International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

The subject of this paper is a generalized approach to relative scalar cardinalities of fuzzy sets. In the main part of the paper, we discuss basic properties of triangular norm-based relative cardinality such as valuation property, the cartesian product rule and complementary rule. Examples of cardinalities satisfying those properties are also given.

The Fuzzy-Product-Limit Estimator (FPLE) is a method for estimating a survival curve and the mean survival time when very few data are available and a high proportion of the data are censored. Considering censored times as vague failure times, the censored values are represented by fuzzy membership functions that represent a belief of continued survival of the associated unit. Associated with any estimate is uncertainty. With the FPLE two distinct types of uncertainty exist in the estimate, the uncertainty due to the randomness in the recorded times and the vague uncertainty in the failure of the censored units. This paper addresses the problem of providing confidence bounds and estimates of uncertainty for the FPLE. Several methods for estimating the vague uncertainty in the estimator are suggested. Among them are the use of Efron's Bootstrap that obtains a confidence interval of the FPLE to quantify random uncertainty and produces an empirical distribution that is used to quantify properties of the vague uncertainty. Also, a method to obtain a graphical representation of the random and vague uncertainties is developed. The new methods provide confidence intervals that quantify statistical uncertainty as well as the vague uncertainty in the estimates. Finally, results of simulations are provided to demonstrate the efficacy of the estimator and uncertainty in the estimates.

In this paper we propose the new extended class of t-norm operators called the boundary weak. The aim of the extension of this operator is that the sum of the fuzzy numbers in the arithmetic based on such t-norm gives the more narrow fuzzy number if compared to arithmetic based on standard t-norm. This extension is based on the replacement of the condition T(x,1)=x by the weaker one: T(x,1)≤x, for x∈[0,1].

The aim of this paper is to o study the evolution of positive HIV population for manifestation of AIDS, the Acquired Immunodeficiency Syndrome.

For this purpose, we suggest a methodology to combine a macroscopic HIV positive population model with an individual microscopic model. The first describes the evolution of the population whereas the second the evolution of HIV in each individual of the population. This methodology is suggested by the way that experts use to conduct public policies, namely, to act at the individual level to observe and verify the manifest population.

The population model we address is a differential equation system whose transference rate from asymptomatic to symptomatic population is found through a fuzzy rule-based system. The transference rate depends on the CD4+ level, the main T lymphocyte attacked by the HIV retrovirus when it reaches the bloodstream. The microscopic model for a characteristic individual in a population is used to obtain the CD4+ level at each time instant. From the CD4+ level, its fuzzy initial value, and the macroscopic population model, we compute the fuzzy values of the proportion of asymptomatic population at each time instant t using the extension principle. Next, centroid defuzzification is used to obtain a solution that represents the number of infected individuals. This approach provides a method to find a solution of a non-autonomous differential equation from an autonomous equation, a fuzzy initial value, the extension principle, and center of gravity defuzzification. Simulation experiments show that the solution given by the method suggested in this paper fits well to AIDS population data reported in the literature.

Independence relations play an important role in uncertain reasoning based on Bayesian networks. In particular, they are useful in decomposing joint distributions into more elementary local ones. Recently, in a possibility theory framework, several qualitative independence relations have been proposed, where uncertainty is encoded by means of a complete pre-order between states of the world. This paper studies the well-known graphoid properties of these qualitative independences. Contrary to the probabilistic independence, several qualitative independence relations are not necessarily symmetric. Therefore, we also analyze the symmetric counterparts of graphoid properties (called reverse graphoid properties).

In this paper, we concentrate on two kinds of fuzzy linear programming problems: linear programming problems with only fuzzy resource variables and linear programming problems in which both the resource variables and the technological coefficients are fuzzy numbers. We consider here only the case of fuzzy numbers with modified s-curve membership functions. We propose here the modified s-curve membership function as a methodology for fuzzy linear programming and use it for solving these problems. We also compare the new proposed method with non-fuzzy linear programming optimization method. Finally, we provide real life application examples in production planning and their numerical solutions.

This section is maintained by Vladik Kreinovich. Please send your abstracts (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.