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Computing with words with the use of inverse RDM models of membership functions

100%
Piegat A., Pluciński M.
International Journal of Applied Mathematics and Computer Science
|
2015
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tom 25
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nr 3
675-688
EN
Computing with words is a way to artificial, human-like thinking. The paper shows some new possibilities of solving difficult problems of computing with words which are offered by relative-distance-measure RDM models of fuzzy membership functions. Such models are based on RDM interval arithmetic. The way of calculation with words was shown using a specific problem of flight delay formulated by Lotfi Zadeh. The problem seems easy at first sight, but according to the authors' knowledge it has not been solved yet. Results produced with the achieved solution were tested. The investigations also showed that computing with words sometimes offers possibilities of achieving better problem solutions than with the human mind.
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Imposing restrictions on density functions utilised in computing with words

100%
Gemeinder M.
International Journal of Applied Mathematics and Computer Science
|
2002
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tom 12
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nr 3
383-390
EN
Applying the generalised extension principle within the area of Computing with Words typically leads to complex maximisation problems. If distributed quantities-such as, e.g., size distributions within human populations-are considered, density functions representing these distributions become involved. Very often the optimising density functions do not resemble those found in nature; for instance, an optimising density function could consist of two single Dirac pulses positioned near the opposite bounds of the interval limiting the possible values of the quantity considered. Therefore, in this article, density functions with certain shapes which enable us to overcome this lack of resemblance are considered. Furthermore, some considerations on solving the resulting maximisation problems are reported.
3
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Synthesis and evaluation analysis of the indicator information in nuclear safeguards applications by computing with words

100%
Liu J., Ruan D., Carchon R.
International Journal of Applied Mathematics and Computer Science
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2002
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tom 12
|
nr 3
449-462
EN
This paper aims at the handling and treatment of nuclear safeguard relevant information by using a linguistic assessment approach. This is based on a hierarchical analysis of a State's nuclear activities in a multi-layer structure of the evaluation model. After a hierarchical analysis of the State's nuclear activities on the basis of the IAEA Physical Model, the addressed objective is divided into several less complex levels. The overall evaluation can be obtained step by step from those lower levels. Special emphasis is put on the synthesis and evaluation analysis of the Physical Model indicator information. Accordingly, the aggregation process with the consideration of the different kinds of qualitative criteria is in focus. Especially, the symbolic approach is considered by the direct computation on linguistic values instead of the approximation approach using the associated membership function. In this framework, several kinds of ordinal linguistic aggregation operators are presented and analyzed. The application of these linguistic aggregation operators to the combination of the Physical Model indicator information is provided. An example is given to support and clarify the mathematical formalism.
4
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An architecture for making judgments using computing with words

88%
Mendel J. M.
International Journal of Applied Mathematics and Computer Science
|
2002
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tom 12
|
nr 3
325-335
EN
Our thesis is that computing with words needs to account for the uncertainties associated with the meanings of words, and that these uncertainties require using type-2 fuzzy sets. Doing this leads to a proposed architecture for making it judgments by means of computing with words, i.e., to a perceptual computer-the Per-C. The Per-C includes an encoder, a type-2 rule-based fuzzy logic system, and a decoder. It lets all human-computer interactions be performed using words. In this paper, a quantitative language is established for the Per-C, and many open issues about the perceptual computer are described.
5
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Computing with words and life data

88%
Grzegorzewski P., Hryniewicz O.
International Journal of Applied Mathematics and Computer Science
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2002
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tom 12
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nr 3
337-345
EN
The problem of statistical inference on the mean lifetime in the presence of vague data is considered. Situations with fuzzy lifetimes and an imprecise number of failures are discussed.
6
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Fuzzy-arithmetic-based Lyapunov synthesis in the design of stable fuzzy controllers: A computing-with-words approach

63%
Zhou C.
International Journal of Applied Mathematics and Computer Science
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2002
|
tom 12
|
nr 3
411-421
EN
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 synthesis approach. Furthermore, the stability of the fuzzy controllers can be guaranteed by means of the fuzzy version of Lyapunov stability analysis. Moreover, by introducing standard and constrained fuzzy arithmetic in CW, the 'words' represented by fuzzy numbers could be efficiently manipulated to design fuzzy controllers. The results obtained are illustrated with the design of stable fuzzy controllers for an autonomous pole balancing mobile robot.
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