fuzzy $r$

In this paper, we have introduced and studied the notion of perspectivity in fuzzy lattices. The motivation is from the work done by Wasadikar and Khubchandani. We have tried to relate $\bigtriangledown_F$-relation with fuzzy perspective relation. Also, we prove that for a pair of a fuzzy atoms, the concept of fuzzy subperspective holds. Subsequently, several related properties are proven.

The explosion of Internet of Things (IoT) devices has created enormous amounts of real-time data, requiring sophisticated Data Mining Methods (DMT) that can rapidly extract valuable insights. Managing the computational complexity of processing high data volumes, integrating various IoT data formats, and ensuring that the system can scale are among the most significant issues. Fuzzy Dynamic Adaptive Classifier Optimization Analysis (FDACOA) is a method that has been suggested as an approach to the difficulties caused by changes in data patterns, processing in real-time, and data heterogeneity. By incorporating Adaptive Fuzzy Logic (AFL) and heuristic optimization, FDACOA enhances data classification accuracy and efficiency while simultaneously assuring that the algorithm can adapt to changes in data streams. This adaptability is crucial in IoT applications, where data fluctuation might affect analysis quality. FDACOA uses dynamic adaptation to alter classifier parameters based on real-time feedback to improve prediction accuracy and reduce computing costs. An optimization layer fine-tunes fuzzy rules and membership functions to optimize performance across data situations. Simulation analyses proved the algorithm's capacity to classify with high accuracy and low computational cost. Smart healthcare, predictive maintenance in industrial IoT, and intelligent transportation systems use FDACOA for real-time decision-making and data-driven insights. FDACOA is a viable approach for dynamic data mining in IoT-enabled big data contexts because of its faster, more accurate, and more adaptable simulation results.

The HyperSoft Set (HSS) is a powerful tool for Multi-Criteria Group Decision-Making (MCGDM) problems because it expands on the concept of the soft set by combining many sets of qualities. The function F in this framework is a multi-argument function. The importance of uncertainty in medical practice is becoming more widely recognized, yet research on this topic remains fragmented across various disciplines. Considering several attributes and their sub-divisions, ambiguity, imprecision, and uncertainty make the Data Mining (DM) complex. The Fuzzy HyperSoft Set (FHSS) combined with the Weight-Based Support Vector Machine (WSVM) algorithm is presented in this study to overcome those complex problems. This study mainly emphasizes detecting critical symptoms to diagnose diseases. Initially, the K-Means Clustering (KMC) algorithm was employed to pre-process the dataset. The noise from the data can be effectively eliminated by this KMC method. This process significantly improved the accuracy of medical Data Classification (DC). This uncertainty became a basic feature of people's lives. Each attribute is attributed to a group of possible objects in the discourse world. The FHSS method uses the Fuzzy Membership (FM) to handle uncertain data. This integration will also support expressing those data in detail, and DM was also enhanced. For medical diagnosis, the WSVM algorithm is then employed. Classification outcomes were improved by employing this WSVM method in a dataset. Experimental outcomes indicate that the suggested FHSS-WSVM algorithm executes better than the current Accuracy, precision, recall, and F-measure methods. The model was evaluated using the Cleveland heart disease dataset, comprising 303 patient records with 13 diagnostic attributes. Comparative analysis is conducted against conventional classifiers such as standard SVM, Random Forest, and fuzzy soft set-based methods. Experimental results demonstrate the superior performance of FHSS-WSVM, achieving 92.3% accuracy, 91.6% precision, 90.8% recall, and an F-measure of 91.1%, outperforming baseline models by statistically significant margins (p < 0.05).

‎Given a continuous Archimedean t-norm and its corresponding continuous additive generator, we introduce a new approach to generate a fuzzy strong $\phi-b-$norm (FS$-\phi-b-$N). Also, we define the notion of a fuzzy strong $\phi-b-$normed algebra (FS$-\phi-b-$NA) in general. Finally, some of the basic and hereditary properties of the defined spaces  are presented.

This paper introduces a family of $F$-fuzzy, Bailey--Nemytskii functions of level $p$ in fuzzy set theory. Then, it defines Bailey and Nemytskii contraction functions on fuzzy metric spaces. Finally, it uses the aforementioned family to show that each of the contraction functions has a fixed point. The paper also generalizes Suzuki contraction functions to fuzzy metric spaces and studies the existence of fixed points for such functions.

This paper explores a specific category of optimization management models tailored for wireless communication systems‎. ‎To enhance the efficiency of managing these systems‎, ‎we introduce a fuzzy relation multi-objective programming approach‎. ‎We define the concept of a feasible index set and present a novel algorithm‎, ‎termed the feasible index set algorithm‎, ‎which is designed to determine the optimal lexicographic solution to the problem‎, ‎demonstrating polynomial computational complexity‎. ‎Previous studies have indicated that the emission base stations within wireless communication systems can be effectively modeled using a series of fuzzy relation inequalities through max-product composition‎. ‎This topic is also addressed in our paper‎. ‎ ‎Wireless communication is widely employed across various sectors‎, ‎encompassing mobile communication and data transmission‎. ‎In this framework‎, ‎information is transmitted via electromagnetic waves generated by fixed emission base stations‎.

We investigate the linear objective function optimization problem constrained by a new system of fuzzy relationequations, utilizing the minimum t-norm for fuzzy compositions. Our findings reveal that the feasible region ischaracterized as a finite union of closed convex cells. We provide necessary and sufficient conditions to determinethe problem’s feasibility. To streamline optimization, seven novel rules are proposed, on which an algorithm is basedto achieve a global optimum. Notably, a specific instance of our problem is shown to be equivalent to the well-knownminimal vertex cover problem. The efficacy of our algorithm is demonstrated through a concrete example.

Preventing the threat of stereotyping is critical for business performance improvements. Because of this situation, businesses must take the necessary precautions. However, these actions have an impact on cost increase for the businesses. The number of studies in the literature performing priority analysis for these factors is quite limited. This situation increases the need for a new study that prioritizes the analysis of these variables. Accordingly, this study aims to evaluate the factors against the stereotype threat in the sustainable business environment. An artificial intelligence model is implemented in the first stage to weigh the experts. In the following stage, selected criteria are evaluated with the help of T-Spherical fuzzy DEMATEL. Thirdly, a comparative analysis was performed using different values. Finally, selected industries are ranked by Spherical Fuzzy RATGOS with respect to the stereotype threat. The weights of the experts can be identified in the analysis process. This situation has a strong contribution to the effectiveness of the findings. It is concluded that training activities are critical to minimizing the threat of stereotypes in companies.

Software Defined Networking (SDN) has been hailed as a revolutionary development in network management, with the potential to transform the landscape of the industry. The core principle behind SDN is the decoupling of the control plane from the data plane, a move that has been widely regarded as a significant step towards more centralized control. Nevertheless, determining the optimal placement of controllers, known as the Controller Placement Problem (CPP), remains a significant challenge due to conflicting objectives such as latency, resilience, and load balancing. This paper proposes a novel approach leveraging fuzzy logic to address the CPP. Distinct from heuristic or optimization algorithms, this approach employs fuzzy set theory to manage imprecise and dynamic network parameters while optimising multiple objectives, including latency, inter-controller communication, and load balancing. The proposed method provides a flexible, adaptable framework for CPP across varying network topologies. Experimental results validate the effectiveness of this approach in achieving balanced trade-offs among objectives, ensuring efficient and scalable SDN management, with a 18.7% reduction in maximum node-to-controller latency and a 22% improvement in load imbalance compared to state-of-the-art methods.

In this paper, we prove  Bellman type inequality for Sugeno integral and generalize it for pseudo-integrals. Furthermore, we generalize the Bellman's inequality in abstract spaces. The strengthened version of this inequality is demonstrated in pseudo-integrals and abstract spaces. Also, we illustrate theorems with some examples.

In this paper, a new form of critic-only Reinforcement Learning algorithm for continuous state spaces control problems is proposed. Our approach, called Fuzzy-RBF Least Square Policy Iteration (FRLSPI), tunes the weight parameters of the fuzzy-RBF network (a hybrid model constituted by combining Takagi-Sugeno fuzzy rule inference system with RBF network) online and is acquired through combining Least Squares Policy Iteration (LSPI) with fuzzy-RBF network as a function approximator. In FRLSPI, based on the basis functions defined in the fuzzy-RBF network, a solution has been provided for the challenge of determining the state-action basis functions in LSPI. We also provide positive theoretical results concerning an error bound between the optimal and the approximated Action Value Function (AVF) for FRLSPI. Our proposed method has suitable features such as positive mathematical analysis, learning rate independency and, comparatively good convergence properties. Simulation studies regarding the mountain-car control task and acrobat problem demonstrate the applicability and performance of our learning framework. The overall results indicate that the proposed idea can outperform previously known reinforcement learning algorithms.

In this study, we employ fuzzy Sumudu transform to find the solution for system of linear fuzzy differential equations where the system possesses fuzzy constant coeffcients instead of crisp. For this purpose, fuzzy Sumudu transform has been revisited and a brief comparison with fuzzy Laplace transform is provided alongside, particularly on the scale preserving property. For the sake of comparison, we introduce to the literature a time scaling theorem for fuzzy Laplace transform. Next, the system with fuzzy constant coeffcients is interpreted under the strongly generalized differentiability. From here, new procedures for solving the systems are proposed. A numerical example is then carried out for solving a system adapted from fuzzy radioactive decay model. Conclusion is drawn in the last section and some potential research directions are given.

In this paper, we introduce a new approach to generate a fuzzy norm using a classic norm and a continuous Archimedean t-norm (CATN). Our method involves two steps. First, we utilize a CATN to create a continuous additive generator (CAG). Then, we employ the corresponding additive generator (AG) and a classic norm to generate a fuzzy norm.

Physical dynamical systems can be described through mathematical models using the theory of differential equations. Many different types of uncertain healing occur in the real-world. Fuzzy logic is an effective mathematical tool for defining the sense of non-random uncertainty. Since fuzzy arithmetic differs from its counterparts, it would be more reliable if we use the differential equation to construct models involving uncertain decision parameters. In this paper, we attempt a detailed review of the existing literature related to the theory and application of fuzzy differential equations. The scientific review of this paper includes surveys of the Literature involving different definitions of fuzzy derivation. Distinguished solution approaches and applications of fuzzy differential equations in the fields of science, technology, and management are discussed in this paper. We also provide hints regarding future research challenges and scopes with the theory of fuzzy differential equations. This paper may be impactful documentation of the history of differential equations linking the past, present and future of the concerned research topic.

In this paper, we continue the investigation started in [1]. We obtain new results derived from novel concepts developed in analogy with others already established, e.g., the fact that leftoids (X, ∗) for φ are super-transitive if and only if φ(φ(x)) = φ(x) for all x ∈ X. In addition we apply fuzzy subsets in this context and we derive a number of results as consequences.
 

A hybrid method for the numerical solution of the system of delayed linear fuzzy mixed Volterra- Fredholm integral equations (FMDVFIES) is introduced. Using the hybrid of Bernstein polynomials and block- pulse functions (HBBFs), an approximate solution for the equations system is provided. Firstly, the HBBFs and their operational matrices are introduced, and some of their characteristics are described. Then by applying the operational matrices on FMDVFIES convert it to the algebraic equations system. The numerical solution is obtained by solving this algebraic system. Then the convergence is investigated and some numerical examples are presented to show the eectiveness of the method.

The focus of this work is to study sequences of interactive fuzzy numbers. The interactivity relation is associated with the concept of joint possibility distribution. In this case, the type of interactivity studied is linked to a family of joint possibility distributions (J ), in which the parameter intrinsically models levels of interactivity between the fuzzy numbers involved. Each element of the sequence of interactive fuzzy numbers is obtained through a discrete equation, and the arithmetic operations present in the equation are extended to this type of fuzzy number. Some simulations are performed to illustrate the behavior of the sequences, called interactive, and to compare them with the sequences obtained by other fuzzy arithmetic operations.

In this work, we defne a new sequence denominated by fuzzy Leonardo numbers. Some algebraic properties of this new sequence are studied and several identities are established. Moreover, the relations between the fuzzy Fibonacci and fuzzy Lucas numbers are explored, and several results are given. In addition, some sums involving fuzzy Leonardo numbers are provided.

states are ranked with respect to the best states to work. In [2], states are ranked with respect to the peace and security for women. We determine the fuzzy similarity measure of these to rankings. We find the similarity to be high for one of the measures and very high for the other. We then break the United States into regions and determine the fuzzy similarity measure of these two rankings for each region. The fuzzy similarity here is medium for one measure and high for the other. Similarity plays a role in many fields. There exists many special definitions of similarity which have been used in different areas. We choose to use fuzzy similarity measures which seem appropriate in rankings. In fact, we develop some new measures.