International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

We study a construction method for binary aggregation operators that generalizes the classical composition. Several examples are given, specially, in the class of aggregation operators with neutral element 1, e.g. semicopulas and copulas.

An important issue when using the OWA aggregation operators is the determination of weights. One approach is to link the weights to a desired attitudinal character for the aggregation. The ME-OWA operators provide a pioneering example of this approach. Here we first present an alternative approach to generating OWA weights with a desired attitudinal character. We accomplish this by using a family of recursive OWA operators (R-OWA). We then generalize this with a class that allows of OWA aggregation by iteration (It-OWA). Both families are built with the constraint of keeping constant the attitudinal character at any recursion or any iteration step. This is particularly useful in aggregations that sequentially add arguments to the aggregation.

Inference problems are one of the main research topics in the artificial intellect field. So far there have been various inference systems, some of them have been applied in fuzzy control according to their feature. In 1989, the concept of truth-valued flow inference was introduced by Wang¹, and its mathematical theory of truth-valued flow inference was set up by Wang² in 1995. In this paper, aimed at the real meaning of the truth-valued in the truth-valued flow inference, we introduce the concepts of the inner product truth-valued and inner product truth-valued flow inference, and analyze some inference algorithms of fuzzy control at present in detail. We reveal that the fuzzy inference algorithms in fuzzy control at present are all regarded as inner product truth-valued flow inference algorithm. Finally, inner product truth-valued flow inference approach is generalized in the multiple inputs and single output.

This paper explores Heilpern's notions of fuzzy mapping and the fixed point theorem for fuzzy mappings. The fixed point theorem for fuzzy mappings as introduced by Heilpern has been generalized and some characterizations are done in this context.

In this paper, by using Sengupta and Pal's method of comparison of interval numbers and a new set of arithmetic operations for interval numbers, we propose a theory for the study of arithmetic operations on interval numbers.

In real world applications, the databases are constantly added with a large number of transactions and hence maintaining latest sequential patterns valid on the updated database is crucial. Existing data mining algorithms can incrementally mine the sequential patterns from databases with binary values. Temporal transactions with quantitative values are commonly seen in real world applications. In addition, several methods have been proposed for representing uncertain data in a database. In this paper, a fuzzy data mining algorithm for incremental mining of sequential patterns from quantitative databases is proposed. Proposed algorithm called IQSP algorithm uses the fuzzy grid notion to generate fuzzy sequential patterns validated on the updated database containing the transactions in the original database and in the incremental database. It uses the information about sequential patterns that are already mined from original database and avoids start-from-scratch process. Also, it minimizes the number of candidates to check as well as number of scans to original database by identifying the potential sequences in incremental database.

This paper proposes an adaptive network architecture, which can emulate the human knowledge as the fuzzy logic rule, and its applications as the controller for nonlinear systems. The structure of this proposed network, multi-input Fuzzy Rule Emulated Network or FREN, is derived based on human knowledge in the form of fuzzy IF-THEN rules. The initial setting of its parameters can be intuitively chosen from expert's experience. During the learning phase based on the gradient search, the learning rate can be adapted itself to remain the stability with the Lyapunov method. The performance of our network is presented by using this network as controller for the single invert pendulum plant and the water bath temperature control system. The comparison results with other conventional control algorithms such as artificial neural networks and PID controllers can be illustrated in each example.

Neural networks are good at representing functions or data transformations. However just as in the case of the biological brain the mathematical description of the data transformation is hidden. In the case of the human brain the transformation, in terms of rules, may be extracted by interviewing the person, In the case of the artificial neural network other approaches have to be utilized.

In the case described here a second neural network that represents the transformation in terms of fuzzy rules is trained using gradient descent. The parameters that are learned are the parameters of the fuzzy sets and also the connection weights in [0,1] between the outputs of the membership function units and the final output units. There is an output unit for each rule and consequent membership function. The fuzzy output set with the highest membership value is taken to be the output fuzzy set. The extracted rules are of the form if x₀ is Small or x₀ is Medium and x₁ is Large or x₁ is Medium then y is Large. x₀ and x₁ are inputs and y is the output.

The cost measure consists of several terms indicating how close the actual output is to a target output, how close the weights are to 0 and 1, and how close the output of membership values is to a 1 of n vector. The cost measure is a linear combination of these individual terms. By changing the constant multipliers the relative importance of the cost measures can be changed and studied.

The method has been tried on randomly generated feedforward neural networks and also on data produced by functions with specific properties. The fizzy network is trained using data produced by the feedforward neural network or the known function. This method can also be used in extracting rules such as control rules implicitly used by a human if input and output data is gathered from the human.

This section is maintained by Vladik Kreinovich. Please send your abstracts (or copies of papers that you want to see reviewed here) to vladik@utep.edu, or by regular mail to: VLADIK KREINOVICH, Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA.