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.
The rapid growth of Internet of Things (IoT) devices has heightened the need for robust cryptographic algorithms to safeguard sensitive data. Selecting the most appropriate algorithm, however, requires a systematic decision-making framework capable of addressing uncertainty and imprecision in expert evaluations. This study proposes a novel distance measure for p,q-quasirung orthopair fuzzy sets (p,q-QOFSs), inspired by the Jensen-Shannon divergence, and examines its fundamental properties, including non-degeneracy, symmetry, boundedness, and compliance with the triangle inequality. Building on this measure, we develop an integrated multi-criteria group decision-making (MCGDM) model that combines the analytical hierarchy process (AHP) for criteria weighting with the compromise ranking of alternatives from distance to ideal solution (CRADIS) method for alternative ranking in a p,q-QOF environment. The proposed approach is applied to the selection of cryptographic algorithms for securing IoT devices, involving four domain experts, six candidate algorithms, and eight evaluation criteria. Results show that RSA (i.e., the alternative A(2)) is identified as the most suitable algorithm. Comparative analysis against CRADIS with other distance measures and established decision-making methods confirms the enhanced ranking accuracy and robustness of the proposed framework. These findings offer practical guidance for cybersecurity practitioners and policymakers in selecting cryptographic solutions tailored to IoT security needs.
Circular intuitionistic fuzzy sets (C-IFS) have lately been regarded as a modified form of intuitionistic fuzzy sets (I-FS). But they are regarded solely for certain elementary algebraic characteristics. This study enhances C-IFS in Dombi aggregation operators (AOs) by including more mathematical characteristics of algebraic laws. The operators encompass C-IF Dombi weighted averaging (C-IFDWA), C-IF Dombi ordered weighted averaging (C-IFDOWA), C-IF Dombi weighted geometric (C-IFDWG), and C-IF Dombi ordered weighted geometric (C-IFDOWG). Furthermore, we delineate the characteristics of idempotency, monotonicity, and boundedness for the suggested operators. Therefore, to calculate the primary component, we determine the multi-attribute decision-making (MADM) technique utilizing the offered operators for C-IF values (C-IFVs) to augment the quantity of the assessed operators. The proposed approach is validated through a numerical example, illustrating the advantages in terms of flexibility and accuracy. The findings contribute to the advancement of decision-making tools for selecting energy storage systems, offering a robust framework for future applications in the field.
This study addresses the berth allocation problem (BAP) in container terminals with irregular layouts under epistemic uncertainty conditions, proposing a mixed-integer linear programming (MILP) model to minimize operational costs via spatial-temporal optimal vessel assignments. To tackle the inherent non-determinism and ambiguity in vessel arrival, handling, departure times, and waiting and delay costs caused by adverse weather, scheduling errors, and equipment failures, a credibility-based fuzzy programming framework with triangular fuzzy numbers is introduced. This approach enables decision-makers to adjust confidence levels (a) for constraint satisfaction, offering flexibility in modeling qualitative uncertainties. An improved genetic algorithm (IGA) is developed, integrating adaptive mutation operators (swap, displacement, and reverse), dynamic mutation rates, various crossover operators, and penalty functions to enhance convergence and solution quality. Additionally, a reduced matrix solution representation is employed to streamline the search space, ensuring scalability for large-scale terminals. Computational experiments demonstrate that IGA outperforms basic genetic algorithms (GA) and simulated annealing (SA) in reducing vessel waiting and delay times, and consequently total operational costs, while maintaining feasibility under complex physical constraints such as berth adjacency, opposition, and blocking. The integration of fuzzy credibility theory with hybrid metaheuristics bridges a critical gap in handling terminals with irregular layouts under uncertainty, which deterministic models inadequately address. This work provides a practical tool for terminal operators to optimize berth utilization and resilience under uncertainty, advancing both theoretical and operational paradigms in maritime logistics.
The agricultural industry plays a vital role in the progress of any agrarian country. So, the utilization of land is a challenging task for agricultural engineers. It is challenging for agrarian engineers to determine the suitability of different land types for various crops. In this critical situation, the multicriteria group decision-making (MCGDM) technique plays a significant role in decision-making (DM). For the solution of these problems, by using intuitionistic fuzzy rough (IFR) set (IFRS) theory, Frank operation, along with power aggregation operators (PAOs), analyzed a new family of aggregation operators (AOs) called IFR Frank power weighted averaging (IFRFPWA), IFR frank power ordered weighted averaging (IFRFPOWA), IFR frank power ordered hybrid averaging (IFRFPHWA), IFR frank power weighted geometric (IFRFPWG), IFR frank power ordered weighted geometric (IFRFPOWG), IFR frank power ordered hybrid geometric (IFRFPHWG) operators. Also, some necessary axioms are known as boundedness, monotonicity, and idempotency. To highlight the significance of the diagnosis approach, illustrate a detailed real-life numerical problem. To check the applicability of the proposed work, compare it with other existing AOs, and discuss the sensitivity analysis of the proposed model. At the end, provide solid conclusions and explain the limitations of the proposed model and future direction.
One popular approach to studying topological concepts is to employ a subclass of topology, such as clopen, regular open, and delta-open sets. Motivated by the advantages of soft topology over classical topologies, we investigate some of these classes in a soft setting. We begin this manuscript by exploring further properties of soft regular open and soft delta-open sets in the context of soft subspaces and soft mappings, as well as describing their behavior in relation to classical topologies. We demonstrate that the condition of an extended soft topology guarantees the symmetry between delta-open sets and soft delta-open sets the realms of soft topology and its crisp topologies. Then, we apply the concept of soft delta-open sets to establish two new classes of soft compactness, namely soft delta-compactness, and soft local delta-compactness. We research the basic properties of these classes, including characterizations and preservation theorems under soft delta-continuous mappings. We reveal the relationship between soft compactness, soft delta-compactness and soft local delta-compactness, and also prove the equivalence between these concepts when the soft topology is soft regular. Finally, the symmetry between our new classes and their counterparts in some classical topologies is studied amply; especially, when the soft topology is extended or stable. The implementations of the current results and relationships are elucidated by some supporting examples.
We first introduce a new kind of algebras named left Ehoop, in which the top element ”1" is changed as one of the maximal elements. Therefore, left Ehoops are generalizations of left hoops, which is one of the most fundamental fuzzy logic algebras as the semantical system of fuzzy logic system. Additionally, we explore the connections between left Ehoops and several related structures, including EL-algebras, CL-algebras, BCK-algebras, and quantum B-algebras. To further clarify the link between left Ehoops and EL-algebras, we also define the concept of self-similar EL-algebra. More importantly, we give an equivalent characterization such that left Ehoops become self-similar EL-algebras. Lastly, we define Bosbach states, Rie č an states, and state-morphisms on left Ehoops, while examining their key properties and interrelationships. Our findings show that the collection of Bosbach states on a left Ehoop constitutes a compact Hausdorff space, and the mapping φ from state-measures to Bosbach states is an affine homeomorphism.
Medical diagnosis involves analyzing symptoms, test results, and patient histories, but uncertainty from vague symptoms and incomplete records complicates the process. Fuzzy logic-based systems address this issue but often depend on manual rule creation, which is time-consuming. This research proposes a hybrid approach integrating fuzzy logic with deep learning techniques (FL-DLT) for intelligent diagnosis. The framework combines adaptive neuro-fuzzy inference system (ANFIS) for handling uncertainty with convolutional neural networks (CNNs) for extracting features from medical images like X-rays and MRIs. ANFIS models relationships between symptoms, results, and diagnoses, while CNNs analyze medical images. Experimental results show high accuracy and reliability, even with noisy or incomplete data. The proposed approach can improve diagnostic accuracy and efficiency, supporting clinicians in decision-making. Key contributions include the development of the FL-DLT framework and its evaluation using a large dataset of patient records and medical images. Additionally, the research offers insights into the application of fuzzy logic and deep learning in medical diagnosis, highlighting their potential to enhance diagnostic outcomes and efficiency in clinical practice.
The development of fuzzy computational intelligence (FCI) has emerged as an effective method for personalized medicine and diagnosis. FCI effectively handles uncertainty and imprecision in medical data, facilitating patient-specific treatment recommendations. Conventional diagnostic and treatment methods typically rely on fixed threshold-based approaches, which fail to account for individual variations in patient responses, leading to suboptimal treatment outcomes. This study proposes the personalized treatment recommendation using fuzzy logic (PTR-FC) framework for diabetes (DB) patients to address these challenges. The framework integrates patient-specific data such as blood glucose levels, diet, exercise, and medication history into the fuzzy inference system (FIS), supporting personalized treatment recommendations. The treatment plans are dynamically adapted based on individual patient outcomes using linguistic factors and fuzzy rules (FR). The proposed method dynamically adjusts recommendations in real time, potentially enhancing personalized treatment and improving decision-making in DB management. Additionally, it promotes lifestyle modifications while reducing the risk of medication-induced complications. The effectiveness of the proposed method was compared to conventional methods, demonstrating improved treatment accuracy, increased patient adherence, and reduced adverse health risks. The PTR-FC framework offers a more adaptive and effective approach to DB management, ensuring better patient outcomes.
Medical diagnosis has become increasingly difficult, requiring sophisticated systems to manage decision-making uncertainty. The proposed medical diagnosis utilizing fuzzy logic framework (MD-FLF) addresses medical data imprecision and ambiguity by employing fuzzy inference techniques. Clinical data ambiguity is often overlooked by conventional diagnosis models. Such models include probabilistic classifiers and threshold-based decision trees. The models use accurate input-output correlations. However, fuzzy inference simplifies incremental membership assignment and rule-based reasoning in MD-FLF. This enhances the system's diagnostic ambiguity detection. The framework uses fuzzy rules to represent complicated non-linear interactions between symptoms and diagnostic data. This improves framework interpretation. MD-FLF models' ambiguity and non-linear relationships between diagnostic inputs and outputs provide interpretable recommendations for complex disorders. Rule-based methods and expert knowledge produce these results. Experimental evaluations showed that MD-FLF improved reliability by 97.68%, uncertainty by 96.84%, ambiguity by 43.56%, patient variability by 98.26%, and diagnostic accuracy by 97.82%. The paradigm addresses uncertainty to increase diagnostic reliability, precision, and confidence while eliminating ambiguity and offering clinical decision-making insights. MD-FLF outperforms deterministic techniques in medical diagnostic decision support systems and is stable and interpretable.
Sorting-based multiple attribute decision-making (MADM) methods address managerial challenges in the hypercompetitive contemporary business life effectively by facilitating efficient organization and retrieval of data, thereby enhancing analysis, optimization, and user experience. Among others, the additive ratio assessment sorting method (ARASsort) is a highly preferable one due to its capacity to offer a dependable sorting mechanism for multi-attribute assessment, characterized by a notable degree of practicality. While experts traditionally assign attribute weights subjectively in sorting methods, robust and objective tools like criteria importance through intercriteria correlation (CRITIC) offer scientific approaches to balance subjectivity. The originality of this study is threefold: First of all, this study is the first one proposing a CRITIC-ARASsort hybrid algorithm to mitigate subjectivity in sorting. Secondly, to address uncertainty in human judgment more comprehensively, it introduces the integration of fuzzy logic, particularly intuitionistic fuzzy sets (IFSs), into ARASsort and thus to the hybrid algorithm, resulting in the development of IF-CRITIC-ARASsort. Furthermore, a new intuitionistic fuzzy standard deviation formula is proposed to overcome the early defuzzification problem in previously proposed versions of IF-CRITIC method in the literature. The applicability of this method is demonstrated in a credit rating scenario, showcasing its utility in complex decision-making processes.
This paper introduces the concepts of SR-fuzzy subalgebras and ideals within the framework of BCK/BCI-algebras. SR-fuzzy subalgebras are defined and illustrated with various examples to elucidate their structure and behaviour under different operations in BCK/BCI-algebras. The research explores the properties of SR-fuzzy subalgebras and ideals, investigating their interrelationships and establishing that every SR-fuzzy ideal is an SR-fuzzy subalgebra, although the reverse is not necessarily true. Conditions under which an SR-fuzzy subalgebra qualifies as an SR-fuzzy ideal are also discussed. Through various examples, this paper illustrates these concepts and highlights potential areas for further exploration. This study contributes to the expanding literature on fuzzy sets and their applications in algebraic structures, offering insights that may benefit future research endeavours.
This paper introduces two new weak forms of soft regularity in soft topology: soft p-regular and soft almost-p-regular. These forms extend their analogous notions in classical topological spaces by incorporating soft sets, providing a flexible framework for dealing with uncertainty or imprecision. We obtain several characterizations of each of them and investigate the correspondences between them and their analogous concepts in classical topological spaces. Also, we prove that soft p-regularity lies strictly between soft regularity and soft almost-p-regularity. Moreover, we show that soft p-regularity (resp. soft almost p-regularity) is preserved under soft alpha- open subspaces (resp. soft regular-open subspaces). In addition, we prove that soft p-regularity and soft almost p-regularity are soft productive. Finally, we obtain some preservation theorems regarding soft pregularity and soft almost-p-regularity.
Real-life decision-making requires evaluative information from humans, which proves difficult because human opinions differ widely among factors. Through CQROFS, decision experts gain powerful tools to collect information by using membership grade (MG), non-membership grade (NMG), and abstinence grade (AG). The framework functions as an uncertainty reducer for dealing with lived information through its capability to present each variable by three specific grades. Implementing a complex q-rung ortho-pair fuzzy set (CQROFS) faces a primary obstacle with information from different-weighted factors. Standard methods ignore differentiating between factors because they apply uniform value treatment to all elements. This paper presents a new aggregation operator (AO) family designed explicitly for decisions that utilize CQROFS-based methodology. We developed two kinds of operators within this family: CQROF-prioritized averaging operators and CQROF-prioritized geometric operators, since both types effectively deal with factor importance. This paper analyses the fundamental features of the aggregation operators presented as a part of the family. A multi-attribute group decision-making (MAGDM) problem receives the proposed approach in a real-world decision-making scenario to show its functional worth.
Gathering information from a real-life scenario is a very difficult process due to involvement of the multiple criteria and human opinion. A complex Pythagorean fuzzy set (CPyFS) is an interesting tool to deal with uncertainty while gathering information from human opinion involved in real-life scenarios. But, the aggregation of the information gathered by CPyFS becomes very hectic. Several aggregation operators (AOs) aggregate the information in the form of complex Pythagorean fuzzy values (CPyFVs). However, they lack the prioritization of attributes according to their weights. In this article, an interesting new class of AOs including complex Pythagorean fuzzy (CPyF) prioritized averaging operator (CPyFPAO) and CPyF prioritized geometric operator (CPyFPGO) is introduced. Basic and necessary properties of the introduced AOs are observed. Furthermore, the case study is discussed where the introduced AOs are applied to seek the most suitable optimized site for starting a pilot health project with the help of the multi-attribute group decision-making (MAGDM) process. The results obtained from all proposed AOs are analyzed and compared with some existing AOs. All the analyses are explained with the help of the tabulated data and graphs.
We propose a new possibilistic data interpolation bagging (pdi-Bagging), which improve the discriminant rate of checking data by adding virtually generated data to the training data. In this paper, we propose a new method to generate virtual data not only for misclassified data but also around correct classified data, and a new method for determining the output class of virtual data. In addition, we discuss the usefulness of pdi-Bagging using Student's t-test and Tukey's HSD test in numerical examples, and finally, we also discuss its application to a vehicle type discrimination system in the large-scale outdoor parking lot.
