The study explores controllability results for fuzzy fractional differential equations involving the Hilfer–Katugampola fractional derivative, a generalization of the Riemann–Liouville and Hadamard fractional derivatives. It establishes existence conditions for mild solutions by applying fractional calculus, semigroup theory, the Laplace transform, and Sadovskii's fixed point theorem. Additionally, an example is included to illustrate the practical applications of the key findings.
Multi-objective optimization problems frequently arise in real-world systems where decision-makers face objectives that are conflicting, imprecise, or uncertain. Goal programming (GP) provides a systematic framework for resolving such conflicts by defining aspiration levels and minimizing deviations across multiple objectives. However, conventional models typically assume that all aspiration levels and parameters are precisely known, an assumption rarely satisfied in complex decision environments. Among various solution methods, approaches based on GP have been widely applied due to their flexibility in handling multi-objective decision problems under practical constraints. This study introduces a new methodology that transforms a fuzzy stochastic multi-objective programming problem into an equivalent GP model. The formulation incorporates fuzzy random variables (FRV) to represent both linguistic vagueness and probabilistic uncertainty in system parameters. The stochastic aspect is handled through an expectation-based transformation in the objective functions, while chance-constrained programming (CCP) is applied to maintain feasibility in the constraints. Triangular membership functions (TMF) are used to represent vague and ambiguous system information within the model, and following the transformation into a single-objective framework, Zimmermann's linear membership function is applied to evaluate the degree of goal satisfaction. Furthermore, a gradient-based conflict and non-conflict analysis is employed to assess interactions among objectives, which helps establish a structured assignment of aspiration levels and priorities. To validate the proposed approach, an existing numerical problem is considered, and its results are compared with those obtained from established methods.
In this paper, a new parametric approach is developed to solve a fuzzy system of equations with type 2 fuzzy uncertainties. NT2TFN are introduced as uncertain values in the fuzzy system of equations. Different properties of NT2TFN are discussed and a simplified transformed representation is developed for easy computation. The proposed transformation reduces the NT2TFN into crisp form. Further, the extension principle is discussed in presence of NT2TFN. For illustration purposes, the transformed representation of NT2TFN is used to solve four example problems. The obtained solutions of example problems are depicted numerically and shown graphically. Using the proposed method, the obtained solution is compared with the solution of other existing methods. Finally, it is observed that the proposed method possesses a good agreement with other existing approaches.
In this article with the external source terms, we have successfully developed approximate solutions of one-dimensional fuzzy fractional partial differential equations using the Laplace residual power series method. The generalized algorithm of the proposed technique is formulated under the Caputo fractional derivative operator. To verify the results, several illustrative examples have been solved to demonstrate the effectiveness of the methodology. Graphs representing the solutions at various fractional orders are plotted and compared with the solutions at the integer-order derivative. The graphical analysis confirms a strong agreement between the fractional solutions and the exact solution. The tables show that the solutions obtained by the present technique are more accurate compared to those obtained by the finite difference method. furthermore, the plots of approximate solutions approach those at the classical order (gamma=1) as the fractional order gamma approaches to its integer value. Therefore, we conclude that fractional calculus effectively captures the global dynamics of problems involving fuzzy concepts.
Technological advancements and artificial intelligence raise security concerns, with facial recognition being a particularly effective security measure. Choosing the best facial recognition software involves a comprehensive decision-making approach due to its sensitivity and potential ambiguities, ensuring the highest level of security. The main aim of the research is to introduce a new theoretical framework called the complex picture fuzzy soft set (CPFS-set), which manages information-based uncertainty, periodicity, and vagueness by combining the flexibility of soft sets and complex picture fuzzy sets. Basic concepts, such as types and set operations, are examined mathematically with numerical examples to clarify the ideas. An intelligent decision-support mechanism is developed using a robust algorithm to illustrate the construction and computation stages of facial recognition software evaluation with the CPFS-set. This comprehensive analysis helps stakeholders make informed decisions based on empirical data and rigorous evaluation.
