Approximate Reasoning Research Articles

Approximate reasoning with aggregation functions satisfying GMP rules

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.

Three-way approximate reduct based on information-theoretic measure

Three-way decision is a typical and popular methodology for decision-making and approximate reasoning, while attribute reduction is an important research topic in three-way decision. However, most attribute reduction methods based on three-way decision strictly rely on the preservation of measure criterion, which not only explicitly limits the efficiency of attribute reduction and also implicitly confines the generalization ability of the resulting reduct. In this study, we present a new three-way approximate attribute reduction method based on information-theoretic measure. More specifically, a unified framework for approximate attribute reduction is first provided. Then, the process of attribute reduction is considered to determine each attribute to be the positive region, boundary region, or negative region in terms of its correlation to the decision attribute. The negative attributes can be removed by the preservation of information-theoretic measure, while some boundary attributes are further iteratively eliminated by relaxing the measure criterion. An approximate reduct is finally formed by the positive attributes and the remaining boundary attributes. On several public UCI data sets, the proposed method achieves a much better attribute reduction rate and simultaneously gains an improvement in performance when comparing with other attribute reduction methods.

Assessment of Quality in Saudi Arabian Roadways

A new assessment model was developed in this work. The developed model introduced a new approach and reference for assessment factors control the quality in Saudi Arabian roads using the fuzzy logic system. Fuzzy logic system was chosen to be used in this research due to its suitability for uncertain and approximate reasoning that involves human intuitive thinking as well as, it requires a little data to achieve the aim of the proposed model. Furthermore, the fuzzy logic has the ability for combining many effects such as the probability of occurrence and the impact of factors on the quality of roadways construction. The methodology of this research included conducting a field survey with construction practitioners in the field of roadways projects across Saudi Arabia. The proposed model was then evaluated and applied using the collected data from the field survey. The study results proved that the proposed model can be successfully used in the assessment of factors affecting quality in roadways. The major factors that found to be significantly affecting the quality in construction of roadways projects were identified according to their importance as; 1) Change order control; 2) Fluctuation default of Subcontractor; 3) Third party delay 4) Contract dispute results from disagreement. The proposed model is considered as a general model that can be easily adapted and applied to other types of projects.

Estimation of Machining Sustainability Using Fuzzy Rule-Based System.

Quantification of a highly qualitative term ‘sustainability’, especially from the perspective of manufacturing, is a contemporary issue. An inference mechanism, based on approximate reasoning, is required to tackle the complexities and uncertainties of the manufacturing domain. The work presents development of a fuzzy rule-based system to quantify sustainability of the most widely utilized manufacturing process: machining. The system incorporates the effects of key control parameters of machining on several sustainability measures, as reported in the literature. The measures are categorized under the three dimensions of sustainability and contribute to the sustainability scores of the respective dimensions with different weightages. The dimensions’ scores are added up in different proportions to obtain the holistic sustainability score of the process. The categories of the control parameters incorporated into the system include type of the process, work material, material hardness, tool substrate and coating, tool geometry, cutting fluids, and cutting parameters. The proposed method yields sustainability scores, ranging between 0 and 100 of machining processes against the given values of their prominent control parameters. Finally, the rule-based system is applied to three different machining processes to obtain the measures of their accomplishment levels regarding economic, environmental, and societal dimensions of sustainability. The sustainability score of each process is then obtained by summing up the three accomplishment levels under the respective weightages of the dimensions. The presented approach holds immense potentials of industrial application as it can conveniently indicate the current sustainability level of a manufacturing process, leading the practitioners to decide on its continuation or improvement.

An emotion-driven virtual counselling system in computer-mediated communication

We present and evaluate a virtual counselling system that is devoted to improving user awareness of emotional situations in computer-mediated communication and making informed decisions on actions to recommend to the users involved in a conversation. Starting from elements such as the moods and emotions of the users involved in a conversation, the system constructs the emotional signatures of individuals and groups that are used to characterize a situation. It then uses an approximate reasoning mechanism based on three-way decisions to classify recognized situations with respect to particular emotional dynamics based on emotional contagion. A prototype of the system has been experimented on in a real context based on collaboration between university students for the realization of project work. The distinctive features of the system have been evaluated with accuracy measures, and the results are promising.

Resolution of Minimal Solutions for Max-Lukasiewicz Fuzzy Relation Equation by Fuzzy Neural Network

Fuzzy relation equation (FRE) was introduced by Sanchez in 1976, which was extensively applied in fuzzy logic, approximate reasoning, intelligent control, artificial intelligence and so on. It is well known that solving the minimal solutions of FRE is a NP-hard problem because of its computational complexity. Many scholars have studied some algorithms to solve the minimal solutions of fuzzy relation equation. Considering that max-lukasiewicz composition operator is widely used, in this paper, we investigate the resolution of minimal solutions for max-lukasiewicz fuzzy relation equation based on fuzzy neural network and propose a novel algorithm. Through continuous downward iteration and conditional constraints, all minimum solutions of FRE are finally obtained. Both mathematical conclusion and simulation experiment show that our algorithm is effective and valid.

Modified FMEA hazard identification for cross-country petroleum pipeline using Fuzzy Rule Base and approximate reasoning

The pipeline industry's existing and new safety challenges require flexible and powerful techniques for performing a risk-based analysis of cross-country petroleum product pipeline systems. One of the traditional tools for the prediction of pipeline failure is the Failure Mode and Effects Analysis (FMEA) technique due to its ease of application. However, many limitations have been identified in its application especially for cross-country pipelines in developing countries. Firstly, failure data is often either unavailable or unreliable, therefore identification of the risk priority numbers for the three failure factors (i.e. probability of failure, severity and detection) relies on experts' elicitation. Secondly, domain experts often provide diverse opinions and knowledge, which could produce different assessment rankings and it is often difficult to harmonise due to the multidisciplinary nature of the FMEA team. Thirdly, there is a lack of a systematic way of accounting for the relative importance of individual failure factors, which carries the risk of the assessment results not representing the true risk picture of the assessed system. Consequently, this paper proposes a new approach, called the modified FMEA, by integrating the noted benefits of hybrid FMEA with Fuzzy Rule Base (FRB) and FMEA with Grey Relations Theory (GRT) in order to overcome the identified drawbacks. The study utilises both the fuzzy and the grey theory to include experts' diverse opinions and to assign a relative weighting to each assessment factor in the risk assessment. The results of the risk assessment are then used to determine the risk priority and rank the failure modes under different types of conditions. A case study of Nigeria's petroleum product pipeline system 2 B is conducted to examine the applicability and validity of the new approach. The results show the practical application of the methodology in this new domain. The new approach offers a more effective method for identifying product pipeline system hazards and risk analysis in geographies with limited or unreliable data. The application of this new methodology in the oil and gas cross-country pipeline domain will aid decision making under uncertainty for pipeline inspection and maintenance.

Modus Ponens property of T-power based implications

Among the great bunch of additional properties which fuzzy implications may satisfy, the so-called invariance with respect to T-powers highlights due to its applications in approximate reasoning. This property ensures the invariance of the truth value of the fuzzy implication when both the antecedent and the consequent are modified using the same quantifier modeled by using powers of t-norms. In order to find the fuzzy implications that satisfy this property, a new class of fuzzy implications named T-power based implications has been proposed. In this paper we study when this kind of fuzzy implication satisfies the Modus Ponens property with respect to a continuous t-norm T♯. Then a characterization theorem on this topic in terms of residual implication generated from a summand of T♯ is presented.

A fuzzy FMEA assessment of hydroelectric earth dam failure modes: A case study in Central Brazil

The good operating practices of hydroelectric plants with earth dams recommend that continuous monitoring of the construction elements should be carried out to ensure their stability and integrity. Engineers have frequently used FMEA to assess mechanisms that can cause damage or failure of such structures because it is a self-documented and straightforward method. We adopted fuzzy approximate reasoning to mitigate the rigidity of the FMEA rating scales and to address the bias and inaccuracy inherent in subjective estimates. This paper applies linguistic variables in a two-stage assessment. In the first stage, we computed the RCI through the combined effect of Occurrence and Severity. In the second stage, we combined the RCI with Detection to compute the FIS-RPN. The failure modes, causes and effects, the rule bases for the two stages and the membership functions were obtained through in-depth interviews with a focus group composed of staff members of the Corumbá IV hydroelectric plant, located in Central Brazil. The fuzzification process assured more consistency to the RPN calculation, treated the imprecision and provided fair management value to prioritize actions and improve monitoring processes.

An Efficient Health Monitoring Method Using Fuzzy Inference System via Cloud

Background: In the midst of invention of sensor mechanization, massive statistics analytics had turn out to be an innovative prototype for quick information processing. Real-time analytics are required for getting access to the information and its processing. Large populace interest in fitness care led to the improvement of health monitoring systems. Methods: This study targets toward the improvement of a cloud based fitness health care system. Here Wireless Body Area Networks (WBAN) is used to blend the information to the server that includes STORM. The analytics are performed on the received physiological data. The non-critical information is ousted and the essential facts are saved and a notification is sent to the medical doctor. Findings: Thus, actual time analytics alongside with the cloud aid to improve the effectiveness of the proposed healthcare device by providing immediate clinical assistance to the users. A sensible selection making device for approximate reasoning that can manage the uncertainty of imperative threat for human fitness with the usage of fuzzy logic is carried out for discovering the health related problems. Novelty: In this study, an analysis to monitor the fitness hazard which is associated to Blood Pressure, Pulse rate and Kidney function is proposed. Levels of blood stress are analyzed with kidney characteristic by using Glomerular Filtration Rate (GFR). Under this concept, fuzzy logic system is proposed to signify the parameters which can also reason the danger for human fitness and evaluation via the usage of rule base component. Keywords: Wireless Body Area Networks; health care system; fuzzy logic

Some Properties of Membership Functions Composed of Triangle Functions and Piecewise Linear Functions

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].

Solution of a pollution sensitive supply chain model under fuzzy approximate reasoning

This article develops a three-layer supply chain (SC) pollution dependent production transportation model with rework on fuzzy approximate reasoning approach. First of all, we develop a cost function of the model of reworkable items, in which pollution generates due to transportation of goods only. The aim of this study is to reduce the aggregated pollution level that simultaneously could optimize the integrated SC cost function under fuzzy approximate reasoning. Basically, the theory of two-tailed (randomized L-R fuzzy) approximate reasoning is introduced first time on demand rate in this model which is an extension of one-tailed (randomized L-fuzzy/R-fuzzy) approximate reasoning in the perspectives of the proposed model. An application of a new heart like approximate dual feasible region has also been utilized here also. However, a comparative study has been made taking numerical examples for crisp, general fuzzy, one- and two-tailed fuzzy approximate reasoning models exclusively. Finally, few numerical analyses with sensitivity and graphical discussions are done to legitimize the model.

Approximate reasoning with fuzzy rule interpolation: background and recent advances

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.

A Burned Area Mapping Algorithm for Sentinel-2 Data Based on Approximate Reasoning and Region Growing

Sentinel-2 (S2) multi-spectral instrument (MSI) images are used in an automated approach built on fuzzy set theory and a region growing (RG) algorithm to identify areas affected by fires in Mediterranean regions. S2 spectral bands and their post- and pre-fire date (Δpost-pre) difference are interpreted as evidence of burn through soft constraints of membership functions defined from statistics of burned/unburned training regions; evidence of burn brought by the S2 spectral bands (partial evidence) is integrated using ordered weighted averaging (OWA) operators that provide synthetic score layers of likelihood of burn (global evidence of burn) that are combined in an RG algorithm. The algorithm is defined over a training site located in Italy, Vesuvius National Park, where membership functions are defined and OWA and RG algorithms are first tested. Over this site, validation is carried out by comparison with reference fire perimeters derived from supervised classification of very high-resolution (VHR) PlanetScope images leading to more than satisfactory results with Dice coefficient > 0.84, commission error < 0.22 and omission error < 0.15. The algorithm is tested for exportability over five sites in Portugal (1), Spain (2) and Greece (2) to evaluate the performance by comparison with fire reference perimeters derived from the Copernicus Emergency Management Service (EMS) database. In these sites, we estimate commission error < 0.15, omission error < 0.1 and Dice coefficient > 0.9 with accuracy in some cases greater than values obtained in the training site. Regression analysis confirmed the satisfactory accuracy levels achieved over all sites. The algorithm proposed offers the advantages of being least dependent on a priori/supervised selection for input bands (by building on the integration of redundant partial burn evidence) and for criteria/threshold to obtain segmentation into burned/unburned areas.

Successor Feature Sets: Generalizing Successor Representations Across Policies

Successor-style representations have many advantages for reinforcement learning: for example, they can help an agent generalize from past experience to new goals, and they have been proposed as explanations of behavioral and neural data from human and animal learners. They also form a natural bridge between model-based and model-free RL methods: like the former they make predictions about future experiences, and like the latter they allow efficient prediction of total discounted rewards. However, successor-style representations are not optimized to generalize across policies: typically, we maintain a limited-length list of policies, and share information among them by representation learning or GPI. Successor-style representations also typically make no provision for gathering information or reasoning about latent variables. To address these limitations, we bring together ideas from predictive state representations, belief space value iteration, successor features, and convex analysis: we develop a new, general successor-style representation, together with a Bellman equation that connects multiple sources of information within this representation, including different latent states, policies, and reward functions. The new representation is highly expressive: for example, it lets us efficiently read off an optimal policy for a new reward function, or a policy that imitates a new demonstration. For this paper, we focus on exact computation of the new representation in small, known environments, since even this restricted setting offers plenty of interesting questions. Our implementation does not scale to large, unknown environments --- nor would we expect it to, since it generalizes POMDP value iteration, which is difficult to scale. However, we believe that future work will allow us to extend our ideas to approximate reasoning in large, unknown environments. We conduct experiments to explore which of the potential barriers to scaling are most pressing.

A Theory of Approximate Reasoning with Type-2 Fuzzy Set

In this paper, an attempt is made to study approximate reasoning based on a Type-2 fuzzy set theory. In the process, we have examined the underlying fuzzy logic structure on which the reasoning is formulated. We have seen that the partial/incomplete/imprecise truth-values of elements of a type-2 fuzzy set under consideration forms a lattice. We propose two new lattice operations which ultimately help us to define a residual and thereby making the structure of truth- values a residuated lattice. We have focused upon two typical rules of inference used mostly in ordinary approximate reasoning methodology based on Type-1 fuzzy set theory. Our proposal is illustrated with typical artificial examples.

A Possibility Theory-Based Approach to the Ranking of Generalized Fuzzy Numbers

The ranking of fuzzy numbers plays a remarkable role in some application systems such as approximate reasoning, decision analysis, optimization and forecasting under fuzzy environments. In this paper, we propose a novel possibility degree formula of ranking generalized fuzzy numbers based on the possibility theory. The combined effects of the possibilistic mean and the variance/standard deviation on the ranking of generalized fuzzy numbers are considered. The axiomatic properties of the proposed ranking method are further verified. It is found that the possibilistic mean exhibits the dominant role as compared to the possibilistic variance or standard deviation. Some comparisons with the existing approaches are reported by carrying out lots of numerical examples. The observations reveal that the shortcomings in an existing method can be overcome. Generalized fuzzy numbers can be distinguished using a possibility degree. The developed ordering procedures of fuzzy numbers are consistent with human intuition, where the inherent uncertainty of fuzzy quantities is revealed.

Intelligent recommendation method integrating knowledge graph and Bayesian network

In recent years, the amount of Internet information data has exploded, and the problem of “information overload” has become a huge challenge for Internet development. Through the prior knowledge of the known data distribution, combined with sample training data to estimate the mathematical model of the overall data. Intelligent recommendation methods based on knowledge graphs and Bayesian networks are a hot spot in the current Internet research, and they are of great significance to search engines and e-commerce. This paper studies the fusion of knowledge graph and Bayesian belief network and its application in personalized recommendation and designs a Bayesian network that describes the purchase behavior of users based on the purchase records of customers across the network. User recommendation is the process of fusing knowledge graphs and Bayesian network reasoning. For the design of the recommendation network, a random reasoning algorithm with approximate reasoning is selected in consideration of calculation scale and accuracy. This paper uses the content filtering technology of KNN algorithm to supplement the sparse matrix, which can improve the quality of collaborative filtering recommendation, thereby improving the quality of final recommendation. In this paper, based on the knowledge graph, the EPCA algorithm and the robust recommendation algorithm are merged to form a robust collaborative recommendation model based on Bayesian probability matrix decomposition. The robust recommendation algorithm further improves the robustness of the recommendation algorithm by introducing the suspected users and target items detected by the EPCA algorithm. Research shows that the PS value of the VarSelect SVD algorithm used in this paper is approximately between 0.36 and 1.04. Compared with the first two algorithms, the PS value of VarSelect SVD has been significantly reduced, and the algorithm robustness has been significantly improved.

First and Second Graders Successfully Reason About Ratios With Both Dot Arrays and Arabic Numerals

Children struggle with exact, symbolic ratio reasoning, but prior research demonstrates children show surprising intuition when making approximate, nonsymbolic ratio judgments. In the current experiment, eighty-five 6- to 8-year-old children made approximate ratio judgments with dot arrays and numerals. Children were adept at approximate ratio reasoning in both formats and improved with age. Children who engaged in the nonsymbolic task first performed better on the symbolic task compared to children tested in the reverse order, suggesting that nonsymbolic ratio reasoning may function as a scaffold for symbolic ratio reasoning. Nonsymbolic ratio reasoning mediated the relation between children's numerosity comparison performance and symbolic mathematics performance in the domain of probabilities, but numerosity comparison performance explained significant unique variance in general numeration skills.

Characterization of a Class of Fuzzy Implications Satisfying the Law of Importation With Respect to Uninorms With Continuous Underlying Operators

The law of importation, given by the equality (x^y)→z ≈ (x→(y→z)), is a tautology in classical logic and has been proved to be widely used in approximate reasoning and image processing. Some open problems of fuzzy implication dealing with the law of importation were suggested on 8th international conference on Fuzzy Set Theory and Applications (FSTA 2006). In this paper, we partially solve one open problem associated with this property. Specifically, we mainly devote ourselves to solving the general form of the law of importation I(U(x, y), z) = I(x, I(y, z)), where I is a fuzzy implication and U is a conjunctive uninorm with a continuous underlying tnorm and a continuous underlying t-conorm. Along this study, given a fixed uninorm with continuous underlying operators, all fuzzy implications that satisfy the law of importation with respect to this uninorm, and having an α-section that is a continuous negation, are characterized.