International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

We propose and examine a simple notion of translation in first order logics to give a basis to similarity-based fuzzy logic.

A fuzzy multi-objective decision-making with nonlinear membership functions is proposed in this paper by assuming that the decision maker has a fuzzy goal for each objective function. The fuzzy goals can be quantified by convex polyhedral membership functions, which are expressed by linguistic terms. The concept of the convex cone is used to formulate a normalized convex polyhedral penalty function, which can also be considered conversely as a convex polyhedral membership function. The most desirable value of membership functions are selected to be reference membership values of achievement of convex polyhedral membership functions that can be viewed as the extension of the idea of reference point method. The formulated model can be solved by existing linear programming solvers and can find the satisficing solution for the decision maker, which can be derived efficiently from among an M-Pareto optimal solution set together with the trade-off rates between the membership functions. The proposed model uses convex polyhedral membership functions to represent vague aspirations of the decision maker. It enriches the existing satisficing methods for fuzzy multi-objective linear programming in a more practical way with the effective method based on convex cone.

The classification of multivariate time-varying data finds application in several fields, such as economics, finance, marketing research, psychometrics, bioinformatics, medicine, signal processing, pattern recognition, etc. In this paper, by considering an exploratory formalization, we propose different unsupervised clustering models for multivariate data time arrays (objects×quantitative variables×times). These models can be classified in two different approaches: the cross sectional and the longitudinal approach. In the first case, after the objects, observed at each time, have been classified, comparison among the classifications made in different time instants will be done. In the second approach, we cluster the time trajectories of the objects; then, we obtain only one classification by comparing the instantaneous and evolutive features of the trajectories of the objects. In particular, in this work, the second approach is analyzed in detail, with reference to the so-called single and double step procedures. Geometric, correlative, instantaneous, evolutive and trend characteristics of the multivariate time arrays are taken into account in the different proposed clustering models. Furthermore, the fuzzy approach, that is particularly suitable in the dynamic classification problem, has been considered. Extensions of a cluster-validity criterion for the proposed fuzzy dynamic clustering models are also suggested. A socio-economic example concludes the paper.

In the present paper, the author introduces the notion of fuzzy IC-bags and does some characterizations of them. The concepts of fuzzy base sets, base equivalent fuzzy IC-Bags, cardinally equispaced fuzzy IC-Bags, and cardinally equivalent fuzzy IC-Bags have been developed. The types of peak elements, and the concerned types of peak membership grades have been discussed. It is observed that the collection of any particular type of peak elements together with their membership grades actually form fuzzy bags. A set of operations on fuzzy IC-Bags have been defined and some propositions have been proved. We note that under the conditions of uncertainty, where the counts of objects are not fixed, then the interval counts can occur with different fuzzy membership grades for each particular object in the collection, and the framework for fuzzy IC-Bags provides us with the opportunity to justify and model the organized complexity as a part of the associated intolerance embedded in the subjective patterns.

In this paper, a computational system is developed that estimates a survival curve and a point estimate when very few data are available and a high proportion of the data are censored. Standard statistical methods require a more complete data set. With any less data expert knowledge or heuristic methods are required. The system uses numerical methods to define fuzzy membership functions about each data point that quantify uncertainty due to censoring. The "fuzzy" data is then used to estimate a survival curve and the mean survival time is calculated from the curve. The new estimator converges to the Product-Limit estimator when a complete data set is available. In addition, this method allows for the incorporation of expert knowledge. Finally, simulation results are provided to demonstrate the performance of the new method and its improvement over the Product-Limit estimator.

A fuzzy variable is a function from a possibility space to the set of real numbers, while a bifuzzy variable is a function from a possibility space to the set of fuzzy variables. In this paper, a concept of chance distribution is originally presented for bifuzzy variable, and the linearity of expected value operator of bifuzzy variable is proved. Furthermore, bifuzzy simulations are designed and illustrated by some numerical experiments.

Intuitionistic fuzzy sets are a generalization of ordinary fuzzy sets which are characterized by a membership function and a non-membership function. In this paper we consider the problem of ranking a set of intuitionistic fuzzy numbers. We adopt a statistical viewpoint and interpret each intuitionistic fuzzy number as an ensemble of ordinary fuzzy numbers. This enables us to define a fuzzy rank and a characteristic vagueness factor for each intuitionistic fuzzy number. We show the reasonablesness of the results obtained by examining several test cases.

In this paper we present the definition and properties of intuitionistic fuzzy implication operators. We study the expression obtained from said operators when fuzzy implication and coimplication operators are applied to different aggregations of degrees of truth and non-truth of the propositions.

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.