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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.)

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]

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]

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]

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.

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]

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]

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]

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]

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]

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]

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]

The ontology knowledge base (KB) can be divided into two parts: TBox and ABox, where the former models schema-level knowledge within the domain, and the latter is a set of statements of assertions or facts about instances. ABox reasoning is a process of discovering implicit knowledge in ABox based on the existing KB, which is of great value in KB applications. ABox reasoning is influenced by both the complexity of TBox and scale of ABox. The traditional logic-based ontology reasoning methods are usually designed to be provably sound and complete but suffer from long algorithm runtimes and do not scale well for ontology KB represented by OWL DL (Description Logic). In some application scenarios, the soundness and completeness of reasoning results are not the key constraints, and it is acceptable to sacrifice them in exchange for the improvement of reasoning efficiency to some extent. Based on this view, an approximate reasoning method for large-scale ABox in OWL DL KBs was proposed, which is named the ChunfyReasoner (CFR). The CFR introduces neural-symbolic learning into ABox reasoning and integrates the advantages of symbolic systems and neural networks (NNs). By training the NN model, the CFR approximately compiles the logic deduction process of ontology reasoning, which can greatly improve the reasoning speed while ensuring higher reasoning quality. In this paper, we state the basic idea, framework, and construction process of the CFR in detail, and we conduct experiments on two open-source ontologies built on OWL DL. The experimental results verify the effectiveness of our method and show that the CFR can support the applications of large-scale ABox reasoning of OWL DL KBs. [ABSTRACT FROM AUTHOR]

Grouping functions, as one new case of not necessarily associative particular binary aggregation functions, have been proposed in the literature for their vast applications in fuzzy community detection problems, image processing and decision making. On the other hand, due to the wide applications in fuzzy reasoning, fuzzy control and approximate reasoning, the investigations of fuzzy implications derived from specific binary aggregation functions become a natural and hot research topic. In this paper, we focus on this research area and consider the ℐ , -implications induced from quasi-grouping functions and negations on bounded lattices. To be precise, firstly, by removing the continuity condition, we extend the notion of grouping functions on the unit closed interval to the so-called quasi-grouping functions on bounded lattices. Secondly, we give some basic properties and two construction methods of quasi-grouping functions on bounded lattices. Finally, we give the concept of ℐ , -implications and focus on the conditions under which they can satisfy the certain algebraic properties possessed by implications on bounded lattices. [ABSTRACT FROM AUTHOR]

This paper proposes a novel approach suitable to design energy-efficient approximate multipliers using both ASIC and FPGAs. The new strategy harnesses specific encoding logics based on bit significance and computes the approximate product performing accurate sub-multiplications by applying an unconventional approach instead of using approximate computational modules implementing traditional static or dynamic bit-truncation approaches. The proposed platform-independent architecture exhibits an energy saving of up to 80% over the accurate counterparts and significantly better behavior in terms of accuracy loss with respect to competitor approximate architectures. When employed in 2D digital filters and edge detectors, the novel approximate multipliers lead to an energy consumption up to ~82% lower than the accurate counterparts, which is up to ~2 times higher than that obtained by state-of-the-art competitors. [ABSTRACT FROM AUTHOR]

Approximate computing is an emerging strategy to improve the energy efficiency of many error-tolerant applications. To design an approximate circuit automatically, many approximate logic synthesis (ALS) methods have been proposed, among which many are greedy. To improve the synthesis quality of these greedy methods, one key is to calculate the errors of all candidate approximate transformations accurately. However, the traditional simulation-based method is time consuming. Instead, many existing methods just perform quick but inaccurate error estimation. In this work, to improve both the accuracy and runtime of error estimation, we propose VECBEE, a versatile efficiency–accuracy configurable batch error estimation method for greedy ALS. It is based on Monte Carlo simulation and an efficient technique to capture whether a signal change due to an introduced approximation will be propagated to each primary output. VECBEE is generally applicable to any statistical error measurement, such as error rate and average error magnitude, and any graph-based circuit representation. It allows a flexible tradeoff between the error estimation accuracy and the runtime, while even the fully accurate version is much faster than the traditional simulation-based method. We apply VECBEE to two representative greedy ALS methods and demonstrate its effectiveness in generating better approximate circuits. The code of VECBEE is made open source. [ABSTRACT FROM AUTHOR]

Approximate computing is an attractive paradigm for reducing the design complexity of error-resilient systems, therefore, improving performance and saving power consumption. In this work, we propose a new two-level approximate logic synthesis method based on cube insertion and removal procedures. The experimental results have shown significant literal count and runtime reduction compared to the state-of-the-art approach. The method scalability is illustrated for a high error threshold over large benchmark circuits. The obtained solutions have presented a literal number reduction up to 38%, 56%, and 93% with respect to an error rate of 1%, 3%, and 5%, respectively. [ABSTRACT FROM AUTHOR]

BACKGROUND: Multi - collector inductively coupled plasma - mass spectrometry ( MC - ICP - MS) has been widely applied to accurate and precise measurements of isotope ratios due to its high sample throughput, strong ionization ability of ICP sources and high mass resolution. For decades, the standard - sample bracketing (SSB) method has been used to correct for instrumental mass bias during the measurement to achieve accurate results. When the content of the target isotope in samples is low, the measurement results are easily influenced by the background signals. “On Peak Zero” correction deducts the background signal from the total signal, which is an effective method to eliminate the background interference and has been widely used, but no research has been conducted to systematically explore the mathematical principles behind this correction. OBJECTIVES: To establish a mathematical model for the “On Peak Zero” correction, and verify its confidence by applying it to isotope measurements of different concentrations of Li, S, Fe, Sr, Nd and Pb standard solutions. METHODS: In this study, a mathematical model of the influence by the background signal on isotopic composition was established by mathematical reasoning and approximate substitution. Standard solutions of different concentrations of Li, S, Fe, Sr, Nd and Pb were prepared for the application of the “On Peak Zero” method through experimental analysis. Two types of blank signals were subtracted separately from the aggregate signals to simulate isotope measurements without and with “On Peak Zero” correction. RESULTS: The results indicate that the lower the concentration of the target element, the greater is the blank solution signal influence on the accuracy of the sample to be tested, and the “On Peak Zero” method can better eliminate the influence of the blank solution on the sample measurements. The simulation results based on this model were consistent with the real experimental results in this study. CONCLUSIONS: The mathematical model and the data explain well the effect of background concentration on the experimental isotope values, and are useful for understanding the application of the “On Peak Zero” method in MC-ICP-MS isotope analysis. [ABSTRACT FROM AUTHOR]

In this article, the authors study the comparison of the generalization differential transform method (DTM) and fuzzy variational iteration method (VIM) applied to determining the approximate analytic solutions of fuzzy fractional KdV, K(2,2) and mKdV equations. Furthermore, we establish the approximation solution two-and three-dimensional fuzzy time-fractional telegraphic equations via the fuzzy reduced differential transform method (RDTM). Finding an exact or closed-approximation solution to a differential equation is possible via fuzzy RDTM. Finally, we present the fuzzy fractional variational homotopy perturbation iteration method (VHPIM) with a modified Riemann-Liouville derivative to solve the fuzzy fractional diffusion equation (FDE). Using this approach achieves a rapidly convergent sequence that approaches the exact solution of the equation. The proposed methods are investigated based on fuzzy fractional derivatives with some illustrative examples. The results reveal that the schemes are highly effective for obtaining the solutions to fuzzy fractional partial differential equations. [ABSTRACT FROM AUTHOR]

Graph distance is also named approximate graph isomorphism, error-tolerant graph matching, it is a measure of similarity (or dissimilarity) between two graphs. The graph distance function is an elusive question remaining a pressing problem in a wide range of fields. In general, graphs are usually enriched with node and edge attributes, namely, heterogeneous graphs, our focus is encapsulating node and edge identities in a graph. In addition, an adequate representation of the graph-adjacency matrix can capture the connectivity of the graph structure, while an adjacency matrix bears high-order combinatorial nature. Solving these challenges in the effective analysis of these graphs is of utmost importance. In this paper, structural and semantic features are both preserved by graphs, so the analysis of row sum and eigenspectra for vertex and edge adjacency matrix has captured the affinity interactions within graphs locally and globally. Therefore, we estimate the geometrical and semantic dissimilarities/distances between graphs extensively and systemically. Several illustrative chemical compound cases implement in practical scenarios, thus, the theory could be easily understood. Our method defines a quantitative distance (or dissimilarity) measure for comparing graphs, it has a good measure of expressiveness and a suited polynomial computation complexity, which paves the way for graph analysis. [ABSTRACT FROM AUTHOR]

Generalized modus ponens (GMP) is a basic model of approximate reasoning. GMP in fuzzy propositions is called fuzzy modus ponen (FMP) and it is called intuitionistic fuzzy modus ponens (IFMP) when fuzzy propositions are generalized to intuitionistic fuzzy propositions. In this paper, we aim to investigate fuzzy reasoning methods for GMP with mixture of fuzzy/intuitionistic fuzzy information. For mixed types of GMP, we present two basic methods to solve GMP problems based on the triple I method (TIM). One is to transform the GMP problem into two FMP problems by decomposition and aggregate the solutions of TIM for FMP problems to obtain the solution for GMP problem. The other is to transform the GMP problem into the IFMP problem by expansion and aggregate the solutions of TIM for the IFMP problem to obtain the solution for the GMP problem. These two methods are called the decomposition triple I method (DTIM) and expansion triple I method (ETIM), respectively. We analyze the relationship between DTIM and ETIM. Furthermore, we discuss the reversibility of DTIM and ETIM. [ABSTRACT FROM AUTHOR]

To strengthen the effectiveness of approximate reasoning in fuzzy modus ponens (FMP) and fuzzy modus tollens (FMT) problems, three approximate reasoning methods with aggregation functions are developed and their validity are investigated respectively in this paper. We firstly study some properties of fuzzy implication generated by an aggregation function. And then present an A-compositional rule of inference as an extension of Zadeh's CRI replacing t-norm by aggregation function. The similarity-based approximate reasoning with aggregation function is further discussed. Moreover, we provide the quintuple implication principle method with aggregation function to solve FMP and FMT problems. Finally, the validity of three approximate reasoning approaches is analyzed respectively using GMP rules in detail. [ABSTRACT FROM AUTHOR]

The most critical and purely heuristic assumption about priority vector estimation on the basis of pairwise comparisons is that which states a positive relationship between the consistency of decision makers' judgments and the quality of estimates of their priorities. As this issue constitutes the area of interest of the Multi-Criteria Decision Making theory in relation to AHP, it's examined in this paper via Monte Carlo simulations from the perspective of a new measure of PCM consistency i.e. Index of Square Logarithm Deviations. It needs to be emphasized that such problems of applied mathematics have been already studied via computer simulations as the only way of this phenomenon examination. [ABSTRACT FROM AUTHOR]

Nowadays, all the applications have been moved to the intelligent world for easy usage and advancements. Hence, the sensed data have been utilized in the smart medical field to analyze the disease based on the symptom and to suggest controlling the disease severity rate. However, predicting the disease severity range based on the sensed disease symptom is more complicated because of the complex and vast data. So, the present work has introduced a novel Generalized approximate Reasoning base Intelligence Control (GARIC) with Ant Lion Optimization (ALO) algorithm to forecast the disease type and measure the severity range. Here, the presence of the Ant lion fitness has afforded the finest disease classification and severity analysis results. Finally, the parameters were measured and compared with other conventional models and have recorded the finest disease prediction score and severity range. This verified the success rate of the designed model in estimating the disease severity range. In addition, the presented system helps to notify the people of medical advice by message, email, or other application. [ABSTRACT FROM AUTHOR]

Much attention is focused on the relationship between rough sets and many-valued modal logic to deal with approximate reasoning. This paper discusses the graded modal logic and puts forward the graded many-valued modal logic G(S5). Secondly, by employing the graded operators that correspond to graded modal operations in G(S5), we introduce the concept of graded upper and lower rough truth degrees of a logical formula. Then, we propose the graded upper and lower conditional rough truth degrees. Several basic interesting properties are addressed. Finally, in order to make a distinction between any two rough formulas in graded many-valued modal logic, the graded upper and lower rough similarity degrees between two graded modal formulas are established in a very natural way. [ABSTRACT FROM AUTHOR]

Artificial intelligence (AI) is an integral part of clinical decision support systems (CDSS), offering methods to approximate human reasoning and computationally infer decisions. Such methods are generally based on medical knowledge, either directly encoded with rules or automatically extracted from medical data using machine learning (ML). ML techniques, such as Artificial Neural Networks (ANNs) and support vector machines (SVMs), are based on mathematical models with parameters that can be optimally tuned using appropriate algorithms. The ever-increasing computational capacity of today's computer systems enables more complex ML systems with millions of parameters, bringing AI closer to human intelligence. With this objective, the term deep learning (DL) has been introduced to characterize ML based on deep ANN (DNN) architectures with multiple layers of artificial neurons. Despite all of these promises, the impact of AI in current clinical practice is still limited. However, this could change shortly, as the significantly increased papers in AI, machine learning and deep learning in cardiology show. We highlight the significant achievements of recent years in nearly all areas of cardiology and underscore the mounting evidence suggesting how AI will take a central stage in the field. [ABSTRACT FROM AUTHOR]

Data-driven and knowledge-driven methods are two mainstream techniques in the pursuit of developing artificial intelligence systems. While data-driven methods seek to develop a decision model from observations in the real world, they are difficult to provide an explanation for the results in human terms. On the other hand, knowledge-driven methods that employ symbolic reasoning based on formal semantics of a knowledge-base are thus more interpretable and explainable, while lacking an ability to deal with incomplete modeling of the structured knowledge-bases. This work aims to tackle these issues on ontology similarity by proposing a general framework that combines the strengths of both approaches for measuring semantic similarity of concepts in a description logic (DL) ontology. More specifically, a neuro-symbolic integrated framework is defined to exploit the pre-trained word embeddings with semantic definitions in an ontology to yield an explainable degree of concept similarity. To demonstrate its applicability, we develop a concrete similarity measure $ {\textsf {sim}}_\epsilon $ conforming to the proposed framework and also introduce an efficient algorithm that can extract an explanation for why such a degree is indicated. The correctness is shown by analyzing theoretical properties that it guarantees to preserve and also by performing an empirical evaluation with a medical ontology SNOMED CT and a medical pre-trained embedding BioWordVec. The results show that our proposed method remains both interpretability and explainability while achieving comparable performance, relative to the state-of-the-art approaches in the data and knowledge-driven methods.

The construction of fuzzy conditional relations has been considered in Raha’s similarity-based inference schema, but inappropriate conclusions will be drawn in some cases due to the use of a single modification function. This paper presents an approximate reasoning method to generate induced conditional relations from distance measures. Two types of modification functions are given, and the type can be chosen according to the inclusion relation between a given fact and the antecedent of a rule. The fuzzy logic operators for constructing conditional relations are discussed, and the monotonicity and approximation properties of the reasoning scheme are inspected. By comparing and analyzing some basic properties of the three reasoning methods, some advantages can be found in the proposed scheme. An example of weld forming prediction is provided to illustrate the application of the algorithm.

In this work, the Optimal Homotopy Asymptotic Method (OHAM) is prolifically implemented to find the optimal solutions of fractional order of fuzzy differential equations. We inspect the competence of the method by examining fractional order time-dependent first order fuzzy initial value problems in the Caputo derivative sense. The concepts of fuzzy sets theory and fractional calculus were used to present a new general fuzzification formulation of the OHAM method followed by fuzzy analysis for the proposed fractional problems are presented in detail. OHAM is recognized as a feasible and convergent method for solving linear and nonlinear models, and it provides a convenient technique for controlling the convergence of approximate solutions optimally. The method's capability is demonstrated by obtaining approximate solutions to linear and nonlinear fuzzy initial value problems in various orders of fractional derivative. The numerical results acknowledge that OHAM is a feasible and transformation mechanism for solving linear and nonlinear fuzzy fractional initial value problems. Also, the results ensure that the method used was succinct, efficient, and simple to use, to deal with a more comprehensive fuzzy fractional differential equation. [ABSTRACT FROM AUTHOR]

The fuzzy logic reasoning based on the "If... then..." rule is not the inaccurate reasoning of AI against ambiguity because fuzzy reasoning is antilogical. In order to solve this problem, a redundancy theory for discriminative weight filtering containing six theorems and one M(1,2,3) model was proposed and the approximate reasoning process was shown, the system logic of AI handling ambiguity as an extension of the classical logic system was proposed. The system is a generalized dynamic logic system characterized by machine learning, which is the practical-application logic system of AI, and can effectively deal with practical problems including conflict, noise, emergencies and various unknown uncertainties. It is characterized by combining approximate reasoning and computing for specific data conversion through machine learning. Its core is data and calculations and the condition is "sufficient" high-quality training data. The innovation is that we proposed a discriminative weight filtering redundancy theory and designed a computable approximate reasoning logic system that combines approximate reasoning and calculation through machine learning to convert specific data. It is a general logic system for AI to deal with uncertainty. The study has significance in theory and practice for AI and logical reasoning research. [ABSTRACT FROM AUTHOR]

Quantifying the related concepts of propositional logic is a new method of propositional logic research. It is differe.nt from the syntax and semantics method and is a powerful tool for studying the structure of propositional sets. By using the Jaccard similarity coefficient, this paper introduces the concepts of Jaccard similarity degree, Jaccard pseudo-metric and Jaccard similarity degree representation method of the truth degree of a formulae in quantitative logic, and constructs a new kind of quantitative model of logic system L. This paper investigates the basic properties of Jaccard logic metric space[(F(S),ρJ),]which is induced by Jaccard pseudo-metric. This paper gets the following results: firstly, contradictory is the only isolated point in logic metric space[(F(S),ρJ);]secondly, every non-empty sphere in [(F(S),ρJ)]is an inconsistency theory.

Fuzzy Petri nets (FPNs) are a useful instrument for modelling expert systems to conduct knowledge representation and reasoning. Many studies have been carried out for improving the performance of FPNs in terms of their accurate representation of knowledge and power of approximate reasoning. Nevertheless, the current representation methods with FPNs are unable to handle the uncertain linguistic knowledge given by domain experts and the reliability of their judgments. In addition, the existing reasoning algorithms have no way to capture the interrelationship of the propositions with the same output transition. Therefore, we present a new type of FPNs, called 2-dimensional uncertain linguistic Petri nets (2DULPNs). The 2-dimensional uncertain linguistic variables (2DULVs) and Choquet integral are combined for knowledge representation and reasoning for the first time. The truth degrees of propositions, thresholds and certainty values of linguistic production rules are denoted as 2DULVs. Some new aggregated operators based on Choquet integral are proposed and used in the approximate reasoning to capture the interactions among antecedent propositions. Finally, an equipment fault diagnosis example is provided to illustrate the correctness and effectiveness of the proposed 2DULPN model. [ABSTRACT FROM AUTHOR]

When TextRank algorithm based on graph model constructs graph associative edges, the co-occurrence window rules only consider the relationships between local terms. Using the information in the document itself is limited. In order to solve the above problems, an improved TextRank keyword extraction algorithm based on rough data reasoning combined with word vector clustering, RDD-WRank, was proposed. Firstly, the algorithm uses rough data reasoning to mine the association between candidate keywords, expands the search scope, and makes the results more comprehensive. Then, based on Wikipedia online open knowledge base, word embedding technology is used to integrate Word2Vec into the improved algorithm, and the word vector of TextRank lexical graph nodes is clustered to adjust the voting importance of nodes in the cluster. Compared with the traditional TextRank algorithm and the Word2Vec algorithm combined with TextRank, the experimental results show that the improved algorithm has significantly improved the extraction accuracy, which proves that the idea of using rough data reasoning can effectively improve the performance of the algorithm to extract keywords. [ABSTRACT FROM AUTHOR]

In this paper we prove a Lindström like theorem for the logic consisting of arbitrary Boolean combinations of first order sentences. Specifically we show the logic obtained by taking arbitrary, possibly infinite, Boolean combinations of first order sentences in countable languages is the unique maximal abstract logic which is closed under finitary Boolean operations, has occurrence number ω1, has the downward Löwenheim-Skolem property to ω and the upward Löwenheim-Skolem property to uncountability, and contains all complete first order theories in countable languages as sentences of the abstract logic. We will also show a similar result holds in the continuous logic framework of [5], i.e. we prove a Lindström like theorem for the abstract continuous logic consisting of Boolean combinations of first order closed conditions. Specifically we show the abstract continuous logic consisting of arbitrary Boolean combinations of closed conditions is the unique maximal abstract continuous logic which is closed under approximate isomorphisms on countable structures, is closed under finitary Boolean operations, has occurrence number ω1, has the downward Löwenheim-Skolem property to ω, the upward Löwenheim-Skolem property to uncountability and contains all first order theories in countable languages as sentences of the abstract logic. [ABSTRACT FROM AUTHOR]

Its goals can be characterized as follows: To express all concepts capable of being expressed in natural language, To characterize all the valid inferences that can be made in natural language, To mesh with adequate linguistic descriptions of all natural languages. In this contribution, the Fuzzy Property Grammar permits to describe linguistic complexity of a natural language and linguistic universality (presence of a grammatical characteristics in all or most natural languages) as vague concepts. In [[1]], we gave reasons to focus on one of the possible future directions of fuzzy logic towards the concept of fuzzy natural logic (FNL). [Extracted from the article]

As a decision support system,fuzzy system can deal with uncertainty and has a clear representation of uncertainty knowledge and inference process.But one problem that exists is that computerized decision support systems,including systems that use fuzzy methods,do not have a clear assessment method to determine whether they can be allowed to be used in the real world.A conceptual framework of indistinguishable lines as a key component in evaluating computerized decision support systems was proposed,and some case studies were given.The case proves that the performance of human experts is not perfect,and the fuzzy system can simulate human performance at the technical level,including the variation of human experts.In summary,fuzzy methods are necessary for the representation and reasoning of uncertainty of the knowledge-based systems.Variation is an important form of learning.When evaluating AI systems,imperfect performance should be accepted.

We present an algorithm for solving unconstrained optimization problems based on the q-gradient vector. The main idea used in the algorithm construction is the approximation of the classical gradient by a q-gradient vector. For a convex objective function, the quasi-Fejér convergence of the algorithm is proved. The proposed method does not require the boundedness assumption on any level set. Further, numerical experiments are reported to show the performance of the proposed method. [ABSTRACT FROM AUTHOR]

Approximate reasoning systems facilitate fuzzy inference through activating fuzzy if–then rules in which attribute values are imprecisely described. Fuzzy rule interpolation (FRI) supports such reasoning with sparse rule bases where certain observations may not match any existing fuzzy rules, through manipulation of rules that bear similarity with an unmatched observation. This differs from classical rule-based inference that requires direct pattern matching between observations and the given rules. FRI techniques have been continuously investigated for decades, resulting in various types of approach. Traditionally, it is typically assumed that all antecedent attributes in the rules are of equal significance in deriving the consequents. Recent studies have shown significant interest in developing enhanced FRI mechanisms where the rule antecedent attributes are associated with relative weights, signifying their different importance levels in influencing the generation of the conclusion, thereby improving the interpolation performance. This survey presents a systematic review of both traditional and recently developed FRI methodologies, categorised accordingly into two major groups: FRI with non-weighted rules and FRI with weighted rules. It introduces, and analyses, a range of commonly used representatives chosen from each of the two categories, offering a comprehensive tutorial for this important soft computing approach to rule-based inference. A comparative analysis of different FRI techniques is provided both within each category and between the two, highlighting the main strengths and limitations while applying such FRI mechanisms to different problems. Furthermore, commonly adopted criteria for FRI algorithm evaluation are outlined, and recent developments on weighted FRI methods are presented in a unified pseudo-code form, easing their understanding and facilitating their comparisons. [ABSTRACT FROM AUTHOR]

Summary. IF-THEN rules in fuzzy inference is composed of multiple fuzzy sets (membership functions). IF-THEN rules can therefore be considered as a pair of membership functions [7]. The evaluation function of fuzzy control is composite function with fuzzy approximate reasoning and is functional on the set of membership functions. We obtained continuity of the evaluation function and compactness of the set of membership functions [12]. Therefore, we proved the existence of pair of membership functions, which maximizes (minimizes) evaluation function and is considered IF-THEN rules, in the set of membership functions by using extreme value theorem. The set of membership functions (fuzzy sets) is defined in this article to verifier our proofs before by Mizar [9], [10], [4]. Membership functions composed of triangle function, piecewise linear function and Gaussian function used in practice are formalized using existing functions. On the other hand, not only curve membership functions mentioned above but also membership functions composed of straight lines (piecewise linear function) like triangular and trapezoidal functions are formalized. Moreover, different from the definition in [3] formalizations of triangular and trapezoidal function composed of two straight lines, minimum function and maximum functions are proposed. We prove, using the Mizar [2], [1] formalism, some properties of membership functions such as continuity and periodicity [13], [8]. [ABSTRACT FROM AUTHOR]