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In this paper a methodology is developed to control linear and nonlinear processes using a fuzzy approach with the main assumption that the output of the process is monotone with respect to the input. Beginning with an empty rule base, a fuzzy model is on-line built. The rule base has a fixed number of rules determined à priori and not depending on the complexity of the process. The controller ...

This paper continues the study of the connection between hyper- groups and fuzzy sets, investigating the length of the sequence of join spaces associated with a hypergroup. The classes of complete hypergroups and of 1-hypergroups are considered and analyzed in this context. Finally, we give a method to construct a nite hypergroup with the strong fuzzy grade equal to a given natural number

The aim of this paper is the study of the sequence of join spacesand fuzzy subsets associated with a hypergroupoid. In thispaper we give some properties of the membership function$widetildemu_{otimes}$ corresponding to the direct pro-duct oftwo hypergroupoids and we determine the fuzzy grade of thehypergroupoid $langle Htimes H, otimesrangle$ in a particularcase.

In this study, we consider two different inequivalent formulations of the logistic difference equation $x_{n+1}= beta x_n(1- x_n), n=0,1,..., $ where $x_n$ is a sequence of fuzzy numbers and $beta$ is a positive fuzzy number. The major contribution of this paper is to study the existence, uniqueness and global behavior of the solutions for two corresponding equations, using the concept of Huku...

Nanda 1 studied sequence of fuzzy numbers and showed that the set of all convergent sequences of fuzzy numbers form a complete metric space. Nuray 2 proved the inclusion relations between the set of statistically convergent and lacunary statistically convergent sequences of fuzzy numbers. Kwon and Shim 3 studied statistical convergence and lacunary statistical convergence of sequences of fuzzy ...

The paper considers a particular family of fuzzy monotone set–valued stochastic processes. The proposed setting allows us to investigate suitable α-level sets of such processes, modeling birth–and–growth processes. A decomposition theorem is established to characterize the nucleation and the growth. As a consequence, different consistent set–valued estimators are studied for growth process. Mor...

One of the most classical results in Ramsey theory is the theorem of Erdős and Szekeres from 1935, which says that every sequence of more than k numbers contains a monotone subsequence of length k + 1. We address the following natural question motivated by this result: Given integers k and n with n > k + 1, how many monotone subsequences of length k + 1 must every sequence of n numbers contain?...

In this paper, we introduce a kernel for monotone data derived from the Choquet integral with its underlying fuzzy measure. While a naïve computation of this kernel has a complexity that is exponential in the number of data attributes, we propose a more efficient approach with quadratic time complexity. Kernel PCA and SVM classification are employed to illustrate characteristics and benefits of...

In this paper experiments are described with three linguistic fuzzy models sharing the same monotone rule base and the same membership functions for the two input variables, but applying different membership functions in the output domain. We investigated which inference methods result in a monotonic input-output behaviour. Apart from the conventional Mamdani–Assilian inference method with Cent...