Calderón Operator on Local Morrey Spaces with Variable Exponents

In this paper, we establish the boundedness of the Calderón operator on local Morrey spaces with variable exponents. We obtain our result by extending the extrapolation theory of Rubio de Francia to the local Morrey spaces with variable exponents. The exponent functions of the local Morrey spaces with the exponent functions are only required to satisfy the log-Hölder continuity assumption at the origin and infinity only. As special cases of the main result, we have Hardy’s inequalities, the Hilbert inequalities and the boundedness of the Riemann–Liouville and Weyl averaging operators on local Morrey spaces with variable exponents.

Variances and Logarithmic Aggregation Operators: Extended Tools for Decision-Making Processes

Variance, as a measurement of dispersion, is a basic component of decision-making processes. Recent advances in intelligent systems have included the concept of variance in information fusion techniques for decision-making under uncertainty. These dispersion measures broaden the spectrum of decision makers by extending the toolset for the analysis and modeling of problems. This paper introduces some variance logarithmic averaging operators, including the variance generalized ordered weighted averaging (Var-GOWLA) operator and the induced variance generalized ordered weighted averaging (Var-IGOWLA) operator. Moreover, this paper analyzes some properties, families and particular cases of the proposed operators. Finally, an illustrative example of the characteristic design of the operators is proposed using real-world information retrieved from financial markets. The objective of this paper is to analyze the performance of some equities based on the expected payoff and the dispersion of its elements. Results show that the equity payoff results present diverse rankings combined with the proposed operators, and the introduced variance measures aid decision-making by offering new tools for information analysis. These results are particularly interesting when selecting logarithmic averaging operators for decision-making processes. The approach presented in this paper extends the available tools for decision-making under ignorance, uncertainty, and subjective environments.

Hamacher Interactive Hybrid Weighted Averaging Operators under Fermatean Fuzzy Numbers

A Fermatean fuzzy set is a more powerful tool to deal with uncertainties in the given information as compared to intuitionistic fuzzy set and Pythagorean fuzzy set and has energetic applications in decision-making. Aggregation operators are very helpful for assessing the given alternatives in the decision-making process, and their purpose is to integrate all the given individual evaluation values into a unified form. In this research article, some new aggregation operators are proposed under the Fermatean fuzzy set environment. Some deficiencies of the existing operators are discussed, and then, new operational law, by considering the interaction between the membership degree and nonmembership degree, is discussed to reduce the drawbacks of existing theories. Based on Hamacher’s norm operations, new averaging operators, namely, Fermatean fuzzy Hamacher interactive weighted averaging, Fermatean fuzzy Hamacher interactive ordered weighted averaging, and Fermatean fuzzy Hamacher interactive hybrid weighted averaging operators, are introduced. Some interesting properties related to these operators are also presented. To get the optimal alternative, a multiattribute group decision-making method has been given under proposed operators. Furthermore, we have explicated the comparison analysis between the proposed and existing theories for the exactness and validity of the proposed work.