Representation Of Fuzzy Rules Research Articles

Why They Escape: Mining Prioritized Fuzzy Decision Rule in Crowd Evacuation

For safety planning in crowd evacuation, it is important to predict the evacuation decisions made by different individuals and understand the reasons behind these decisions. To this end, this paper proposes an automated approach that can learn prioritized fuzzy decision rules from crowd data to predict and understand the evacuation decisions of a real human. A coevolutionary fuzzy rule miner based on genetic fuzzy-system is designed to select necessary decision features from available ones and learn both rule structure and associated rule parameters from training data. The learned fuzzy rule contains multiple sub-rules, each of which can represent evacuation strategies of different individuals in a given scenario and the features in the fuzzy condition of the sub-rule are organized and evaluated in a sequential order to reflect the priorities of different features. Based on training and testing on four evacuations scenarios of two real-world datasets, it is shown that our proposed approach can learn decision rules that are competitive to the existing evacuation decision models in terms of prediction accuracy. More importantly, it is also demonstrated that our learned rules complying with the proposed prioritized fuzzy rule representation can facilitate the interpretation of evacuation behaviors, such as “herding under zero visibility of exit” and “diminished importance on the distance to exit”, which are aligned to the field observations from real crowd evacuation.

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.

Transformation-Based Fuzzy Rule Interpolation Using Interval Type-2 Fuzzy Sets

In support of reasoning with sparse rule bases, fuzzy rule interpolation (FRI) offers a helpful inference mechanism for deriving an approximate conclusion when a given observation has no overlap with any rule in the existing rule base. One of the recent and popular FRI approaches is the scale and move transformation-based rule interpolation, known as T-FRI in the literature. It supports both interpolation and extrapolation with multiple multi-antecedent rules. However, the difficult problem of defining the precise-valued membership functions required in the representation of fuzzy rules, or of the observations, restricts its applications. Fortunately, this problem can be alleviated through the use of type-2 fuzzy sets, owing to the fact that the membership functions of such fuzzy sets are themselves fuzzy, providing a more flexible means of modelling. This paper therefore, extends the existing T-FRI approach using interval type-2 fuzzy sets, which covers the original T-FRI as its specific instance. The effectiveness of this extension is demonstrated by experimental investigations and, also, by a practical application in comparison to the state-of-the-art alternative approach developed using rough-fuzzy sets.

Double Fuzzy Point Extension of the Two-step Fuzzy Rule Interpolation Methods

The rule representation opens a new dimension for expressing changes of fuzziness in fuzzy rule-based systems. In the case of standard Fuzzy rule representations, it is difficult to describe fuzzy functions in which crisp observations are required to have fuzzy conclusions, or in which an increase in the fuzziness of observations leads to reduced fuzziness in conclusions. These problems are mainly due to a lack of information. A fuzzy point rule determines the connection between a pair of fuzzy sets taken from the domain and the range of the rule. Expressing the fuzzy function through a set of fuzzy points and fuzzy interpolation between pairs of those points, each fuzzy point can be considered as a node point with given location and fuzziness. In common, sparse rule-base definitions, these node points are usually disjunctive on the domain, defining only single antecedent-consequent fuzziness connections at the location of the fuzzy points. However, this kind of information is insufficient when the goal is to express changes in the fuzziness of a given location in the domain. One solution to this problem is the double fuzzy point rule representation concept. Double fuzzy points are pairs of fuzzy points which share the same reference locations, but have different fuzziness properties. The existence of two different fuzziness values in a single location within the domain creates new possibilities for introducing fuzzy interpolation methods capable of interpolating not only between locations, but between changes in local fuzziness values as well. The main goal of this paper is to discuss how two-step Rule Interpolation methods can be adapted to be able to handle the double fuzzy point concept. To this end, an approach referred to as the Generalized Double Point Methodology (GDFPM) is proposed.

On the representation of fuzzy rules

In fuzzy logic, connectives have a meaning that, can frequently be known through the use of these connectives in a given context. This implies that there is not a universal-class for each type of connective, and because of that several continuous t-norms, continuous t-conorms and strong negations, are employed to represent, respectively, the and, the or, and the not. The same happens with the case of the connective If/then for which there is a multiplicity of models called T-conditionals or implications. To reinforce that there is not a universal-class for this connective, four very simple classical laws translated into fuzzy logic are studied.

On the representation of fuzzy rules in terms of crisp rules

There are two classical ways of viewing a fuzzy set in terms of a combination of crisp sets; either as a weighted max-aggregation of its level-cuts, or as a convex combination of the latter. These views are applied to the particular case of fuzzy relations which are induced by fuzzy rules, where the rules are modeled by implication connectives (defined on a finite subset of the unit interval). The paper studies more closely the representation of such fuzzy rules in terms of a convex combination of gradual rules, a special type of implication-based fuzzy rule inducing a crisp relation. This representation, which might be interpreted in a probabilistic way, is shown to be unique on the assumption that the implication operator used for modeling the fuzzy rule does not satisfy a special kind of strict monotonicity condition. In this case, the crisp relations induced by the involved gradual rules correspond to level-cuts of the fuzzy relation associated with the fuzzy rule. However, other representations might exist if the aforementioned property is not satisfied. Under a slightly stronger (strict) monotonicity condition, the existence of further (non-consonant) representations is even guaranteed. Then, the crisp relations induced by gradual rules do not necessarily correspond to level-cuts of the underlying fuzzy relation. In this sense, the decomposition of a fuzzy rule into a class of crisp implication-based rules is more general than the classical decomposition of fuzzy sets.

A clustering algorithm for fuzzy model identification

The fuzzy model proposed by Takagi and Sugeno can represent highly nonlinear systems and is widely used for the representation of fuzzy rules. In this paper, the model is firstly modified to make its identification easier. Based on the fuzzy c-partition space, four criteria are proposed for optimization of the model parameters. Following that, a clustering algorithm composed of fuzzy c-linear functions clustering and like fuzzy c-means clustering is developed for minimizing the four criteria. An identification scheme for rule's premise and consequence parameters is deduced from the clustering algorithm in succession. Finally, four examples are demonstrated to verify the effectiveness of the proposed algorithm.

A Neuro-Fuzzy Approach to Identify LettuceGrowth and Greenhouse Climate

A hybrid neuro-fuzzy approach called the NUFZY system, which embeds fuzzy reasoning into a triple-layered network structure, has been developed to identify nonlinear systems. A set of membership functions at the input layer is partially linked with a layer of rules, using pre-set parameters. By means of a simplified centroid of gravity defuzzification method, the output becomes linear in the weights. Therefore, very fast estimation of the weight parameters can be achieved by using the orthogonal least squares (OLS) method, which also provides a method to efficiently remove the redundant fuzzy rules from the prototype rule base of the NUFZY system. In this paper, the NUFZY system is applied to identify lettuce growth and greenhouse temperature from real experimental data. Results show that the NUFZY model with the fast OLS training can perform quite well in predicting both lettuce growth and greenhouse temperature. In contrast to the mechanistic modeling procedures, the neuro-fuzzy approach offers an easier route and a fast way to build the nonlinear mapping of inputs and outputs. In addition, the resulting internal network structure of the NUFZY system is a self-explanatory representation of fuzzy rules. Under this frame, it is a perspective that one is able to incorporate the human knowledge in this approach, and, hopefully, to deduce any interpretable rules that describe the systems‘ behavior.

ニューラルネットワークによるファジィルールの表現(<特集>ファジィ・ニューラルネットワーク)

ニューラルネットワークによるファジィルールの表現(<特集>ファジィ・ニューラルネットワーク)

Distributed representation of fuzzy rules and its application to pattern classification

This paper introduces the concept of distributed representation of fuzzy rules and applies it to classification problems. Distributed representation is implemented by superimposing many fuzzy rules corresponding to different fuzzy partitions of a pattern space. This means that we simulatenously employ many fuzzy rule tables corresponding to different fuzzy partitions in fuzzy inference. In order to apply distributed representation of fuzzy rules to pattern classification problems, we first propose an algorithm to generate fuzzy rules from numerical data. Next we propose a fuzzy inference method using the generated fuzzy rules. The classification power of distributed representation is compared with that of ordinary fuzzy rules which can be viewed as local representation.