Enhancing ELECTRE I Method with Complex Spherical Fuzzy Information

This article is concerned to delineate the strategic approach of ELiminating Et Choice Translating REality (ELECTRE) method for multi-attribute group decision-making (MAGDM) in terms of complex spherical fuzzy sets. The feasible, well-suited, and marvelous structure of complex spherical fuzzy set compliments the decision-making efficiency and ranking calibre of ELECTRE I approach to present a beneficial and supreme aptitude strategy for MAGDM. Beside the proposed methodology, a few non-fundamental properties of complex spherical fuzzy weighted averaging (CSFWA) operator inclusive of shift invariance, homogenous, linearity, and additive property are also explored. The proposed procedure validates the individual opinions into an acceptable form by the dint of CSFWA operator and the aggregated opinions are further analyzed by the proposed complex spherical fuzzy- ELECTRE I (CSF-ELECTRE I) method. Within the consideration of proposed methodology, normalized Euclidean distances of complex spherical fuzzy numbers are also contemplated. In CSF-ELECTRE I method, the score, accuracy, and refusal degrees determine the concordance and discordance sets for each pair of alternatives to calculate the concordance and discordance indices, respectively. Based on aggregated outranking matrix, a decision graph is constructed to attain the ELECTREcally outranked solutions and the best alternative. This article provides supplementary approach at the final step to profess a linear ranking order of the alternatives. The versatility and feasibility of the presented method are embellished with two case studies from the business and IT field. Moreover, to ratify the intensity and aptitude of the presented methodology, we provide a comparative study with complex spherical fuzzy-TOPSIS method.

A further investigation on q-rung orthopair fuzzy Einstein aggregation operators

Aggregation of q-rung orthopair fuzzy information serves as an important branch of the q-rung orthopair fuzzy set theory, where operations on q-rung orthopair fuzzy values (q-ROFVs) play a crucial role. Recently, aggregation operators on q-ROFVs were established by employing the Einstein operations rather than the algebraic operations. In this paper, we give a further investigation on operations and aggregation operators for q-ROFVs based on the Einstein operational laws. We present the operational principles of Einstein operations over q-ROFVs and compare them with those built on the algebraic operations. The properties of the q-rung orthopair fuzzy Einstein weighted averaging (q-ROFEWA) operator and q-rung orthopair fuzzy Einstein weighted geometric (q-ROFEWG) operator are investigated in detail, such as idempotency, monotonicity, boundedness, shift-invariance and homogeneity. Then, the developed operators are applied to multiattribute decision making problems under the q-rung orthopair fuzzy environment. Finally, an example for selecting the design scheme for a blockchain-based agricultural product traceability system is presented to illustrate the feasibility and effectiveness of the proposed methods.

Multicriteria Decision-Making Approach for Aggregation Operators of Pythagorean Fuzzy Hypersoft Sets

The Pythagorean fuzzy hypersoft set (PFHSS) is the most advanced extension of the intuitionistic fuzzy hypersoft set (IFHSS) and a suitable extension of the Pythagorean fuzzy soft set. In it, we discuss the parameterized family that contracts with the multi-subattributes of the parameters. The PFHSS is used to correctly assess insufficiencies, anxiety, and hesitancy in decision-making (DM). It is the most substantial notion for relating fuzzy data in the DM procedure, which can accommodate more uncertainty compared to available techniques considering membership and nonmembership values of each subattribute of given parameters. In this paper, we will present the operational laws for Pythagorean fuzzy hypersoft numbers (PFHSNs) and also some fundamental properties such as idempotency, boundedness, shift-invariance, and homogeneity for Pythagorean fuzzy hypersoft weighted average (PFHSWA) and Pythagorean fuzzy hypersoft weighted geometric (PFHSWG) operators. Furthermore, a novel multicriteria decision-making (MCDM) approach has been established utilizing presented aggregation operators (AOs) to resolve decision-making complications. To validate the useability and pragmatism of the settled technique, a brief comparative analysis has been conducted with some existing approaches.

The Fusion of Multi-Focus Images Based on the Complex Shearlet Features-Motivated Generative Adversarial Network

The traditional methods for multi-focus image fusion, such as the typical multi-scale geometric analysis theory-based methods, are usually restricted by sparse representation ability and the transferring efficiency of the fusion rules for the captured features. Aiming to integrate the partially focused images into the fully focused image with high quality, the complex shearlet features-motivated generative adversarial network is constructed for multi-focus image fusion in this paper. Different from the popularly used wavelet, contourlet, and shearlet, the complex shearlet provides more flexible multiple scales, anisotropy, and directional sub-bands with the approximate shift invariance. Therefore, the features in complex shearlet domain are more effective. With of help of the generative adversarial network, the whole procedure of multi-focus fusion is modeled to be the process of adversarial learning. Finally, several experiments are implemented and the results prove that the proposed method outperforms the popularly used fusion algorithms in terms of four typical objective metrics and the comparison of visual appearance.

SIS-BAM Algorithm for Angular Parameter Estimation of 2-D Incoherently Distributed Sources

For two-dimensional (2-D) incoherently distributed sources, this paper presents an effective angular parameter estimation method based on shift invariant structure (SIS) of the beamspace array manifold (BAM), named as SIS-BAM algorithm. In the proposed method, a shift invariance structure (SIS) of the observed vectors is firstly established utilizing a generalized array manifold of an uniform linear orthogonal array (ULOA). Secondly, based on Fourier basis vectors and the SIS, a beamspace transformation matrix can be performed. It projects received signals into the corresponding beamspace, so as to carry out dimension reduction of observed signals in beamspace domain. Finally, according to the SIS of beamspace observed vectors, the closed form solutions of the nominal azimuth and elevation are derived. Compared with the previous works, the presented SIS-BAM method provides better estimation performance, for example: 1) the computational complexity is reduced due to dealing with low-dimension beamspace signals and avoiding spectral search; 2) it can not only improve the angular parameter estimation accuracy but also have excellent robustness to the change of signal-to-noise ratio (SNR) and snapshot number. The theoretical analysis and simulation results confirm the effectiveness of the proposed method.

Unbounded Wiener–Hopf Operators and Isomorphic Singular Integral Operators

Some basics of a theory of unbounded Wiener–Hopf operators (WH) are developed. The alternative is shown that the domain of a WH is either zero or dense. The symbols for non-trivial WH are determined explicitly by an integrability property. WH are characterized by shift invariance. We study in detail WH with rational symbols showing that they are densely defined, closed and have finite dimensional kernels and deficiency spaces. The latter spaces as well as the domains, ranges, spectral and Fredholm points are explicitly determined. Another topic concerns semibounded WH. There is a canonical representation of a semibounded WH using a product of a closable operator and its adjoint. The Friedrichs extension is obtained replacing the operator by its closure. The polar decomposition gives rise to a Hilbert space isomorphism relating a semibounded WH to a singular integral operator of Hilbert transformation type. This remarkable relationship, which allows to transfer results and methods reciprocally, is new also in the thoroughly studied case of bounded WH.

Features of application of ESPRIT method for different configurations of antenna arrays

The paper discusses the features of the application of the ESPRIT method, which provides direction finding of a variety of radio sources with minimal computational costs, including in real time. To be able to use ESPRIT, antenna arrays are required that have the property of shift invariance, and for practical implementation, antenna arrays are required that allow you to form estimates of the directions of arrival of the largest number of signals that overlap in the spectrum, with a minimum number of antennas and reception channels. The aim of the work is to analyze the influence of the antenna array configuration on the features of ESPRIT application for different antenna array with the same number of antennas. A comparative qualitative analysis of the properties and features compared to the MUSIC method is presented. The algorithms developed by the authors for processing multichannel data received by angle and square antenna arrays are presented. It is shown analytically that when using a corner antenna array, it is necessary to take into account the possible presence of signals from indistinguishable-mirror directions of arrival. With a square antenna array, there are no mirror directions of arrival of different signals, which simplifies the implementation of the algorithm. It is shown analytically and by simulation modeling that the configuration of a square antenna array allows to increase the number of simultaneously tracked signals that overlap in the spectrum, compared to a corner antenna array with the same number of antennas.

Set Theoretic Rajan Transform and its Properties

In this paper, we describe the formulation of a novel transform called Set Theoretic Rajan Transform (STRT) which is an extension of Rajan Transform (RT). RT is a coding morphism by which a number sequence (integer, rational, real, or complex) of length equal to any power of two is transformed into a highly correlated number sequence of same length. STRT was introduced by G. Sathya. In STRT, RT is applied to a sequence of sets instead of sequences of numbers. Here the union (U) is analogous to addition (+) operation and symmetric difference (~) is analogous to subtraction (-). This transform satisfies some interesting set theoretic properties like Cyclic Shift Invariance, Dyadic Shift invariance, Graphical Inverse Invariance. This paper explains in detail about STRT and all of its set theoretic properties.