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In the present study, the vibration characteristics of a cylindrical shell (CS) made up of four layers are investigated. The ring is placed in the axial direction of a four-layered functionally graded material (FGM) cylindrical shell. The layers are made of functionally graded material (FGM). The materials used are stainless steel, aluminum, zirconia, and nickel. The frequency equations are derived by employing Sander's shell theory and the Rayleigh–Ritz (RR) mathematical technique. Vibration characteristics of functionally graded materials have been investigated using polynomial volume fraction law for all FGM layers. The characteristic beam functions have been used to determine the axial model dependency. The natural frequencies are obtained with simply supported boundary conditions by using MATLAB software. Several analogical assessments of shell frequencies have also been conducted to confirm the accuracy and dependability of the current technique. [ABSTRACT FROM AUTHOR]

The enumeration of fuzzy subgroups is a complex problem. Several authors have computed results for special instances of groups. In this paper, we present a novel algorithm that is designed to enumerate the fuzzy subgroups of a finite group. This is achieved through the computation of maximal chains of subgroups. This approach is also useful for writing a program to compute the number of fuzzy subgroups. We provide further elucidation by computing the number of fuzzy subgroups of the groups Q8 and D8. [ABSTRACT FROM AUTHOR]

The dual hesitant fuzzy linguistic term set (DHFLTS) is defined by two functions that express the grade of membership and the grade of non-membership using a set of linguistic terms. In the present work, we first quote an example to point out that the existing complement operation of DHFLTS is on the wrong track. Meanwhile, we redefine this operation to fill the holes in the existing ones. Next, the notion of information energy under a dual hesitant fuzzy linguistic background is provided in order to build the criteria weight determination model. To further facilitate the theory of DHFLTS, we propose two vector similarity measures, i.e., Jaccard and Dice similarity measures, and their weighted forms for DHFLTS. In addition, we pioneer some generalized similarity measures of DHFLTSs and indicate that the Dice similarity measures are particular instances of the generalized similarity measures for some parameter values. Afterward, the similarity measures-based model with unknown weight information under the background of dual hesitant fuzzy linguistic environment is constructed. Lastly, an illustrated example is included to validate the method's application, along with sensitivity analysis and comparative analysis, demonstrating the practicality and validity of its results. [ABSTRACT FROM AUTHOR]

Hussain, Yau, and Zuo introduced the Lie algebra L k (V) from the derivation of the local algebra M k (V) : = O n / (g + J 1 (g) + ⋯ + J k (g)) . To find the dimension of a newly defined algebra is an important task in order to study its properties. In this regard, we compute the dimension of Lie algebra L 5 (V) and justify the sharp upper estimate conjecture for fewnomial isolated singularities. We also verify the inequality conjecture: δ 5 (V) < δ 4 (V) for a general class of singularities. Our findings are novel and an addition to the study of Lie algebra. [ABSTRACT FROM AUTHOR]

This research article expands the formal representation of human thinking to a most generalized hybrid theory, namely, complex q -rung orthopair fuzzy N -soft set. It is able to capture a great deal of graded imprecision and vagueness, which so often appear together in human interpretations. This model renders a parameterized mathematical tool for the ranking-based fuzzy modeling of two-dimensional paradoxical data. To that purpose, the proposed theory integrates complex q -rung orthopair fuzzy sets with the parametric structure of N -soft sets. The framework that arises captures information beyond the confined space of complex intuitionistic fuzzy N -soft sets and complex Pythagorean fuzzy N -soft sets, with the assistance of a parameter q. We establish the basic set-theoretical operations of this model and prove some of its fundamental properties. The Einstein and other elementary algebraic operations on complex q -rung orthopair fuzzy N -soft values shall be introduced to broaden the mathematical toolbox of this field. Its relationships with contemporary approaches shall demonstrate its outstanding flexibility. Moreover, we establish two competent multicriteria decision-making algorithms that capture the nuances of periodical inconsistent data. Their feasibility shall be demonstrated with an explicit application to the selection of optimum aerospace technology required for the economic development of the Mexican space agency. A comparative analysis of both strategies with the prevailing techniques substantiates their rationality. In addition, we illustrate this comparative study with an explicative bar chart that shows the compatibility of their outcomes. Finally, we examine the functionality of the proposed model and compare it with alternative theories. [ABSTRACT FROM AUTHOR]