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. (C) 2014 Elsevier Inc. All rights reserved.
Countering cyber threats, especially attack detection, is a challenging area of research in the field of information assurance. Intruders use polymorphic mechanisms to masquerade the attack payload and evade the detection techniques Many supervised and unsupervised learning approaches from the field of machine learning and pattern recognition have been used to increase the efficacy of intrusion detection systems (IDSs). Supervised learning approaches use only labeled samples to train a classifier, but obtaining sufficient labeled samples is cumbersome, and requires the efforts of domain experts. However, unlabeled samples can easily be obtained in many real world problems. Compared to supervised learning approaches, semi-supervised learning (SSL) addresses this issue by considering large amount of unlabeled samples together with the labeled samples to build a better classifier. This paper proposes a novel fuzziness based semi-supervised learning approach by utilizing unlabeled samples assisted with supervised learning algorithm to improve the classifier's performance for the IDSs. A single hidden layer feed-forward neural network (SLFN) is trained to output a fuzzy membership vector, and the sample categorization (low, mid, and high fuzziness categories) on unlabeled samples is performed using the fuzzy quantity. The classifier is retrained after incorporating each category separately into the original training set. The experimental results using this technique of intrusion detection on the NSL-KDD dataset show that unlabeled samples belonging to low and high fuzziness groups make major contributions to improve the classifier's performance compared to existing classifiers e.g., naive bayes, support vector machine, random forests, etc. (C) 2016 Elsevier Inc. All rights reserved.
We propose a model for the pricing of the minimum guarantee option embedded in equity-linked life insurance policies under uncertainty of randomness and fuzziness. The future lifetime of the insured is modelled as a random variable and the asset price evolution is described using a fuzzy binomial-tree model. In order to deal with both randomness and fuzziness, we model the present value of liabilities as a fuzzy random variable. Our results can be used by the actuary to understand the incidence of the minimum guarantee on the premium and to define the appropriate coverage strategies. A numerical example illustrates how our methodology works. (C) 2017 Elsevier Inc. All rights reserved.
In this work we introduce a new flexible fuzzy GARCH model for conditional density estimation. The model combines two different types of uncertainty, namely fuzziness or linguistic vagueness, and probabilistic uncertainty. The probabilistic uncertainty is modeled through a GARCH model while the fuzziness or linguistic vagueness is presented in the antecedent and combination of the rule base system. The fuzzy GARCH model under study allows for a linguistic interpretation of the gradual changes in the output density, providing a simple understanding of the process. Such a system can capture different properties of data, such as fat tails, skewness and multimodality in one single model. This type of models can be useful in many fields such as macroeconomic analysis, quantitative finance and risk management. The relation to existing similar models is discussed, while the properties, interpretation and estimation of the proposed are provided. The model performance is illustrated in simulated time series data exhibiting complex behavior and a real data application of volatility forecasting for the S&P 500 daily returns series.
Rough set theory and fuzzy set theory are two useful mathematical tools for dealing with uncertainty and granularity in information systems. Motivated by the studies of roughness and fuzziness in algebraic systems and partially ordered sets such as semigroups, rings and lattices, in this paper we introduce first the notions of fuzzy (prime, semi-prime, primary) ideals of quantales and investigate their properties. Several characterizations of such ideals are presented. Then, we introduce the concepts of weak fuzzy prime ideals and strong fuzzy prime ideals of quantales, and establish relationships between these ideals and fuzzy prime ideals of quantales. By applying rough set theory to fuzzy ideals of quantales, we furthermore define rough fuzzy (prime, semi-prime, primary) ideals of quantales, generalizing Yang and Xu’s work on quantales to the fuzzy environment. Finally, relationships between the upper (resp. lower) rough fuzzy ideals of quantales and the upper (resp. lower) approximations of their homomorphic images are also discussed.
Multiple attribute decision making forms an important part of the decision process for both small (individual) and large (organization) problems. When available information is precise, many methods exist to solve this problem. But the uncertainty and fuzziness inherent in the structure of information make rigorous mathematical models inappropriate for solving this type of problems. This paper incorporates the fuzzy set theory and the basic nature of subjectivity due to the ambiguity to achieve a flexible decision approach suitable for uncertain and fuzzy environment. The proposed method can take both real and fuzzy inputs. An outranking intensity is introduced to determine the degree of overall outranking between competing alternatives, which are represented by fuzzy numbers. Numerical examples finally illustrate the approach.
We present a new approach for defining similarity measures for Atanassov's intuitionistic fuzzy sets (AIFS), in which a similarity measure has two components indicating the similarity and hesitancy aspects. We justify that there are at least two facets of uncertainty of an AIFS, one of which is related to fuzziness while other is related to lack of knowledge or non-specificity. We propose a set of axioms and build families of similarity measures that avoid counterintuitive examples that are used to justify one similarity measure over another. We also investigate a relation to entropies of AIFS, and outline possible application of our method in decision making and image segmentation.
We consider a multi-objective linear programming model with type-2 fuzzy objectives. The considered model has the flexibility for the user to specify the more general membership functions for objectives to reflect the inherent fuzziness, while being simple and practical. We develop two solution strategies with reasonable computing costs. The additional cost, as compared to the type-1 fuzzy model, is indeed insignificant. These two algorithms compute Pareto optimal solutions of the type-2 problems, one being based on a maxmin approach and the other on aggregating the objectives. Finally, applying the proposed algorithms, we work out two illustrative examples.
The Main objective of this contribution is to develop information about how entropy measures of linguistic terms can be designed. Two different ideas have been put forward to explain this designation: (1) The idea that comes from the seminal definition of fuzziness measure; (2) The idea of transforming similarity measures to entropy ones. To demonstrate the utility and effectiveness of the proposed entropy measures, an entropy-based approach of determining objective weights of attributes is developed to solve multiple attribute decision-making problems in the context of linguistic term sets. (C) 2016 Elsevier Inc. All rights reserved.