Current Issue : January-March Volume : 2022 Issue Number : 1 Articles : 5 Articles
In this paper, we introduce and study the GD0-operations, which are a hyper class of the known D0-operations. GD0-operations are in fact D0-operations, that are generated not only from the same fuzzy negation. Similar with D0-operations, they are not always fuzzy implications. Nevertheless, some sufficient, but not necessary conditions for a GD0-operation to be a fuzzy implication, will be proved. A study for the satisfaction, or the violation of the basic properties of fuzzy implications, such as the left neutrality property, the exchange principle, the identity principle and the ordering property will also be made. This study also completes the study of the basic properties of D0-implications. At the end, surprisingly an unexpected new result for the connection of the QL-operations and D-operations will be presented....
Fuzzy systems (FSs) are popular and interpretable machine learning methods, represented by the adaptive neuro-fuzzy inference system (ANFIS). However, they have difficulty dealing with high-dimensional data due to the curse of dimensionality. To effectively handle high-dimensional data and ensure optimal performance, this paper presents a deep neural fuzzy system (DNFS) based on the subtractive clustering-based ANFIS (SC-ANFIS). Inspired by deep learning, the SC-ANFIS is proposed and adopted as a submodule to construct the DNFS in a bottom-up way. Through the ensemble learning and hierarchical learning of submodules, DNFS can not only achieve faster convergence, but also complete the computation in a reasonable time with high accuracy and interpretability. By adjusting the deep structure and the parameters of the DNFS, the performance can be improved further. This paper also performed a profound study of the structure and the combination of the submodule inputs for the DNFS. Experimental results on five regression datasets with various dimensionality demonstrated that the proposed DNFS can not only solve the curse of dimensionality, but also achieve higher accuracy, less complexity, and better interpretability than previous FSs. The superiority of the DNFS is also validated over other recent algorithms especially when the dimensionality of the data is higher. Furthermore, the DNFS built with five inputs for each submodule and two inputs shared between adjacent submodules had the best performance. The performance of the DNFS can be improved by distributing the features with high correlation with the output to each submodule. Given the results of the current study, it is expected that the DNFS will be used to solve general high-dimensional regression problems efficiently with high accuracy and better interpretability....
This paper is devoted to describe the notion of a parameterized degree of continuity for mappings between L-fuzzy soft topological spaces, where L is a complete De Morgan algebra.The degrees of openness, closedness, and being a homeomorphism for the fuzzy soft mappings are also presented.The properties and characterizations of the proposed notions are pictured. Besides, the degree of continuity for a fuzzy soft mapping is unified with the degree of compactness and connectedness in a natural way....
The present paper deals with notions from the field of complex analysis which have been adapted to fuzzy sets theory, namely, the part dealing with geometric function theory. Several fuzzy differential subordinations are established regarding the operator Lma , given by Lma : An ! An, Lma f (z) = (1 a)Rm f (z) + aSm f (z), where An = f f 2 H(U), f (z) = z + an+1zn+1 + . . . , z 2 Ug is the subclass of normalized holomorphic functions and the operators Rm f (z) and Sm f (z) are Ruscheweyh and S˘al˘agean differential operator, respectively. Using the operator Lma , a certain fuzzy class of analytic functions denoted by SLmF (d, a) is defined in the open unit disc. Interesting results related to this class are obtained using the concept of fuzzy differential subordination. Examples are also given for pointing out applications of the theoretical results contained in the original theorems and corollaries....
In this paper, we studied the relations between new types of fuzzy retractions, fuzzy foldings, and fuzzy deformation retractions, on fuzzy fundamental groups of the fuzzy Minkowski space.........................
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