Fuzzy Interpolative Reasoning Research Articles

Dual Rule-Based Weighted Fuzzy Interpolative Reasoning Module and Temporal Encoder-Decoder Bayesian Network for Reagent Addition Control

Dual Rule-Based Weighted Fuzzy Interpolative Reasoning Module and Temporal Encoder-Decoder Bayesian Network for Reagent Addition Control

Interpretable mammographic mass classification with fuzzy interpolative reasoning

Breast mass cancer remains a great challenge for developing advanced computer-aided diagnosis (CADx) systems, to assist medical professionals for the determination of benignancy or malignancy of masses. This paper presents a novel approach to building fuzzy rule-based CADx systems for mass classification of mammographic images, via the use of weighted fuzzy rule interpolation. It describes an integrated implementation of such a classification system that ensures interpretable classification of masses through firing the rules that match given observations, while having the capability of classifying unmatched observations through fuzzy rule interpolation (FRI). In particular, a feature weight-guided FRI scheme is exploited to enable such inference. The work is implemented through integrating feature weights with a popular scale and move transformation-based FRI, with the individual feature weights derived from feature selection as a preprocessing process. The efficacy of the proposed CADx system is systematically evaluated using two real-world mammographic image datasets, demonstrating its explicit interpretability and potential classification performance.

Adaptive fuzzy interpolative reasoning based on similarity measures of polygonal fuzzy sets and novel move and transformation techniques

In this paper, we propose a new adaptive fuzzy interpolative reasoning (AFIR) method based on similarity measures of polygonal fuzzy sets (PFSs) and novel move and transformation techniques for solving contradictory fuzzy interpolative reasoning (FIR) results that occur at FIR components. The proposed AFIR method is applied for dealing with the diarrheal disease prediction problem. The experimental results show that the proposed AFIR method obtains a higher consistency degree between the FIR results compared to the ones obtained by Chen and Adam's AFIR method (2017), Chen and Adam's AFIR method (2018), Chen and Barman's AFIR method (2019), Cheng et al.’s AFIR method (2016), Yang et al.’s AFIR method (2017) and Yang and Shen's AFIR method (2011).

Adaptive weighted fuzzy interpolative reasoning based on representative values and similarity measures of interval type-2 fuzzy sets

In this paper, we propose an adaptive weighted fuzzy interpolative reasoning (AWFIR) method based on representative values (RVs) and similarity measures of interval type-2 polygonal fuzzy sets (IT2PFSs). The proposed AWFIR method can overcome the shortcomings of Cheng et al.’s adaptive fuzzy interpolative reasoning (AFIR) method (2016), Chen and Adam's AFIR method (2018), Yang and Shen's AFIR method (2011) and Yang et al.’s AFIR method (2017) to deal with the diarrheal disease prediction problem. The advantages of the proposed AWFIR method are (1) it produces higher degrees of consistency between the FIR results and (2) it deals with AWFIR using IT2PFSs rather than type-1 fuzzy sets (T1FSs).

Fuzzy Rule Based Interpolative Reasoning Supported by Attribute Ranking

Using fuzzy rule interpolation (FRI) interpolative reasoning can be effectively performed with a sparse rule base where a given system observation does not match any fuzzy rules. While offering a potentially powerful inference mechanism, in the current literature, typical representation of fuzzy rules in FRI assumes that all attributes in the rules are of equal significance in deriving the consequents. This is a strong assumption in practical applications, thereby, often leading to less accurate interpolated results. To address this challenging problem, this paper employs feature selection (FS) techniques to adjudge the relative significance of individual attributes and therefore, to differentiate the contributions of the rule antecedents and their impact upon FRI. This is feasible because FS provides a readily adaptable mechanism for evaluating and ranking attributes, being capable of selecting more informative features. Without requiring any acquisition of real observations, based on the originally given sparse rule base, the individual scores are computed using a set of training samples that are artificially created from the rule base through an innovative reverse engineering procedure. The attribute scores are integrated within the popular scale and move transformation-based FRI algorithm (while other FRI approaches may be similarly extended following the same idea), forming a novel method for attribute ranking-supported fuzzy interpolative reasoning. The efficacy and robustness of the proposed approach is verified through systematic experimental examinations in comparison with the original FRI technique over a range of benchmark classification problems while utilizing different FS methods. A specific and important outcome that is supported by attribute ranking, only two (i.e., the least number of) nearest adjacent rules are required to perform accurate interpolative reasoning, avoiding the need of searching for and computing with multiple rules beyond the immediate neighborhood of a given observation.

Adaptive fuzzy interpolation based on ranking values of interval type-2 polygonal fuzzy sets

In recent years, some adaptive fuzzy interpolative reasoning (AFIR) methods have been proposed to deal with contradictions occurred during fuzzy interpolation processes. However, the degrees of consistency of the AFIR results of the existing AFIR methods are not good enough. Moreover, the existing AFIR methods are based on type-1 fuzzy sets (T1FSs), which cannot deal with AFIR using interval type-2 fuzzy sets (IT2FSs), where IT2FSs are more suitable to represent the fuzziness of information than T1FSs. In this paper, we propose a new AFIR method based on the ranking values of interval type-2 polygonal fuzzy sets (IT2PFSs). We also apply the proposed AFIR method based on IT2PFSs to deal with the diarrheal disease prediction problem. The proposed AFIR method based on the ranking values of IT2PFSs can overcome the shortcomings of Yang and Shen's AFIR method (2011) and Cheng et al.’s AFIR method (2016) because it gets a higher consistency of the AFIR results in terms of the degree of similarity between the AFIR results and it deals with AFIR based on IT2PFSs rather than T1FSs.

Estimation of Food Security Risk Level UsingZ-Number-Based Fuzzy System

Fuzzy logic systems based on If-Then rules are widely used for modelling of the systems characterizing imprecise and uncertain information. These systems are basically based on type-1 fuzzy sets and allow handling the uncertain and imprecise information to some degree in the developed models. Zadeh extended the concept of fuzzy sets and proposedZ-number characterized by two components, constraint and reliability parameters, which are an ordered pair of fuzzy numbers. Here, the first component is used to represent uncertain information, and the second component is used to evaluate the reliability or the confidence in truth.Z-number is an effective approach to solving uncertain problems. In this paper,Z-number-based fuzzy system is proposed for estimation of food security risk level. To construct fuzzy If-Then rules, the basic parameters cereal yield, cereal production, and economic growth affecting food security are selected, and the relationship between these input parameters and risk level are determined through If-Then fuzzy rules. The fuzzy interpolative reasoning is proposed for construction of inference mechanism of aZ-number-based fuzzy system. The designed system is tested using Turkey cereal data for assessing food security risk level and prediction periods of the food supply.

Weighted fuzzy interpolated reasoning based on ranking values of polygonal fuzzy sets and new scale and move transformation techniques

In this paper, we propose a new transformation-based weighted fuzzy interpolative reasoning (FIR) method based on ranking values of polygonal fuzzy sets (PFSs) and the proposed new scale and move transformation techniques. The proposed weighted FIR method gets more reasonable FIR results than the ones of the existing methods, where the weight of each antecedent variable and the weight of each fuzzy rule are generated automatically. Moreover, the proposed new scale and move transformation techniques can deal with FIR using singleton fuzzy sets and PFSs. We also apply the proposed weighted FIR method to predict the diarrheal disease rates in remote villages. The proposed weighted FIR method provides us with a very useful way for weighted FIR in sparse fuzzy rule-based systems.

Adaptive fuzzy interpolation based on general representative values of polygonal fuzzy sets and the shift and modification techniques

Adaptive fuzzy interpolative reasoning (AFIR) can overcome the limitation of the conventional fuzzy interpolation techniques because it can find and solve the contradictions of the fuzzy interpolative reasoning (FIR) results in order to ensure that the derived FIR results are consistent. In this paper, we propose a new AFIR method to solve the inconsistencies occurring after the FIR process. The proposed AFIR method is based on the general representative values of polygonal fuzzy sets and the proposed shift and modification techniques. The proposed AFIR method includes a new contradictions solving method to get a higher similarity degree between the AFIR results. In order to demonstrate the higher consistency of the AFIR results obtained by the proposed AFIR method, we apply the proposed AFIR method to deal with the diarrheal disease prediction problem. The experimental results show that the proposed AFIR method outperforms Yang and Shen's AFIR method (2011) and Cheng et al.’s AFIR method (2016) in terms of the degree of similarity between the AFIR results.

Rough-fuzzy rule interpolation

Fuzzy rule interpolation forms an important approach for performing inference with systems comprising sparse rule bases. Even when a given observation has no overlap with the antecedent values of any existing rules, fuzzy rule interpolation may still derive a useful conclusion. Unfortunately, very little of the existing work on fuzzy rule interpolation can conjunctively handle more than one form of uncertainty in the rules or observations. In particular, the difficulty in defining the required precise-valued membership functions for the fuzzy sets that are used in conventional fuzzy rule interpolation techniques significantly restricts their application. In this paper, a novel rough-fuzzy approach is proposed in an attempt to address such difficulties. The proposed approach allows the representation, handling and utilisation of different levels of uncertainty in knowledge. This allows transformation-based fuzzy rule interpolation techniques to model and harness additional uncertain information in order to implement an effective fuzzy interpolative reasoning system. Final conclusions are derived by performing rough-fuzzy interpolation over this representation. The effectiveness of the approach is illustrated by a practical application to the prediction of diarrhoeal disease rates in remote villages. It is further evaluated against a range of other benchmark case studies. The experimental results confirm the efficacy of the proposed work.

Adaptive fuzzy interpolation based on ranking values of polygonal fuzzy sets and similarity measures between polygonal fuzzy sets

After the fuzzy interpolative reasoning processes, if two unequal fuzzy interpolative reasoning results are derived (or one derived and another observed) for a consequence variable of a fuzzy rule, then it is called a contradiction in the fuzzy interpolative reasoning process. In recent years, some adaptive fuzzy interpolation methods for sparse fuzzy rule-based systems have been presented to solve contradictions after fuzzy interpolative reasoning processes. In this paper, a new adaptive fuzzy interpolation method is proposed for sparse fuzzy rule-based systems based on ranking values and similarity measures of polygonal fuzzy sets, which can solve contradictions occurred in fuzzy interpolative reasoning processes. We also apply the proposed adaptive fuzzy interpolation method to predict the diarrheal disease rates in roadless villages. The diarrheal disease prediction problem focuses on the issue to measure how the construction of a new road or railway in a previously roadless area may affect the epidemiology of infectious diseases in northern coastal Ecuador. The experimental results show that the proposed adaptive fuzzy interpolation method can overcome the drawbacks of the existing methods.

Weighted fuzzy interpolative reasoning for sparse fuzzy rule-based systems based on piecewise fuzzy entropies of fuzzy sets

In this paper, we propose a new method for weighted fuzzy interpolative reasoning in sparse fuzzy rule-based systems based on piecewise fuzzy entropies of fuzzy sets. First, the proposed method uses the representative values of antecedent fuzzy sets, the representative values of observation fuzzy sets, and the representative values of consequence fuzzy sets of fuzzy rules to get the characteristic points of the fuzzy interpolative result represented by a fuzzy set. Then, it calculates the piecewise fuzzy entropies between any two characteristic points of the antecedent fuzzy sets, the piecewise fuzzy entropies between any two characteristic points of the observation fuzzy sets, and the piecewise fuzzy entropies between any two characteristic points of the consequence fuzzy sets of the fuzzy rules, respectively. Then, it calculates the weights of the antecedent fuzzy sets of each fuzzy rule, respectively, and calculates the weight of each fuzzy rule. Then, it calculates the piecewise fuzzy entropies between any two characteristic points of the fuzzy interpolative result. Finally, it uses the secant method to calculate the degree of membership of each obtained characteristic point of the fuzzy interpolative result. The experimental results show that the proposed method outperforms the existing methods for dealing with the multivariate regression problems, the Mackey–Glass chaotic time series prediction problem, and the time series prediction problems.

Fuzzy interpolative reasoning based on ranking values of polygonal fuzzy sets and automatically generated weights of fuzzy rules

In this paper, we propose a new fuzzy interpolative reasoning method for sparse fuzzy rule-based systems based on ranking values of polygonal fuzzy sets and automatically generated weights of fuzzy rules. First, the proposed method gets the characteristic points of the observation polygonal fuzzy sets and the characteristic points of the antecedent polygonal fuzzy sets of the fuzzy rules, respectively, by using the α-cut operations, respectively, where α ∈ [0, 1]. Then, it calculates the ranking value of each observation polygonal fuzzy set and the ranking value of each antecedent polygonal fuzzy set, respectively. Then, it calculates the difference between the ranking value of each observation polygonal fuzzy set and the ranking value of each antecedent polygonal fuzzy set. Then, it calculates the weight of each fuzzy rule based on the obtained differences between the ranking values of the observation polygonal fuzzy sets and the ranking values of the antecedent polygonal fuzzy sets. Then, based on the obtained characteristic points of the observation polygonal fuzzy sets, the obtained characteristic points of the antecedent polygonal fuzzy sets, and the obtained weights of the fuzzy rules, it gets the characteristic points of the fuzzy interpolative reasoning result represented by a polygonal fuzzy set. The experimental results show that the proposed method can overcome the drawbacks of the existing methods for fuzzy interpolative reasoning in sparse fuzzy rule-based systems.

Fuzzy interpolative reasoning based on the ratio of fuzziness of rough-fuzzy sets

In this paper, we propose a method to construct a polygonal rough-fuzzy set from a set of polygonal fuzzy sets representing the aggregation of multiple experts’ opinions and propose a new fuzzy interpolative reasoning method for sparse fuzzy rule-based systems based on the ratio of fuzziness of the constructed polygonal rough-fuzzy sets, where the values of the antecedent variables and the consequence variable appearing in the fuzzy rules are represented by the constructed polygonal rough-fuzzy sets. The proposed fuzzy interpolative reasoning method can overcome the drawbacks of the existing method due to the fact that it can deal with fuzzy interpolative reasoning using polygonal rough-fuzzy sets and it gets more reasonable fuzzy interpolative reasoning results than the existing method.

An Alternative Backward Fuzzy Rule Interpolation Method

Fuzzy set theory allows for the inclusion of vague human assessments in computing problems. Also, it provides an effective means for conflict resolution of multiple criteria and better assessment of options. Fuzzy rule interpolation offers a useful means for enhancing the robustness of fuzzy models by making inference possible in sparse rule-based systems. However, in real-world applications of inter-connected rule bases, situations may arise when certain crucial antecedents are absent from given observations. If such missing antecedents were involved in the subsequent interpolation process, the final conclusion would not be deducible using conventional means. To address this issue, an approach named backward fuzzy rule interpolation and extrapolation has been proposed recently, allowing the observations which directly relate to the conclusion to be inferred or interpolated from the known antecedents and conclusion. As such, it significantly extends the existing fuzzy rule interpolation techniques. However, the current idea has only been implemented via the use of the scale and move transformation-based fuzzy interpolation method, which utilise analogical reasoning mechanisms. In order to strengthen the versatility and feasibility of backward fuzzy interpolative reasoning, in this paper, an alternative a-cut-based interpolation method is proposed. Two numerical examples and comparative studies are provided in order to demonstrate the efficacy of the proposed work.

Weighted Fuzzy Interpolative Reasoning Based on the Slopes of Fuzzy Sets and Particle Swarm Optimization Techniques.

In this paper, we propose a new weighted fuzzy interpolative reasoning method for sparse fuzzy rule-based systems based on the slopes of fuzzy sets. We also propose a particle swarm optimization (PSO)-based weights-learning algorithm to automatically learn the optimal weights of the antecedent variables of fuzzy rules for weighted fuzzy interpolative reasoning. We apply the proposed weighted fuzzy interpolative reasoning method using the proposed PSO-based weights-learning algorithm to deal with the computer activity prediction problem, the multivariate regression problems, and the time series prediction problems. The experimental results show that the proposed weighted fuzzy interpolative reasoning method using the proposed PSO-based weights-learning algorithm outperforms the existing methods for dealing with the computer activity prediction problem, the multivariate regression problems, and the time series prediction problems.

MULTIPLE FUZZY RULES INTERPOLATION WITH WEIGHTED ANTECEDENT VARIABLES IN SPARSE FUZZY RULE-BASED SYSTEMS

This paper presents a new method for multiple fuzzy rules interpolation with weighted antecedent variables in sparse fuzzy rule-based systems based on polygonal membership functions. First, the proposed method calculates the normalized weighting vector of each closest fuzzy rule. Then, it calculates the composite weight of each closest fuzzy rule. Then, it calculates the left normal point [Formula: see text] and the right normal point [Formula: see text] of the fuzzy interpolative reasoning result [Formula: see text], respectively. Finally, it calculates the characteristic points [Formula: see text] and [Formula: see text] of the fuzzy interpolative reasoning result B*, respectively. The experimental results show that the proposed method can generate more reasonable fuzzy interpolative reasoning results than the existing methods for sparse fuzzy rule-based systems. The proposed method can overcome the drawbacks of Chang etal.'s method (IEEE Trans. Fuzzy Syst.16(5) (2008) 1285–1301), Chen and Ko's method (IEEE Trans. Fuzzy Syst.16(6) (2008) 1626–1648) and Huang and Shen's method (IEEE Trans. Fuzzy Syst.14(2) (2006) 340–359) for multiple fuzzy rules interpolation. It provides us with a useful way for dealing with multiple fuzzy rules interpolation in sparse fuzzy rule-based systems.

Weighted fuzzy interpolative reasoning systems based on interval type-2 fuzzy sets

In this paper, we present a weighted fuzzy interpolative reasoning method for sparse fuzzy rule-based systems based on interval type-2 fuzzy sets. We also apply the proposed weighted fuzzy interpolative reasoning method to deal with the truck backer-upper control problem. The proposed method satisfies the seven evaluation indices for fuzzy interpolative reasoning. The experimental results show that the proposed method outperforms the existing methods. It provides us with a useful way for dealing with fuzzy interpolative reasoning in sparse fuzzy rule-based systems.

Fuzzy interpolative reasoning for sparse fuzzy rule-based systems based on the slopes of fuzzy sets

In this paper, we present a new fuzzy interpolative reasoning method for sparse fuzzy rule-based systems based on the slopes of fuzzy sets. The proposed method can deal with fuzzy rules interpolation involving complex polygonal fuzzy sets with the advantages of simplest calculation and get more reasonable fuzzy interpolative reasoning results. We also make some experiments to compare the fuzzy interpolative reasoning results of the proposed method with the ones of the existing methods. The experimental results show that the proposed method outperforms the existing fuzzy interpolative reasoning methods for sparse fuzzy rule-based systems.

Adaptive Fuzzy Interpolation

Fuzzy interpolative reasoning strengthens the power of fuzzy inference by the enhancement of the robustness of fuzzy systems and the reduction of the systems’ complexity. However, after a series of interpolations, it is possible that multiple object values for a common variable are inferred, leading to inconsistency in interpolated results. Such inconsistencies may result from defective interpolated rules or incorrect interpolative transformations. This paper presents a novel approach for identification and correction of defective rules in interpolative transformations, thereby removing the inconsistencies. In particular, an assumption-based truth-maintenance system (ATMS) is used to record dependences between interpolations, and the underlying technique that the classical general diagnostic engine (GDE) employs for fault localization is adapted to isolate possible faulty interpolated rules and their associated interpolative transformations. From this, an algorithm is introduced to allow for the modification of the original linear interpolation to become first-order piecewise linear. The approach is applied to a realistic problem, which predicates the diarrheal disease rates in remote villages, to demonstrate the potential of this study.