International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

Weighted logics are important tools for reasoning under uncertain knowledge. A weighted knowledge base is a set of weighted formulas of the form (φ_i, α_i) where φ_i is a propositional formula and α_i is the certainty degree associated with φ_i. This paper addresses two issues in the possibility theory framework: i) how to compare two weighted knowledge bases with respect to their information contents? and ii) how to syntactically define the concept of forgetting variables? We show that comparing knowledge bases is the counterpart of the concept of the specificity relation defined between possibility distributions.

The well-known Boolean-law “α → (β → α) = 1” can be generalized to fuzzy context as I(x, I(y, x)) = 1, where I is a fuzzy implication. In this paper we show the necessary and sufficient conditions under which this generalization holds in fuzzy logics. We focus the investigation on the following classes of fuzzy implication: (S,N)-, R-, QL-, D- and (N, T)-implications. In addition, we demonstrate that a fuzzy implication I satisfies such Boolean-like law if, and only if, its Ф-conjugate also satisfies it.

Covering rough set theory is an important generalization of traditional rough set theory. So far, the studies on covering generalized rough sets mainly focus on constructing different types of approximation operations. However, little attention has been paid to uncertainty measurement in covering cases. In this paper, a new kind of partial order is proposed for coverings which is used to evaluate the uncertainty measures. Consequently, we study uncertain measures like roughness measure, accuracy measure, entropy and granularity for covering rough set models which are defined by neighborhoods and friends. Some theoretical results are obtained and investigated.

In this paper we consider Steffensen's integral inequality for the Sugeno integral

The paper considers the usefulness of a control strategy based on a fuzzy relational model of the controller to counteract uncertainties caused by measurement noise and unmeasured disturbances. The fuzzy relational model is identified using a combination of feedback error learning and fuzzy identification. An important feature of the resulting fuzzy relational model is that it will generate a fuzzy output in the presence of uncertainties. Two causes of uncertainty are considered separately, the first cause of uncertainty is due to the noise on the sensor measuring the controlled variable and the second one is an unmeasured input disturbance. Results are presented that show that the fuzzy control signal is representative of the uncertainties and that conditional defuzzification can then be used to improve the control performance by reducing the control activity.

Outliers may have many anomalous causes, for example, credit card fraud, cyberintrusion or breakdown of a system. Several research areas and application domains have investigated this problem. The popular fuzzy c-means algorithm is sensitive to noise and outlying data. In contrast, the possibilistic partitioning methods are used to solve these problems and other ones. The goal of this paper is to introduce cluster algorithms for partitioning a set of symbolic interval-type data using the possibilistic approach. In addition, a new way of measuring the membership value, according to each feature, is proposed. Experiments with artificial and real symbolic interval-type data sets are used to evaluate the methods. The results of the proposed methods are better than the traditional soft clustering ones.

In recent years, tremendous amounts of data streams are generated in different application areas. The new challenges in these data need fast and online data processing, especially in classification problems. One of the most challenging problems in field of data streams that reduces the performance of traditional methods is concept change. To handle this problem, it is necessary to update the classifier system after every alteration of the concept of data. However, updating a classifier can often be a time consuming and expensive process. In this paper, an efficient method is proposed for quickly and easily updating of a fuzzy rule-based classifier by setting a weight for each rule. Then, two online procedures for online adjustment of the rule weights are proposed. The experimental results show the high performance of these methods against a non-weighted approach.

In this paper, several useful inequalities for uncertain variables are proved. A Borel-Cantelli lemma for uncertain measures is obtained and some convergence theorems for continuous uncertain measures are derived. Finally, these theorems are applied to compute the uncertainty distribution of Liu integral. We prove that the uncertain integral of a deterministic function with respect to a Liu process has a normal uncertainty distribution.

For intuitionistic fuzzy values (IFVs), there are more or less some drawbacks in the existing comparison methods, so it is necessary for us to develop a more proper technique for comparing or ranking IFVs in this paper. To do so, we first formalize an IFV as a fuzzy subset in order to analyze the fuzzy meaning of an IFV, and then according to the basic properties of the fuzzy subset, we determine the dominance relation (order relation) between two IFVs by defining a dominance degree. In order to explain the feasibility of the dominance relations, we validate the monotonicity of intuitionistic fuzzy operational laws, and additionally, we improve and prove the monotonicity of several intuitionistic fuzzy aggregation operators on the basis of the dominance relations. Because it is of importance for some practical problems (e.g., intuitionistic fuzzy multi-attribute decision making) to rank IFVs, we finally develop a method for ranking IFVs by constructing a dominance matrix based on the dominance degrees. A simple example is taken to illustrate the validity of our ranking method.