Upper and lower regression models (dual possibilistic models) are proposed for data analysis with crisp inputs and interval or fuzzy outputs. Based on the given data, the dual possibilistic models can be derived from upper and lower directions, respectively, where the inclusion relationship between these two models holds. Thus, the inherent uncertainty existing in the given phenomenon can be ap...

AbstructTraditionally, prototype-based fuzzy clustering algorithms such as the Fuzzy C Means (FCM) algorithm have been used to find “compact” or “filled” clusters. Recently, there have been attempts to generalize such algorithms to the case of hollow or “shell-like” clusters, i.e., clusters that lie in subspaces of feature space. The shell clustering approach provides a powerful means to solve ...

We have already formalized several models of the possibilistic linear regression analysis, where it is assumed that possibilistic parameters are non-interactive, i.e., the joint possibilistic distribution of parameters is defined by minimum operators. In this paper, we will deal with the interactive case in which quadratic membership functions defined by A. Celmins are considered. With the same...

Unsupervised fuzzy clustering algorithms are one of many approaches used in image segmentation. The Fuzzy C-means algorithm (FCM) and the Possibilistic C-means algorithm (PCA) have been widely used. There is also the generalized possibilistic algorithm (GPCA). GPCA was proposed recently and is a general form of the previous algorithms. These clustering algorithms can be trapped to the local opt...

This paper is a first step in the direction of extending possibilistic planning to take advantage of the expressive power and reasoning capabilities of fuzzy description logics. Fuzzy description logics are used to describe knowledge about the world and about actions. Fundamental definitions are given and the possibilistic planning problem is recast in this new setting.

This paper deals in a preliminary way with the problem of clustering of three-way data. A method of the problem solving is based on the application of a direct possibilistic clustering algorithm based on the concept of allotment among fuzzy cluster to a matrix of feeble fuzzy tolerance, which represent a structure of the set of objects under uncertainty. The paper provides the description of ba...

This article proposes a novel approach to ranking fuzzy numbers based on WLUPM ( weighted lower and upper possibilistic means ). At first, by using this significance, we will compose WIVPM ( weighted intervalvalue possibilistic mean ), that this interval can be used as a crisp set approximation with respect to a fuzzy quantity. Therefore, with that, we define a method for ordering. This method ...

In 2001 Carlsson and Fullér introduced the possibilistic mean value, variance and covariance of fuzzy numbers. In 2002 Fullér and Majlender introduced the notations of crisp weighted possibilistic mean value, variance and covariance of fuzzy numbers, which are consistent with the extension principle. In this paper we will show some (normative) properties of possibility distributions.

The solution of the prediction problem is presented for the finite possibilistic modelling [3,4,6,7]. A recurrent variant of finite possibilistic models is considered. In this variant, we define the regularization condition for constructing a quasi-optimal estimator of fuzzy transition operator (FTO). We construct the discrete recurrent extremal fuzzy process with possibilistic uncertainty, the...