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ON VARIOUS ALGEBRAIC STRUCTURES IN MULTIDIMENSIONAL FUZZY SETS
One recent generalization of Zadeh's fuzzy sets is the concept of multidimensional fuzzy sets. This work extends this concept further by introducing a generalized form of multidimensional fuzzy algebra. By focusing on multidimensional t-norms and t-conorms, we develop a comprehensive theory. This includes the notion of strong multidimensional fuzzy algebras and explores their properties, such as multidimensional groupoids, monoids, and groups. Additionally, we introduce equivalence relations on the collection of all multidimensional fuzzy sets and present an example of specific monoids within this collection. Finally, we demonstrate how a group structure can be imposed on a subcollection of orderless multidimensional fuzzy sets. Keywords: Multidimensional fuzzy algebra, Multidimensional t-norm, Multidimensional t-conorm, Strong multidimensional fuzzy algebra, Equivalence classes, Multidimensional groups, Multidimensional fuzzy groupoid.
Journal Article
Multidimensional poverty: an analysis of definitions, measurement tools, applications and their evolution over time through a systematic review of the literature up to 2019
The paper provides an overview of definitions, measurements and applications of the concept of multidimensional poverty through a systematic review. The literature is classified according to three research questions: (1) what are the main definitions of multidimensional poverty?; (2) what methods are used to measure multidimensional poverty?; (3) what are the dimensions empirically measured?. Findings indicate that (1) the research on multidimensional poverty has grown in recent years; (2) multidimensional definitions do not necessarily imply to leave behind the dominance of the economic sphere; (3) the most popular methods proposed in the literature deal with the Alkire–Foster methodology, followed by latent variable models. Recommendations for future research emerge: new methodologies or the improvement of current ones are rather relevant; intangible aspects of poverty start to deserve attention calling for new definitions; there is evidence of under researched geographical areas, thereby calling for new empirical works that expand the geographical scope.
Journal Article
Disentangled latent factors for muti-cause treatment effect estimation
Existing methods estimate treatment effects from observational data and assume that covariates are all confounders. However, observed covariates may not directly represent confounding variables that influence both treatment and outcome. They always include variables that only affect the treatment or the outcome. In addition, for multi-dimensional binary treatments, disentangled methods are mainly designed for binary variables and ignore the impact of multi-cause treatment variables on the inference of latent factors. To address these two issues, based on variable decomposition and proxy inference, we propose the Disentangled Latent Factors for Multi-cause Treatment Estimation (DEMTE) algorithm. It utilizes an identifiable autoencoder to infer and disentangle latent factors based on the joint distribution of variables in observational data. DEMTE evaluates the treatment effect on the disentangled factors. Synthetic experiments and semi-synthetic experiments demonstrate the effectiveness of the inference and disentanglement techniques and our method achieves more accurate treatment effect estimation.
Journal Article
Hausdorff type operators and wavelet transform associated with the multidimensional Fourier-Bessel transform
In the present paper, we introduce the Hausdorff operators associated with the multidimensional Fourier-Bessel operator Δ
α
; and we prove the boundedness of the multidimensional Fourier-Bessel-Hausdorff operators on the space
L
α
2
(
ℝ
+
d
)
. We investigate multidimensional Fourier-Bessel wavelet transform, and obtain some useful results. The relation between the multidimensional Fourier-Bessel wavelet transform and multidimensional Fourier-Bessel-Hausdorff operators is also established. The properties of the adjoint multidimensional Fourier-Bessel-Hausdorff operators are further discussed. The results of this paper are illustrated by some examples and figures.
Journal Article
Multidimensional Gas Chromatography in Essential Oil Analysis. Part 1: Technical Developments
Multidimensional gas chromatography (MDGC) is now established as a technique which can help resolve most of the co-elution problems presenting with conventional gas chromatography for highly complex samples. Essential oils (EOs) are often used in the optimisation and development of novel MDGC methods and related technologies, to demonstrate and assess performance. In this review, recent trends and technical developments in the optimisation of MDGC, modulation and system configuration, pertinent and applied to EO analysis, will be critically discussed. Optimisation of MDGC will be discussed with reference to different column configurations, modulation periods and detection. Attention is given to novel modulation systems, development of multiplex MDGC systems and new approaches which combine heart-cut and comprehensive modes within one system. A section of this review will be dedicated to the preparative application of the MDGC and its application in the isolation of less abundant compounds from complex EO matrices.
Journal Article
The Myth of Firm Performance
Firm performance is one of the most prominent concepts in organizational research. Despite its importance, and despite the many developmental critiques that have appeared over the years, performance continues to be a difficult concept to apply in a scientifically rigorous way. After surfacing three potentially viable approaches for conceptualizing performance, we find that most studies are internally inconsistent in their use of these approaches, a situation that creates substantial difficulty in effectively interpreting research. The primary source of inconsistency lies in the use of a generalized abstract conceptualization of performance in theory building (the latent multidimensional approach) coupled with the adoption of one or two narrow aspects of performance in the empirical work (the separate constructs approach). Follow-up analyses designed to determine the best path for resolving these mismatches indicate that our field's heavy use of abstract performance in theorizing is not scientifically grounded and should be replaced with more specific aspects of performance to match existing practices in empirical work. Although this change would profoundly affect the field and would be resisted by many, it offers a concrete path away from indefensible practices. We offer several explanations for current practices but emphasize forces related to institutional theory. From an institutional perspective, it appears that firm performance is treated in a general fashion in many areas of our academic lives because it has been embraced as an instrument of legitimacy rather than as a scientific tool that facilitates dialogue and the accumulation of knowledge. We recommend and begin a conversation designed to highlight the long-run dangers of focusing our attention on an abstract concept of performance and suggest a set of specific steps that could help to move all of us in a new direction as we attempt to enhance the scientific rigor of our field.
Journal Article
Would ChatGPT-facilitated programming mode impact college students’ programming behaviors, performances, and perceptions? An empirical study
ChatGPT, an AI-based chatbot with automatic code generation abilities, has shown its promise in improving the quality of programming education by providing learners with opportunities to better understand the principles of programming. However, limited empirical studies have explored the impact of ChatGPT on learners’ programming processes. This study employed a quasi-experimental design to explore the possible impact of ChatGPT-facilitated programming mode on college students’ programming behaviors, performances, and perceptions. 82 college students were randomly divided into two classes. One class employed ChatGPT-facilitated programming (CFP) practice and the other class utilized self-directed programming (SDP) mode. Mixed methods were utilized to collect multidimensional data. Data analysis uncovered some intriguing results. Firstly, students in the CFP mode had more frequent behaviors of debugging and receiving error messages, as well as pasting console messages on the website and reading feedback. At the same time, students in the CFP mode had more frequent behaviors of copying and pasting codes from ChatGPT and debugging, as well as pasting codes to ChatGPT and reading feedback from ChatGPT. Secondly, CFP practice would improve college students’ programming performance, while the results indicated that there was no statistically significant difference between the students in CFP mode and the SDP mode. Thirdly, student interviews revealed three highly concerned themes from students' user experience about ChatGPT: the services offered by ChatGPT, the stages of ChatGPT usage, and experience with ChatGPT. Finally, college students’ perceptions toward ChatGPT significantly changed after CFP practice, including its perceived usefulness, perceived ease of use, and intention to use. Based on these findings, the study proposes implications for future instructional design and the development of AI-powered tools like ChatGPT.
Journal Article
Multidimensional scaling methods can reconstruct genomic DNA loops using Hi-C data properties
This paper proposes multidimensional scaling (MDS) applied to high-throughput chromosome conformation capture (Hi-C) data on genomic interactions to visualize DNA loops. Currently, the mechanisms underlying the regulation of gene expression are poorly understood, and where and when DNA loops are formed remains undetermined. Previous studies have focused on reproducing the entire three-dimensional structure of chromatin; however, identifying DNA loops using these data is time-consuming and difficult. MDS is an unsupervised method for reconstructing the original coordinates from a distance matrix. Here, MDS was applied to high-throughput chromosome conformation capture (Hi-C) data on genomic interactions to visualize DNA loops. Hi-C data were converted to distances by taking the inverse to reproduce loops via MDS, and the missing values were set to zero. Using the converted data, MDS was applied to the log-transformed genomic coordinate distances and this process successfully reproduced the DNA loops in the given structure. Consequently, the reconstructed DNA loops revealed significantly more DNA-transcription factor interactions involved in DNA loop formation than those obtained from previously applied methods. Furthermore, the reconstructed DNA loops were significantly consistent with chromatin immunoprecipitation followed by sequencing (ChIP-seq) peak positions. In conclusion, the proposed method is an improvement over previous methods for identifying DNA loops.
Journal Article
Multidimensional Fractional Calculus: Theory and Applications
In this paper, we introduce several new types of partial fractional derivatives in the continuous setting and the discrete setting. We analyze some classes of the abstract fractional differential equations and the abstract fractional difference equations depending on several variables, providing a great number of structural results, useful remarks and illustrative examples. Concerning some specific applications, we would like to mention here our investigation of the fractional partial differential inclusions with Riemann–Liouville and Caputo derivatives. We also establish the complex characterization theorem for the multidimensional vector-valued Laplace transform and provide certain applications.
Journal Article