Displaying similar documents to “Computing with words with the use of inverse RDM models of membership functions”

Fuzzy-arithmetic-based Lyapunov synthesis in the design of stable fuzzy controllers: A computing-with-words approach

Changjiu Zhou (2002)

International Journal of Applied Mathematics and Computer Science

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A novel approach to designing stable fuzzy controllers with perception-based information using fuzzy-arithmetic-based Lyapunov synthesis in the frame of computing with words (CW) is presented. It is shown that a set of conventional fuzzy control rules can be derived from the perception-based information using the standard-fuzzy-arithmetic-based Lyapunov synthesis approach. On the other hand, a singleton fuzzy controller can be devised by using a constrained-fuzzy-arithmetic-based Lyapunov...

A New Approach to Fuzzy Arithmetic

Popov, Antony (2010)

Serdica Journal of Computing

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This work shows an application of a generalized approach for constructing dilation-erosion adjunctions on fuzzy sets. More precisely, operations on fuzzy quantities and fuzzy numbers are considered. By the generalized approach an analogy with the well known interval computations could be drawn and thus we can define outer and inner operations on fuzzy objects. These operations are found to be useful in the control of bioprocesses, ecology and other domains where data uncertainties exist. ...

A new definition of the fuzzy set

Andrzej Piegat (2005)

International Journal of Applied Mathematics and Computer Science

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The present fuzzy arithmetic based on Zadeh's possibilistic extension principle and on the classic definition of a fuzzy set has many essential drawbacks. Therefore its application to the solution of practical tasks is limited. In the paper a new definition of the fuzzy set is presented. The definition allows for a considerable fuzziness decrease in the number of arithmetic operations in comparison with the results produced by the present fuzzy arithmetic.

Fuzzy numbers, definitions and properties.

Miguel Delgado, José Luis Verdegay, M. Amparo Vila (1994)

Mathware and Soft Computing

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Two different definitions of a Fuzzy number may be found in the literature. Both fulfill Goguen's Fuzzification Principle but are different in nature because of their different starting points. The first one was introduced by Zadeh and has well suited arithmetic and algebraic properties. The second one, introduced by Gantner, Steinlage and Warren, is a good and formal representation of the concept from a topological point of view. The objective of this paper is...

A context-based approach to linguistic hedges

Martine De Cock, Etienne Kerre (2002)

International Journal of Applied Mathematics and Computer Science

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We present a framework of L-fuzzy modifiers for L being a complete lattice. They are used to model linguistic hedges that act on linguistic terms represented by L-fuzzy sets. In the modelling process the context is taken into account by means of L-fuzzy relations, endowing the L-fuzzy modifiers with a clear inherent semantics. To our knowledge, these L-fuzzy modifiers are the first ones proposed that are suitable to perform this representation task for a lattice L different from the...

The Formal Construction of Fuzzy Numbers

Adam Grabowski (2014)

Formalized Mathematics

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In this article, we continue the development of the theory of fuzzy sets [23], started with [14] with the future aim to provide the formalization of fuzzy numbers [8] in terms reflecting the current state of the Mizar Mathematical Library. Note that in order to have more usable approach in [14], we revised that article as well; some of the ideas were described in [12]. As we can actually understand fuzzy sets just as their membership functions (via the equality of membership function...