni$_3$TeO$_6$. Our findings provide evidence for the interplay between magnetism and crystal chirality in natural optical activity. Additionally, we establish the first example of a new class of magnetic materials exhibiting circular dichroism with time-reversal symmetry.Comment: Accepted by Advanced Materials (2024.2.16) Revised title: Giant X-ray circular dichroism in a time-reversal invariant altermagnet Revised drafts: Main 14 pages, 4 figures, and SI 20 pages, 8 figure

A network meta-analysis of 12,116 individuals from randomized controlled trials in the treatment of depression after acute coronary syndrome

Background: Post-acute coronary syndrome (ACS) depression is a common but not well understood complication experienced by ACS patients. Research on the effectiveness of various therapies remains limited. Hence, we sought to conduct a network meta-analysis to assess the efficacy of different interventions for post-ACS depression in improving patient outcomes. Methods and findings: Three electronic databases were searched for randomised controlled trials describing different depression treatment modalities in post-ACS patients. Each article was screened based on inclusion criteria and relevant data were extracted. A bivariate analysis and a network meta-analysis was performed using risk ratios (RR) and standardized mean differences (SMD) for binary and continuous outcomes, respectively. A total of 30 articles were included in our analysis. Compared to standard care, psychosocial therapy was associated with the greatest reduction in depression scores (SMD:-1.21, 95% CI: -1.81 to -0.61, p<0.001), followed by cognitive behavioural therapy (CBT) (SMD: -0.75, 95% CI: -0.99 to -0.52, p<0.001), antidepressants (SMD: -0.73, 95% CI: -1.14 to -0.31, p<0.001), and lastly, combination therapy (SMD: -0.15, 95% CI: -0.28 to -0.03, p = 0.016). No treatment modalities was found to be more effective in reducing depression scores when compared to one another. Additional analysis showed that these treatment modalities did not have significant impact on the overall mortality, cardiac mortality and recurrent myocardial infarction. Conclusion: This network meta-analysis found that the treatment effect of the various psychological modalities on depression severity were similar. Future trials on psychological interventions assessing clinical outcomes and improvement in adherence to ACS-specific interventions are needed

A qualitative systematic review of anonymous/unspecified living kidney and liver donors’ perspectives

Objectives & background: Anonymous live organ donors or unspecified donors are individuals willing to be organ donors for any transplant recipient with whom they have no biological or antecedent emotional relationship. Despite excellent recipient outcomes and the potential to help address organ scarcity, controversy surrounds the unconditional act of gifting one’s organs to an unrelated recipient. This qualitative systematic review provides insights into the first-hand experiences, motivations, and challenges that unspecified donors face. Methods: A systematic search was conducted on Medline, Embase, CINAHL, PsycINFO, and Web of Science database for qualitative literature regarding unspecified living donors’ motivations and experiences in liver and kidney transplantation. An inductive thematic analysis was conducted to generate themes and supportive subthemes. Results: 12 studies were included. The four major themes were (i) motivations, (ii) perception of risks, (iii) donor support, and (iv) benefits of donation. Unspecified donors demonstrated a deep sense of social responsibility but tended to underestimate health risks in favour of benefits for recipients. Despite the lack of emotional support from family and friends, the decision to donate was a resolute personal decision for donors. Majority benefitted emotionally and did not express regret. Conclusion: This qualitative review bridges the gap in literature on unspecified living donor psychology and provides a comprehensive understanding of the decision-making matrix and experiences of donors