International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

As we know that human intellectual activities are performed by the use of language; a human being thinks and reasons with language. In this paper, we propose a new simulation method which imitates human information processing based on the use of language. — An ordinary simulation method uses mathematical equations to estimate the future trends of a dynamic system, however, we propose a new simulation method which uses a model consists of natural language, which is called a linguistic model. A linguistic model does not have a fixed structure, but the structure of the model itself will be generated so that model should become the most appropriate model to estimate the future behavior of a dynamic system. We regard that human intellectual activities such as thinking, reasoning, etc. are also texts realized by context as well as a linguistic text is done by context. We show a human linguistic reasoning model generation with an example of forecast of foreign exchange rate (FER) changes.

We re-take the possibilistic model for information sources recently put forward by the first author, as opposed to the standard probabilistic models of information theory. Based on an interpretation of possibilistic source coding inspired by utility functions, we define a notion of possibilistic entropy for a suitable class of interactive possibilistic sources, and compare it with the possibilistic entropy of stationary non-interactive sources. Both entropies have a coding-theoretic nature, being obtained as limit values for the rates of optimal compression codes. We list properties of the two entropies, which might support their use as measures of "possibilistic ignorance".

The need for monotone approximation of scattered data often arises in many problems of regression, when the monotonicity is semantically important. One such domain is fuzzy set theory, where membership functions and aggregation operators are order preserving. Least squares polynomial splines provide great flexbility when modeling non-linear functions, but may fail to be monotone. Linear restrictions on spline coefficients provide necessary and sufficient conditions for spline monotonicity. The basis for splines is selected in such a way that these restrictions take an especially simple form. The resulting non-negative least squares problem can be solved by a variety of standard proven techniques. Additional interpolation requirements can also be imposed in the same framework. The method is applied to fuzzy systems, where membership functions and aggregation operators are constructed from empirical data.

The Analytic Hierarchy Process provides the decision maker with a method for improving the consistency of pairwise comparison matrices. Although it is one of the most commonly used method it presents some disadvantages related generally with the consistency problem. The purpose of this paper is to provide an alternative method for improving consistency and show how it can be applied to pairwise comparison matrices. The contribution to this method and also its limitations are shown at the end.

This work presents a fuzzy TOPSIS model under group decisions for solving the facility location selection problem, where the ratings of various alternative locations under different subjective attributes and the importance weights of all attributes are assessed in linguistic values represented by fuzzy numbers. The objective attributed are transformed into dimensionless indices to ensure compatibility with the linguistic ratings of the subjective attributes. Furthermore, the membership function of the aggregation of the ratings and weights for each alternative location versus each attribute can be developed by interval arithmetic and α-cuts of fuzzy numbers. The ranking method of the mean of the integral values is applied to help derive the ideal and negative-ideal fuzzy solutions to complete the proposed fuzzy TOPSIS model. Finally, a numerical example demonstrates the computational process of the proposed model.

This paper provide a formal fuzzy object inference model to solve the following four significant drawbacks identified in extant fuzzy rule-based languages. First, they have difficulty in handling composite objects as a unit of inference. Second, they don't support fuzzy reasoning which is semantically easy to understand and conceptually simple to use. Third, their knowledge representation and reasoning style have a great semantic gap with those of current database models in syntax and semantics. Finally, they do not provide a comprehensive framework in treating uncertainties. In this paper, we demonstrate that the proposed model naturally models a target application environment in terms of composite objects possibly containing uncertain information, and successfully performs a fuzzy inference between them. To practically model the environment, we use the constructs of ICOT (Integrated C-Object Tool) extended for well implementing the structural semantics of the proposed model.

In this paper, we propose a method to calculate the correlation coefficient of fuzzy numbers by means of "α-cut". This value obtained from our formula tells us not only the strength of relationship between the fuzzy numbers, but also whether the fuzzy numbers are positively or negatively related. This approach looks better than previous methods which only evaluate the strength of the relation. Furthermore, we extend the "α-cut" method to interval-valued fuzzy numbers. The value of the correlation coefficient between interval-valued fuzzy numbers lies in the interval [-1, 1], as computed from our formula.

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