Soft Similarity Measures in Decision Making
A Common Fixed-Point Theorem for Semi-Compatible Mappings in a Complete Metric Space of an Implicit Relation via Inverse C-Class Functions
Residue Classes Euclidean Ring Over Integral Domain of Gaussian Integers
Mathematical Modeling and Stability Analysis of Ecological Species: A Review
Solutions for Nonlinear Diffusion Equations: A Comprehensive Review
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Surfaces in R3 with density
In many real-world scenarios, decision making is crucial especially under uncertainty. Such environments require appropriate models to evaluate the data effectively. One such task is assessing how closely stakeholder's opinions or judgements align with the ideal or actual values. To address this, we suggest a prototype using soft similarity measures between two soft sets for making decisions. We define various soft similarity measures in relation to a reference soft set (ℱ, P)and analyze properties of these measures like monotonicity, sub additivity and additivity. We introduce concepts such as Pseudo signed soft similarity measures, Pseudo positive soft sets, Pseudo negative soft sets and soft integral. We applied this framework to the problem of selecting a reliable stock market analyst by comparing analyst's predictions with actual data across multiple trails. The result showed that the method effectively identified the most consistent analyst. This approach offers a flexible and functional procedure for making decisions in the contexts of uncertainty where human judgement is the key factor.
The aim of the paper is to obtain a common fixed-point theorem in a complete metric space through inverse C-class functions for six self-maps in. The result extends previous work by incorporating semi-compatible and reciprocally continuous pairs of mappings, along with commutatively conditions. A generalized contraction condition involving an implicit relation ensures convergence to a unique common fixed point. The results generalizes and improves upon the main results, contributing to the broader framework of fixed-point theory.
Z√i = {m + in: m, n ∈ Z} is an integral domain under the addition defined by (m1+in1) ⊕ (m2+in2) = (m1+nm2) + i(n1+nn2) and multiplication defined by (m1+in1) ʘ (m2+in2) = (m1m2+n(-n1n2)) + i(m1n2+nn1m2). Taking nth - degree polynomials taking coefficients from the integral domain of Gaussian integers and using the residue classes modulo n operation on this integral domain, the degree of the polynomial is used to define the ordering relation and create a partially ordered set and further, defining the same addition and multiplication operations to join and meet respectively, this integral domain can be verified as the not distributive lattice.
Mathematical ecology focuses on the interactions between ecological species and their environments, using quantitative tools to understand population dynamics, species interactions, and ecosystem stability. This review provides an overview of key mathematical models that describe these ecological processes, including the classical Lotka- Volterra equations, predator-prey dynamics, and models of competition and mutualism. Particular emphasis is placed on the role of stability analysis in predicting system behaviour, with discussions on both linear and nonlinear techniques. Additionally, the review highlights selected recent developments and applications of these models in resource management and conservation contexts. Rather than claiming an exhaustive compilation of advances, this work aims to outline foundational concepts alongside representative modern contributions to the field.
Nonlinear diffusion equations (NDEs) are fundamental mathematical models describing a vast array of phenomena across science, engineering, and biology. Due to their inherent nonlinearities, obtaining exact or even approximate solutions for these equations poses significant challenges. This paper provides a comprehensive review of various established and emerging methodologies employed to solve NDEs, drawing insights from both analytical and numerical approaches. We explore methods such as the Differential Transform Method (DTM), Generalized Integral Transform Technique (GITT), Lie Symmetry Method, and Residual Power Series Method (RPSM) for analytical and semi-analytical solutions. For numerical approaches, we delve into the Differential Quadrature Method (DQM), Finite Difference Method (FDM), Finite Element Method (FEM), Collocation Methods, and the Method of Lines. The review highlights the applicability of these methods to diverse NDE types, including those with reaction terms, convection, and delays, emphasizing their strengths, limitations, and the critical importance of error analysis and stability considerations.
