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People who lead hectic lives daily suffer from a variety of illnesses, including diabetes, high blood pressure, hypertension, etc. For someone to survive, they must become aware of these illnesses promptly. The Internet of Things (IoT) and cloud computing are the two critical prerequisites for digital healthcare. In the present research, the attacked data are detected and removed using the security module to enhance the security of the healthcare system. However, an accurate prediction mechanism is needed for the early diagnosis of the diseases. To predict the sickness and its severity more accurately, a unique Dragon Fly-based Generalised Approximate Reasoning Intelligence Control (DF-GARIC) is devised in this article. This system was primarily responsible for preprocessing the cloud medical records entered into the system. Additionally, the regression algorithm extracts the relevant features. Based on the retrieved features, the dragonfly function is used to classify the disease and estimate its severity. Subsequently, a warning is given to the providers for the abnormal condition via SMS or e-mail. The system validated a higher accuracy level of 99.8% from the MATLAB execution. [ABSTRACT FROM AUTHOR]

This study introduces an innovative interval-valued fuzzy inference system (IFIS) integrated with federated learning (FL) to enhance posture detection, with a particular emphasis on fall detection for the elderly. Our methodology significantly advances the accuracy of fall detection systems by addressing key challenges in existing technologies, such as false alarms and data privacy concerns. Through the implementation of FL, our model evolves collaboratively over time while maintaining the confidentiality of individual data, thereby safeguarding user privacy. The application of interval-valued fuzzy sets to manage uncertainty effectively captures the subtle variations in human behavior, leading to a reduction in false positives and an overall increase in system reliability. Furthermore, the rule-based system is thoroughly explained, highlighting its correlation with system performance and the management of data uncertainty, which is crucial in many medical contexts. This research offers a scalable, more accurate, and privacy-preserving solution that holds significant potential for widespread adoption in healthcare and assisted living settings. The impact of our system is substantial, promising to reduce the incidence of fall-related injuries among the elderly, thereby enhancing the standard of care and quality of life. Additionally, our findings pave the way for future advancements in the application of federated learning and fuzzy inference in various fields where privacy and precision in uncertain environments are of paramount importance. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Mahani Mathematical Research Center is the property of Shahid Bahonar University of Kerman, Department of Pure Mathematics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Modelling with fuzzy relations in approximate reasoning is obstructed sometimes by the inconsistency of obtained fuzzy relational equations. This paper tackles the inconsistency resolving problem for a finite system of max–min equations by modifying only the right-hand side vector as slightly as possible with respect to the sum of absolute deviations. It is demonstrated that this problem may be reformulated equivalently as a polynomial-sized mixed integer linear programming problem. Although such a reformulation results in a problem of much larger size than its original compact form, it may be solved to optimality on instances of moderate size or even large size by an off-the-shelf solver for mixed integer linear programming and in some sense does not require a tailored solving method. [ABSTRACT FROM AUTHOR]

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The management of time is essential in most AI-related applications. In addition, we know that temporal information is often not precise. In fact, in most cases, it is necessary to deal with imprecision and/or uncertainty. On the other hand, there is the need to handle the implicit common-sense information present in many temporal statements. In this paper, we present FTCProlog, a logic programming language capable of handling fuzzy temporal constraints soundly and efficiently. The main difference of FTCProlog with respect to its predecessor, PROLogic, is its ability to associate a certainty index with deductions obtained through SLD-resolution. This resolution is based on a proposal within the theoretical logical framework FTCLogic. This model integrates a first-order logic based on possibilistic logic with the Fuzzy Temporal Constraint Networks (FTCNs) that allow efficient time management. The calculation of the certainty index can be useful in applications where one wants to verify the extent to which the times elapsed between certain events follow a given temporal pattern. In this paper, we demonstrate that the calculation of this index respects the properties of the theoretical model regarding its semantics. FTCProlog is implemented in Haskell. [ABSTRACT FROM AUTHOR]

The document "Advances in Uncertain Information Fusion" published in the journal Entropy discusses the importance of information fusion in drawing accurate inferences from multiple sources. It explores various theories, such as Dempster–Shafer evidence theory, fuzzy set theory, possibility theory, and classical Bayesian theory, for handling uncertain information. The document features six articles that delve into measuring uncertainty in negation evidence, correlation between belief functions, membership function assignment, autonomous search for targets, multi-modal fusion for emotion recognition, and combining segmentation models for improved performance. The conclusion highlights the significance of representing and qualifying uncertainty in next-generation information fusion systems, emphasizing the integration of classical approximate reasoning theories with advanced deep learning models for future developments. [Extracted from the article]

The development of mathematical reasoning skills has increasingly been of focus for the teaching and learning of mathematics. This research utilizes a teaching simulation using the methodology of scriptwriting, in which prospective teachers are asked to complete a script of a dialogue from a classroom simulation involving fraction multiplication and division with justification, assisting fictional students to work through their difficulties and helping them to justify their reasoning. Such tasks allow for the examination of the prospective teacher moves to support student reasoning through their imagined action and choice of words. Scripts from forty-one prospective primary teachers were examined for the study, and five clusters based on the type of teacher move for supporting student reasoning were found. Overall, the prospective teachers emphasized the elicitation and facilitation of students' ideas. The cluster analysis, however, provided a nuanced examination of the cohort's teacher moves. While cluster one saw the highest incident of eliciting teacher moves, albeit only in the low potential category, clusters two and three mostly used facilitating teacher moves, but varied in their use of high and low potential moves. Cluster four concentrated moves on facilitating, eliciting, and responding to student reasoning. Cluster five employed teacher moves from all main categories, with some instances of high potential moves in all categories except extending student reasoning, which can better support reasoning. The prospective mathematics teachers' scripts and the five clusters that were found during analysis are discussed with implications for future teacher education and the support of building mathematical reasoning. [ABSTRACT FROM AUTHOR]

Rough sets are used in numerous knowledge representation contexts and are then empowered with varied ontologies. These may be intrinsically associated with ideas of rationality under certain conditions. In recent papers, specific granular generalisations of graded and variable precision rough sets are investigated by the present author from the perspective of rationality of approximations (and the associated semantics of rationality in approximate reasoning). The studies are extended to ideal-based approximations (sometimes referred to as subsethood-based approximations). It is additionally shown that co-granular or point-wise approximations defined by σ-ideals/filters (for an arbitrary relation σ) fit easily into the entire scheme. Concepts of the rationality of objects (vague or crisp) and their types are introduced and are shown to be applicable to most general rough sets by the present author. Surprising results on these are proved on these by her in this part of the research paper. The present paper is the first of a three part study on the topic. [ABSTRACT FROM AUTHOR]

We consider a normal autonomous system of differential equations with a small parameter, which has a critical linear approximation at zero value of the parameter. We introduce the concept of orbital stability with respect to the parameter; according to this concept, the closeness of the right semitrajectories is achieved not only due to the proximity of initial values of solutions, but also due to the smallness of the parameter. We examine the problem of branching of a stable periodic solution with a period close to the period of solutions of the corresponding linear homogeneous system. Sufficient conditions for the solvability of the problem are established. Our reasonings are based on the properties of the first homogeneous nonlinear approximation of the monodromy operator. [ABSTRACT FROM AUTHOR]

We investigate the combined planning problem involving the routing of technicians and the stocking of spare parts for servicing geographically distributed repair tasks. The problem incorporates many operational uncertainties, such as future repair requests and the required spare parts to replace malfunctioned components. We model the problem as a sequential decision problem where decisions are made at the end of each day about the next day's technician route and spare part inventory in the van. We show that exact methods are intractable because of the inherent high-dimensional state, decision, and transition spaces involved. To overcome these challenges, we present two novel algorithmic techniques. First, we suggest a hybrid value function approximation method that combines a genetic search with a graph neural network capable of reasoning, learning, and decision making in high-dimensional, discrete decision spaces. Second, we introduce a unique state-encoding method that employs multiattribute graphs and spatial markers, eliminating the need for manually designed basis functions and allowing efficient learning. We illustrate the general adaptive learning capacity by solving a variety of instance settings without instance-specific hyperparameter tuning. An extensive numerical study demonstrates that our hybrid learning technique outperforms other benchmark policies and adapts well to changes in the environment. We also generate a wide range of insights that not only shed light on the algorithmic components but also offer guidance on how to execute on-site repair tasks more efficiently. The techniques showcased are versatile and hold potential for application in other dynamic and stochastic problems, particularly in the realm of transportation planning. Funding: This work was supported by Deutsche Forschungsgemeinschaft (DFG). The Research Training Group 2201 [Grant 277991500], "Advanced Optimization in a Networked Economy," funded by the DFG, has provided partial support for this work. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0434. [ABSTRACT FROM AUTHOR]

Some theories of rational belief assume that beliefs should be closed under conjunction. I motivate the rejection of the conjunction closure, and point out that the consequences of this rejection are not as severe as it is usually thought. An often raised objection is that without the conjunction closure people are unable to reason. I outline an approach in which we can – in usual cases – reason using conjunctions without accepting the closure in its whole generality. This solution is based on the notion of confidence levels , which can be defined using probabilities. Moreover, on this approach, reasoning has a scalable computational complexity adaptable to cognitive abilities of both rationally bounded and perfectly rational agents. I perform a simulation to assess its error rate, and compare it to reasoning with conjunction closure. [ABSTRACT FROM AUTHOR]

The generalized hypothetical syllogism (GHS) is an important property of fuzzy implications for its applications in approximate reasoning. Due to the complexity of the (GHS) and the variety of fuzzy implications, in this work, we study the (GHS) property with respect to a strict t-norm T for fuzzy implications which come from some well known families of fuzzy implications, viz., (S,N)-, QL-, g-, (U,N)-, (T,N)-implications. First, some results on the (GHS) for fuzzy implications are presented. Second, the (GHS) property of (S,N)-, QL-, g-, (U,N)-, and (T,N)-implications is studied. Finally, the (GHS) property for the fuzzy implications generated from old ones using the method of sup-T composition is also studied. [ABSTRACT FROM AUTHOR]

AI stands at the forefront of transforming global industries, achieving remarkable progress in recent years, largely driven by advanced deep learning techniques adept at processing extensive datasets. However, a crucial question arises when confronted with limited and ambiguously characterised data for a novel problem: Can AI maintain its effectiveness under such constraints? This paper delves into addressing this query, emphasising the role of Fuzzy Rule Interpolation (FRI) in enabling approximate reasoning amidst sparse or incomplete knowledge. This becomes particularly significant when traditional rule based inference mechanisms struggle due to misalignment with observations. Extensive research into FRI techniques within computational intelligence has yielded various methodologies. The focus of this paper centres on a notable subset, Transformationbased FRI (T-FRI). T-FRI operates by mathematically adjusting rules that share similarities with unmatched observations, utilising linear transformations of the nearest rules chosen automatically relative to an unmatched observation. Examples are included to showcase the successful applications of T-FRI in tackling challenging real-world problems. [ABSTRACT FROM AUTHOR]

In order to solve the problem of emergency decision-making with incomplete information and deal with the accident information in different time series at the scenes of major accidents, this paper proposes a method of sequential decision-making by utilizing the relevant knowledge of D-S evidence theory and game theory. Firstly, we took an oil tank fire accident as an example and sorted out historical cases and expert experiences to establish a logical relationship between key accident scenes and accident scene symptoms in the accident. Meanwhile, we applied the logistic regression analysis method to obtain the basic probability distribution of each key accident scene in the oil tank fire, and on this basis, we constructed an evidence set of the fire. Secondly, based on the D-S evidence theory, we effectively quantified the knowledge uncertainty and evidence uncertainty, with the incomplete and insufficient information taken as an evidence system of the development of key accident scenes to construct a situation prediction model of these accident scenes. Thirdly, based on the game theory, we viewed emergency decision-makers and major accidents as two sides of the game to compare and analyze accident states at different time points and solve the contradiction between loss costs of decision-making and information collection costs. Therefore, this paper has provided a solution for the optimization of accident schemes at different time stages, thus realizing the sequential decision-making at the scenes of major accidents. Furthermore, we combined the situation prediction model with sequential decision-making, with the basic steps described below: (1) We drew up an initial action plan in the case of an extreme lack of information; then, we (2) started to address the accident and constructed a framework of accident identification, (3) collected and dealt with the continuously added evidence information with the evolution of the accident, (4) calculated the confidence levels of key accident scenarios after evaluating different evidence and then predicted the accident state in the next stage, and (5) calculated the profit–loss ratio between the current decision-making scheme and the decision-making scheme of the next stage. Finally, we (6) repeated steps (3) to (5) until the accident completely vanished. We verified the feasibility of the proposed method with the explosion accident of the Zhangzhou P.X. project in Fujian on 6 April used as an example. Based on the D-S evidence theory, this method employs approximate reasoning on the incomplete and insufficient information obtained at the scenes of major accidents, thus realizing the situation prediction of key scenes of these accidents. Additionally, this method uses the game theory to solve the contradiction between decision-making loss costs and information collection costs, thus optimizing the decision-making schemes at different time stages of major accidents. [ABSTRACT FROM AUTHOR]

The concept of Z-number was introduced by Zadeh in order to deal with partial reliability of information. This concept describes a fusion of fuzzy and probabilistic types of uncertainty. In turn, one of the main fields of dealing with imperfect information is approximate reasoning. For the case of pure fuzzy information this field is well-developed. In contrast, existing studies on reasoning with Z-valued “if-then” rules are scarce. One of the main reasons is high analytical and computational complexity. In this work, we develop an approach to reasoning with such kind of rules. The original approach proposed here allows to deal with sparse rule base and is characterized by relatively low computational complexity. The new concept of similarity of Z-numbers based on Jaccard similarity index and measure of divergence of probability distributions is introduced. Based on similarity degrees of current input Z-numbers and Z-numbers located in rule antecedents, weights of linear combination of Z-numbers in rule consequents are determined. The linear combination is based on operations with Z-numbers proposed by authors. Applications of the proposed approach to evaluation of economic development level for a country and control problem are considered. [ABSTRACT FROM AUTHOR]

Spherical fuzzy sets are more powerful in modelling the uncertain situations than picture fuzzy sets, fermatean fuzzy sets, Pythagorean fuzzy sets, intuitionistic fuzzy sets, and fuzzy sets. In this paper, we first define the variance and covariance of spherical fuzzy sets. Then, using variance and covariance, we define the unique spherical fuzzy set correlation metric in line with the statistical coefficient of correlation. Two spherical fuzzy sets are correlated in both direction and strength using the provided measure of correlation. We discussed its many characteristics. We compared the measure of correlation with the current ones through linguistic variables. We established its validity by showing its application in bidirectional approximate reasoning. We also resolve a pattern identification issue in the spherical fuzzy environment using the provided correlation function, and we compare the results with several current measurements. [ABSTRACT FROM AUTHOR]

Abstract In this research, fuzzy linear regression (FLR) method combined with three well-known fuzzy implications was implemented for evaluating the relation among the amount of fly ash in concrete mixture and the compressive strength of concrete. More specifically, 267 experimental data 40 of which were used for testing the validation of the process were subjected to FLR method for calculating the truth values, which indicated the degree of how the experimental outputs belong to the predicted ones. Also, the degree of fuzziness was calculated for performing the sensitivity analysis of the model. The truth values that emerged were used for applying three basic fuzzy implications such as Lukasiewicz, Reinchenbach, and Kleene-Dienes implication. By evaluating and comparing the results of every fuzzy implication, it was concluded that Lukasiewicz was the most appropriate implication method as it yielded the smallest deviation of truth values (σ = 4.00) in contrast to the theoretical ones (σ = 4.83 in Reinchenbach and σ = 12.31 in Kleene-Dienes fuzzy implication). The accuracy of the FLR method was also validated for calculating the coefficient of the mean absolute percentage error level (MAPE = 5.56%) of the blind prediction process, and the results revealed that the application of fuzzy linear regression method is suitable for evaluating the truth values of experimental data in order to be used in fuzzy implications. Thus, it is a satisfactory procedure for making inferences between concrete parameters.

In this paper, a novel Z-number based Fuzzy Neural Network (Z-FNN) based on the integration of Z-valued fuzzy logic and neural networks is proposed. Z-valued fuzzy rule base is presented and its inference process is described using interpolative approximate reasoning. Accordingly, the structure of the Z-FNN is proposed using a distance measure and interpolative approximate reasoning scheme. Based on presented architecture the learning algorithm of Z-FNN is designed. The updating of the unknown parameters of the network is carried out using Genetic Algorithms (GA). The proposed Z-FNN system is utilized for dynamic plant identification. The effectiveness of Z-FNN has been tested by comparing its performance with the performances of other fuzzy systems available in the literature. The proposed approach has been proven to be a suitable alternative for the identification of nonlinear systems characterized by uncertain and imprecise information. [ABSTRACT FROM AUTHOR]

The Boiti–Leon–Mana–Pempinelli Equation (BLMPE) is an essential mathematical model describing wave propagation in incompressible fluid dynamics. In the present manuscript, a novel generalization of the BLMPE is introduced, called herein the functional BLMPE (F-BLMPE), which involves different functions, including exponential, logarithmic and monomaniacal functions. In these cases, the F-BLMPE reduces to an explicit form in the dependent variable. In addition to this, it is worth deriving approximate similarity solutions of the F-BLMPE with constant coefficients using the extended unified method (EUM). In this method, nonlinear partial differential equation (NLPDE) solutions are expressed in polynomial and rational forms through an auxiliary function (AF) with adequate auxiliary equations. Exact solutions are estimated using formal solutions substituted into the NLPDEs, and the coefficients of the AF of all powers are set equal to zero. This approach is valid when the NLPDE is integrable. However, this technique is not valid for non-integrable equations, and only approximate solutions can be found. The maximum error can be controlled by an adequate choice of the parameters in the residue terms (RTs). Multiple similarity solutions are derived, and the ME is depicted in various examples within this work. The results found here confirm that the EUM is an efficient method for solving NLPDEs of the F-BLMPE type. [ABSTRACT FROM AUTHOR]

We give a formalism for approximate isomorphism in continuous logic simultaneously generalizing those of two papers by Ben Yaacov [2] and by Ben Yaacov, Doucha, Nies, and Tsankov [6], which are largely incompatible. With this we explicitly exhibit Scott sentences for the perturbation systems of the former paper, such as the Banach‐Mazur distance and the Lipschitz distance between metric spaces. Our formalism is simultaneously characterized syntactically by a mild generalization of perturbation systems and semantically by certain elementary classes of two‐sorted structures that witness approximate isomorphism. As an application, we show that the theory of any R$\mathbb {R}$‐tree or ultrametric space of finite radius is stable, improving a result of Carlisle and Henson [8]. [ABSTRACT FROM AUTHOR]

Ontological reasoning has great prospects in applications based on domain-specific knowledge graphs (KG). However, it is difficult for existing logic reasoners to quickly perform inference over large-scale assertional boxes (ABoxes) in domain-specific KGs with complex ontologies. To address this challenge, a novel method named the "neural-symbolic ontological reasoner" is proposed. By incorporating neural-symbolic learning into ABox reasoning, a reasoner named the TimGangReasoner (TGR) is built. The TGR synthesizes graph data using an ontology, trains an ABox reasoning network (ABRN) model, and then approximately compiles the logic reasoning process of the ontology (represented by OWL+SWRL) into neural networks (NNs). The ABRN model encodes instances into vectors and then executes parallel vector computations to accelerate ABox reasoning. Experiments conducted on three open-source complex ontologies show that the TGR can achieve high-quality approximate deductive reasoning on ABoxes. The reasoning time consumption of the TGR increases linearly with the increase in the number of assertions, providing better scalability for large-scale ABoxes. Therefore, the TGR is able to reason quickly and accurately on domain-specific KGs that have complex underlying ontologies and contain large-scale ABoxes. [ABSTRACT FROM AUTHOR]

Causal reasoning is an aspect of learning, reasoning, and decision-making that involves the cognitive ability to discover relationships between causal relata, learn and understand these causal relationships, and make use of this causal knowledge in prediction, explanation, decision-making, and reasoning in terms of counterfactuals. Can we fully automate causal reasoning? One might feel inclined, on the basis of certain groundbreaking advances in causal epistemology, to reply in the affirmative. The aim of this paper is to demonstrate that one still has good skeptical grounds for resisting any conclusions in favour of the automation of causal reasoning. If by causal reasoning is meant the entirety of the process through which we discover causal relationships and make use of this knowledge in prediction, explanation, decision-making, and reasoning in terms of counterfactuals, then one relies besides on tacit knowledge, as might be constituted by or derived from the epistemic faculty virtues and abilities of the causal reasoner, the value systems and character traits of the causal reasoner, the implicit knowledge base available to the causal reasoner, and the habits that sustain our causal reasoning practices. While certain aspects of causal reasoning may be axiomatized and formalized and algorithms may be implemented to approximate causal reasoning, one has to remain skeptical about whether causal reasoning may be fully automated. This demonstration will involve an engagement with Meno's Paradox. [ABSTRACT FROM AUTHOR]

The representations of deep convolutional neural networks (CNNs) are formed from generalizing similarities and abstracting from differences in the manner of the empiricist theory of abstraction (Buckner, Synthese 195:5339–5372, 2018). The empiricist theory of abstraction is well understood to entail infinite regress and circularity in content constitution (Husserl, Logical Investigations. Routledge, 2001). This paper argues these entailments hold a fortiori for deep CNNs. Two theses result: deep CNNs require supplementation by Quine's "apparatus of identity and quantification" in order to (1) achieve concepts, and (2) represent objects, as opposed to "half-entities" corresponding to similarity amalgams (Quine, Quintessence, Cambridge, 2004, p. 107). Similarity amalgams are also called "approximate meaning[s]" (Marcus & Davis, Rebooting AI, Pantheon, 2019, p. 132). Although Husserl inferred the "complete abandonment of the empiricist theory of abstraction" (a fortiori deep CNNs) due to the infinite regress and circularity arguments examined in this paper, I argue that the statistical learning of deep CNNs may be incorporated into a Fodorian hybrid account that supports Quine's "sortal predicates, negation, plurals, identity, pronouns, and quantifiers" which are representationally necessary to overcome the regress/circularity in content constitution and achieve objective (as opposed to similarity-subjective) representation (Burge, Origins of Objectivity. Oxford, 2010, p. 238). I base myself initially on Yoshimi's (New Frontiers in Psychology, 2011) attempt to explain Husserlian phenomenology with neural networks but depart from him due to the arguments and consequently propose a two-system view which converges with Weiskopf's proposal ("Observational Concepts." The Conceptual Mind. MIT, 2015. 223–248). [ABSTRACT FROM AUTHOR]

Since isosceles triangular and trapezoidal membership functions [4] are easy to manage, they were applied to various fuzzy approximate reasoning [10], [13], [14]. The centroids of isosceles triangular and trapezoidal membership functions are mentioned in this article [16], [9] and formalized in [11] and [12]. Some propositions of the composition mapping (f + · g, or f +* g using Mizar formalism, where f, g are a ne mappings), are proved following [3], [15]. Then different notations for the same isosceles triangular and trapezoidal membership function are formalized. We proved the agreement of the same function expressed with different parameters and formalized those centroids with parameters. In addition, various properties of membership functions on intervals where the endpoints of the domain are fixed and on general intervals are formalized in Mizar [1], [2]. Our formal development contains also some numerical results which can be potentially useful to encode either fuzzy numbers [7], or even fuzzy implications [5], [6] and extends the possibility of building hybrid rough-fuzzy approach in the future [8]. [ABSTRACT FROM AUTHOR]

Now a days, electric power infrastructure is an essential section of the world due to the increase in power demand and industrialization. The smart grid is also one of the profoundly evolved innovations, which influences the synchronization between demand and renewable energy reactions. The smart grids contain many operations with power calculations such as smart functions, assurance, and control techniques to provide steadiness and proficiency to the system performance. However, the quality of power such as voltage deviation minimization, sag/swell, power loss minimization, and Total Harmonic Distortion (THD) appear to be the major issue. Therefore, in this paper, a novel Generalized Approximate Reasoning Intelligent Control along with Multi-objective African Buffalo Optimization is proposed to control the imperatives of the smart grid. In the grid, current controllers are upgraded by the proposed Optimal Pseudospectral Bang Bang Control technique, and voltage controllers are improved by the proposed Bessel Filter Sallen Key Topology. The simulation of the proposed method is actualized with MATLAB/Simulink. Consequently, the projected results are compared with the traditional control techniques and the outcomes show that the projected replica improved system efficiency concerning power quality problems in terms of reduced 14 MW of power loss and 2.18% of THD. [ABSTRACT FROM AUTHOR]

In this research, fuzzy linear regression (FLR) method combined with three well-known fuzzy implications was implemented for evaluating the relation among the amount of fly ash in concrete mixture and the compressive strength of concrete. More specifically, 267 experimental data 40 of which were used for testing the validation of the process were subjected to FLR method for calculating the truth values, which indicated the degree of how the experimental outputs belong to the predicted ones. Also, the degree of fuzziness was calculated for performing the sensitivity analysis of the model. The truth values that emerged were used for applying three basic fuzzy implications such as Lukasiewicz, Reinchenbach, and Kleene-Dienes implication. By evaluating and comparing the results of every fuzzy implication, it was concluded that Lukasiewicz was the most appropriate implication method as it yielded the smallest deviation of truth values (σ = 4.00) in contrast to the theoretical ones (σ = 4.83 in Reinchenbach and σ = 12.31 in Kleene-Dienes fuzzy implication). The accuracy of the FLR method was also validated for calculating the coefficient of the mean absolute percentage error level (MAPE = 5.56%) of the blind prediction process, and the results revealed that the application of fuzzy linear regression method is suitable for evaluating the truth values of experimental data in order to be used in fuzzy implications. Thus, it is a satisfactory procedure for making inferences between concrete parameters. [ABSTRACT FROM AUTHOR]

Recently, Jiang, H. B., and B. Q. Hu. [2022. "On (O,G)-Fuzzy Rough Sets Based on Overlap and Grouping Functions Over Complete Lattices." International Journal of Approximate Reasoning 144: 18–50. doi:10.1016/j.ijar.2022.01.012] constructed a (G , O) -fuzzy rough set model with the logical connectives–a grouping function G and an overlap function O on a complete lattice, which provided a new constructive approach to fuzzy rough set theory. The axiomatic approach is as important as the constructive approach in rough set theory. In this paper, we continue to study axiomatic characterizations of (G , O) -fuzzy rough set. Traditionally, the associativity of the logical connectives plays a vital role in the axiomatic research of existing fuzzy rough set models. However, a grouping function G and an overlap function O lack the associativity. So we explore a novel axiomatic approach to O -upper and G -lower fuzzy rough approximation operators without associativity. Further, we provide single axioms to characterize O -upper and G -lower fuzzy rough approximation operators instead of sets of axioms. Finally, we use single axioms to characterize fuzzy rough approximation operators generated by various kinds of fuzzy relations including serial, reflexive, symmetric, G -transitive, O -transitive fuzzy relations as well as their compositions. [ABSTRACT FROM AUTHOR]

Fuzzy rule interpolation (FRI) offers a reliable approach for providing an interpretable approximate decision with a sparse rule base, when a new observation does not match any existing rules. As the mainstream application of a fuzzy rule base is to extract valuable approximate information from each individual rules, existing FRI methods typically work by postulating that the more rules used to implement the interpolation the better the reasoning outcomes. Yet, empirical results have shown that using a large number of rules in an FRI process may adversely lead to worsening the accuracy of the inference outcomes, not just degrading efficiency. The objective of this work is to set a firm theoretical foundation for the eventual establishment of a novel FRI approach. It achieves this goal by mapping the structural patterns within a given fuzzy rule base onto a mathematically isomorphic data space, such that the essential information embedded in the original rule base can be effectively captured, represented and analysed. The resulting mathematically mapped patterns enable the production of a theorem that determines the upper limit of the number of rules required to effectively and efficiently perform FRI. The experimental investigations reported herein demonstrate that the number of required rules to perform FRI obeys the theorem discovered in this work. [ABSTRACT FROM AUTHOR]

In recent times, the modern power system has become more complex because of high penetration of generation power, heavy load changes, voltage fluctuation, high reactive power, and environmental and economic problems. These problems can cause voltage disintegration issues in the power system. Thus, the voltage stability in the system should be predicted and required to improve the stable conditions. However, the earlier investigations do not significantly improve the coordination's voltage stability. For this reason, in this research, a novel generalized approximate reasoning based intelligent control based unified voltage collapse proximity indicator is proposed for calculating the system's weak buses voltage. Moreover, the African buffalo optimization is proposed to estimate the finest location of unified power flow controller based flexible alternative current transmission system devices in the scheme for voltage strength enrichment. The implementation of these proposed approaches is done via MATLAB/Simulink. The projected system has been experienced on IEEE 118 and IEEE 30 bus systems. Consequently, the simulation outcome indicates that the proposed methods effectively predict and upgrade the voltage stability index. The results are compared with the conventional models concerning cost, real power loss, and computational time. The proposed system attained real power for IEEE 118 bus is 4.5502 MW and IEEE 30 bus for 4.902 MW, which is very low compared with the existing methods. [ABSTRACT FROM AUTHOR]

Binary relations, coverings and neighborhood systems/operators are useful tools to study fuzzy rough set theory. In this paper, we use the notion of real-valued hemimetric, a weak version of the standard metric, as the basic structure to define and study fuzzy rough sets by using the usual addition and subtraction of real numbers. We define a pair of fuzzy upper and lower rough approximation operators and investigate their properties and interrelations. These two operators have nice logical descriptions by using the Lukasiewicz logical system. It is shown that upper definable fuzzy subsets, lower definable fuzzy subsets and Lipschitz fuzzy subsets are the same thing in this model. Definable fuzzy subsets are exactly the upper sets with respect to the induced fuzzy preorder, which form a stratified Alexandrov fuzzy topology. A comparison between hemimetric-based fuzzy rough sets and fuzzy preorder-based fuzzy rough sets has been made. Results show that the former can be considered as a real-valued extension of the latter. At the end, an application of the hemimetric-based rough set model to contour extraction of digital surfaces is proposed. [ABSTRACT FROM AUTHOR]

Failure mode and effects analysis (FMEA) is a proactive risk management approach. Risk management under uncertainty with the FMEA method has attracted a lot of attention. The Dempster–Shafer (D-S) evidence theory is a popular approximate reasoning theory for addressing uncertain information and it can be adopted in FMEA for uncertain information processing because of its flexibility and superiority in coping with uncertain and subjective assessments. The assessments coming from FMEA experts may include highly conflicting evidence for information fusion in the framework of D-S evidence theory. Therefore, in this paper, we propose an improved FMEA method based on the Gaussian model and D-S evidence theory to handle the subjective assessments of FMEA experts and apply it to deal with FMEA in the air system of an aero turbofan engine. First, we define three kinds of generalized scaling by Gaussian distribution characteristics to deal with potential highly conflicting evidence in the assessments. Then, we fuse expert assessments with the Dempster combination rule. Finally, we obtain the risk priority number to rank the risk level of the FMEA items. The experimental results show that the method is effective and reasonable in dealing with risk analysis in the air system of an aero turbofan engine. [ABSTRACT FROM AUTHOR]

In the (1 + ε , r) -approximate near-neighbor problem for curves (ANNC) under some similarity measure δ , the goal is to construct a data structure for a given set C of curves that supports approximate near-neighbor queries: Given a query curve Q, if there exists a curve C ∈ C such that δ (Q , C) ≤ r , then return a curve C ′ ∈ C with δ (Q , C ′) ≤ (1 + ε) r . There exists an efficient reduction from the (1 + ε) -approximate nearest-neighbor problem to ANNC, where in the former problem the answer to a query is a curve C ∈ C with δ (Q , C) ≤ (1 + ε) · δ (Q , C ∗) , where C ∗ is the curve of C most similar to Q. Given a set C of n curves, each consisting of m points in d dimensions, we construct a data structure for ANNC that uses n · O (1 ε) md storage space and has O(md) query time (for a query curve of length m), where the similarity measure between two curves is their discrete Fréchet or dynamic time warping distance. Our method is simple to implement, deterministic, and results in an exponential improvement in both query time and storage space compared to all previous bounds. Further, we also consider the asymmetric version of ANNC, where the length of the query curves is k ≪ m , and obtain essentially the same storage and query bounds as above, except that m is replaced by k. Finally, we apply our method to a version of approximate range counting for curves and achieve similar bounds. [ABSTRACT FROM AUTHOR]

This article proposes a new methodology of unsupervised event prediction from videos. Detecting events from videos without prior information is a challenging task, as there are no well-accepted definitions about events in a video. It is commonly known that the presence of moving elements in a video scene could be considered as part of an event. The possibility of an event occurring becomes higher if there is an abrupt change in the motion patterns of different object(s) present in that video scene. In this paper, we defined a method to model this phenomenon of object motion. Since we have not considered any prior information while modeling it, the initial event and nonevent classification is carried out with rough set-based approximations, namely positive, boundary, and negative, in the incomplete knowledge base, resulting in an event-nonevent rough sets. We generate three regions with rough sets. Negative class labels are assigned for static objects and those moving with predictable paths. The objects with a huge change in motion are labeled to be positive events. The remaining objects are kept in the boundary region. However, if there is a gradual change in the motion pattern, there arises some possibility of an event occurring. To define the terms, like possible events and must be event, we have fuzzified the boundary region of event-nonevent rough set and assigned different degrees of possibility of an event to occur if there is a change in motion patterns in the trajectory of the objects. That is, the event, nonevent regions are classified with rough sets, and the boundary region is fuzzified with fuzzy sets. We have validated this newly defined event-nonevent rough-fuzzy sets with experimental demonstrations where the proposed method successfully predicted the events to occur in video sequences. [ABSTRACT FROM AUTHOR]

In fuzzy logic, most of the implication operators are based on generalizations of the classical, material implication. That is, these implications are defined as the disjunction of the negated value of the first argument and the value of the second argument, while the underlying disjunction operators are associative triangular conorms. In our study, we concentrate on how a class of implication operators, called the preference implication operators, can be used in approximate reasoning. Using this implication operator family, we present a novel, Modus Ponens-like approximate reasoning method, in which we have two premises: (1) a statement and (2) a preference implication with an antecedent of this statement. Here, we show how the continuous logical value of the consequent of the preference implication can be derived from the continuous logical values of the premises. We point out that this novel approximate reasoning method is strongly connected with the so-called aggregative operator, which is a representable uninorm. Next, we also present a threshold value-based generalization of the Modus Ponens syllogism and demonstrate that the Modus Tollens syllogism can be generalized in the same way. Lastly, we provide an illustrative example. [ABSTRACT FROM AUTHOR]

The relevance of polynomial classes of formulas to deductive efficiency motivated their further research, and currently, a great number of such classes is known. Nevertheless, they have been exclusively sought in the setting of propositional logic and clausal form, which is of course expressively limiting for real-world applications. Along these lines and towards making tractability applicable beyond propositional clausal logic, firstly, we define the R egular many-valued H orn Non-Clausal (NC) class, or RH , obtained by suitably amalgamating both regular classes: Horn and NC. Then we show that recognizing whether any NC formula is Horn-NC takes only linear time. Secondly, we demonstrate that the relationship between RH and: (1) its subclass of regular Horn formulas is that syntactically RH subsumes the Horn class but semantically both classes are equivalent; and (2) its superclass of regular non-clausal formulas is that RH contains all non-clausal formulas whose clausal form is Horn. Thirdly, we define Regular Non-Clausal Unit-Resolution, or RU R NC , and prove that RU R NC is complete for RH and also checks its satisfiability in polynomial time. Altogether, RH is a class recognized and solved polynomially, which shows that our intended goal is reached since RH is many-valued, non-clausal and tractable. Fourthly, based on RH , we characterize extensive classes of Horn-NC-like formulas, super-classes of RH , which are composed of formulas that are logically equivalent to some formula in RH. We furnish syntactical patterns of such Horn-NC-like formulas, being outside RH and whose satisfiability test is also decidable in polynomial time. As RH and RU R NC are, both, basic in the DPLL scheme, the most efficient in propositional logic, and can be extended to some other non-classical logics, we argue that they pave the way for efficient non-clausal DPLL-based approximate reasoning. Field: Tractable Approximate Automated Reasoning. [ABSTRACT FROM AUTHOR]

The map-based localization method is considered an effective supplement to the localization under the GNSS-denied environment. However, since the map is constituted by the dispersed keyframes, it sometimes happens that the initial position of the unmanned ground vehicle (UGV) lies between the map keyframes or is not on the mapping trajectory. In both cases, it will be impossible to precisely estimate the pose of the vehicle directly via the relationship between the current frame and the map keyframes, leading to localization failure. In this regard, we propose a localization algorithm based on the global descriptor and dynamic range search (LA-GDADRS). In specific, we first design a global descriptor shift and rotation invariant image (SRI), which improves the rotation invariance and shift invariance by the methods of coordinates removal and de-centralization. Secondly, we design a global localization algorithm for shift and rotation invariant branch-and-bound scan matching (SRI-BBS). It first leverages SRI to obtain an approximate priori position of the unmanned vehicle and then utilizes the similarity between the current frame SRI and the map keyframes SRI to select a dynamic search range around the priori position. Within the search range, we leverage the branch-and-bound scanning matching algorithm to search for a more precise pose. It solves the problem that global localization tends to fail when the priori position is imprecise. Moreover, we introduce a tightly coupled factor graph model and a HD map engine to achieve real-time position tracking and lane-level localization, respectively. Finally, we complete extensive ablation experiments and comparative experiments to validate our methods on the benchmark dataset (KITTI) and the real application scenarios at the campus. Extensive experimental results demonstrate that our algorithm achieves the performance of mainstream localization algorithms. [ABSTRACT FROM AUTHOR]

Let L be a commutative unital quantale. For every L-fuzzy relation E on a nonempty set X, we define an upper rough approximation operator on LX, which is a fuzzy extension of the classical Pawlak upper rough approximation operator. We show that this operator has close relation with the subsethood operator on X. Conversely, by an L-fuzzy closure operator on X, we can easily get an L-fuzzy relation. We show that this relation can be characterized by more smooth ways. Without the help of the lower approximation operator, L-fuzzy rough sets can still be studied by means of constructive and axiomatic approaches, and L-fuzzy similarities and L-fuzzy closure operators are one-to-one corresponding. We also show that, the L-topology induced by the upper rough approximation operator is stratified and Alexandrov. [ABSTRACT FROM AUTHOR]