Rough sets are efficient for data pre-process in data mining. Lower and upper approximations are two core concepts of rough sets. This paper studies generalized rough sets based on symmetric and transitive relations from the operator-oriented view by matroidal approaches. We firstly construct a matroidal structure of generalized rough sets based on symmetric and transitive relations, and provide an approach to study the matroid induced by a symmetric and transitive relation. Secondly, this paper establishes a close relationship between matroids and generalized rough sets. Approximation quality and roughness of generalized rough sets can be computed by the circuit of matroid theory. At last, a symmetric and transitive relation can be constructed by a matroid with some special properties.

This paper investigates value function approximation in the context of zero-sum Markov games, which can be viewed as a generalization of the Markov decision process (MDP) framework to the two-agent case. We generalize error bounds from MDPs to Markov games and describe generalizations of reinforcement learning algorithms to Markov games. We present a generalization of the optimal stopping problem to a two-player simultaneous move Markov game. For this special problem, we provide stronger bounds and can guarantee convergence for LSTD and temporal difference learning with linear value function approximation. We demonstrate the viability of value function approximation for Markov games by using the Least squares policy iteration (LSPI) algorithm to learn good policies for a soccer domain and a flow control problem.

We use princiles of fuzzy logic to develop a general model representing several processes in a system's operation characterized by a degree of vagueness and/or uncertainy. Further, we introduce three altenative measures of a fuzzy system's effectiveness connected to the above model. An applcation is also developed for the Mathematical Modelling process illustrating our results.

Results are presented on the performance of Adaptive Neuro-Fuzzy Inference system (ANFIS) for wind velocity forecasts in the Isthmus of Tehuantepec region in the state of Oaxaca, Mexico. The data bank was provided by the meteorological station located at the University of Isthmus, Tehuantepec campus, and this data bank covers the period from 2008 to 2011. Three data models were constructed to carry out 16, 24 and 48 hours forecasts using the following variables: wind velocity, temperature, barometric pressure, and date. The performance measure for the three models is the mean standard error (MSE). In this work, performance analysis in short-term prediction is presented, because it is essential in order to define an adequate wind speed model for eolian parks, where a right planning provide economic benefits.

In this paper, first we present a new explanation for the relation between logical circuits and artificial neural networks, logical circuits and fuzzy logic, and artificial neural networks and fuzzy inference systems. Then, based on these results, we propose a new neuro-fuzzy computing system which can effectively be implemented on the memristor-crossbar structure. One important feature of the proposed system is that its hardware can directly be trained using the Hebbian learning rule and without the need to any optimization. The system also has a very good capability to deal with huge number of input-out training data without facing problems like overtraining.

Case Based Reasoning (CBR) is an intelligent way of thinking based on experience and capitalization of already solved cases (source cases) to find a solution to a new problem (target case). Retrieval phase consists on identifying source cases that are similar to the target case. This phase may lead to erroneous results if the existing knowledge imperfections are not taken into account. This work presents a novel solution based on Fuzzy logic techniques and adaptation measures which aggregate weighted similarities to improve the retrieval results. To confirm the efficiency of our solution, we have applied it to the industrial diagnosis domain. The obtained results are more efficient results than those obtained by applying typical measures.

In this paper secured wireless communication using fuzzy logic based high speed public key cryptography (FLHSPKC) has been proposed by satisfying the major issues likes computational safety, power management and restricted usage of memory in wireless communication. Wireless Sensor Network (WSN) has several major constraints likes inadequate source of energy, restricted computational potentiality and limited memory. Though conventional Elliptic Curve Cryptography (ECC) which is a sort of public key cryptography used in wireless communication provides equivalent level of security like other existing public key algorithm using smaller parameters than other but this traditional ECC does not take care of all these major limitations in WSN. In conventional ECC consider Elliptic curve point p, an arbitrary integer k and modulus m, ECC carry out scalar multiplication kP mod m, which takes about 80% of key computation time on WSN. In this paper proposed FLHSPKC scheme provides some novel strategy including novel soft computing based strategy to speed up scalar multiplication in conventional ECC and which in turn takes shorter computational time and also satisfies power consumption restraint, limited usage of memory without hampering the security level. Performance analysis of the different strategies under FLHSPKC scheme and comparison study with existing conventional ECC methods has been done.

Rough set theory is a useful tool to deal with uncertain, granular and incomplete knowledge in information systems. And it is based on equivalence relations or partitions. Matroid theory is a structure that generalizes linear independence in vector spaces, and has a variety of applications in many fields. In this paper, we propose a new type of matroids, namely, partition-circuit matroids, which are induced by partitions. Firstly, a partition satisfies circuit axioms in matroid theory, then it can induce a matroid which is called a partition-circuit matroid. A partition and an equivalence relation on the same universe are one-to-one corresponding, then some characteristics of partition-circuit matroids are studied through rough sets. Secondly, similar to the upper approximation number which is proposed by Wang and Zhu, we define the lower approximation number. Some characteristics of partition-circuit matroids and the dual matroids of them are investigated through the lower approximation number and the upper approximation number.

We look at the problem of revising fuzzy belief bases, i.e., belief base revision in which both formulas in the base as well as revision-input formulas can come attached with varying truth-degrees. Working within a very general framework for fuzzy logic which is able to capture a variety of types of inference under uncertainty, such as truth-functional fuzzy logics and certain types of probabilistic inference, we show how the idea of rational change from 'crisp' base revision, as embodied by the idea of partial meet revision, can be faithfully extended to revising fuzzy belief bases. We present and axiomatise an operation of partial meet fuzzy revision and illustrate how the operation works in several important special instances of the framework.

The aim of this research is to develop a reasoning under uncertainty strategy in the context of the Fuzzy Inductive Reasoning (FIR) methodology. FIR emerged from the General Systems Problem Solving developed by G. Klir. It is a data driven methodology based on systems behavior rather than on structural knowledge. It is a very useful tool for both the modeling and the prediction of those systems for which no previous structural knowledge is available. FIR reasoning is based on pattern rules synthesized from the available data. The size of the pattern rule base can be very large making the prediction process quite difficult. In order to reduce the size of the pattern rule base, it is possible to automatically extract classical Sugeno fuzzy rules starting from the set of pattern rules. The Sugeno rule base preserves pattern rules knowledge as much as possible. In this process some information is lost but robustness is considerably increased. In the forecasting process either the pattern rule base or the Sugeno fuzzy rule base can be used. The first option is desirable when the computational resources make it possible to deal with the overall pattern rule base or when the extracted fuzzy rules are not accurate enough due to uncertainty associated to the original data. In the second option, the prediction process is done by means of the classical Sugeno inference system. If the amount of uncertainty associated to the data is small, the predictions obtained using the Sugeno fuzzy rule base will be very accurate. In this paper a mixed pattern/fuzzy rules strategy is proposed to deal with uncertainty in such a way that the best of both perspectives is used. Areas in the data space with a higher level of uncertainty are identified by means of the so-called error models. The prediction process in these areas makes use of a mixed pattern/fuzzy rules scheme, whereas areas identified with a lower level of uncertainty only use the Sugeno fuzzy rule base. The proposed strategy is applied to a real biomedical system, i.e., the central nervous system control of the cardiovascular system.