Reasoning system with fuzzy uncertainty

This paper focuses on a fuzzy reasoning method based on a generalized If-Then rule. Firstly, the antecedent and the consequent of an If-Then rule are considered and expressed as a component of a kind of binary L-type fuzzy relation on the product of the universes of discourse and the range of definition for a certain fuzzy attribute. Then a generalized extension principle based on this L-type fuzzy relation (FR-GEP) is constructed. Moreover, the paper gives a detailed description of this generalized If-Then rule using 20 well-known common implication operators in the framework of the composition of L-type fuzzy relations. Consequently, an L-type binary fuzzy reasoning method based on this generalized If-Then rule is established according to FR-GEP.

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“…(1)-(3) are straightforward. We only prove (4) and (6). (5) and (7) can be proved in the same way as (4) and (6).…”

Section: Remarkmentioning

confidence: 88%

“…then B ! ͑y, ␤͒ ϭ ∨ xʦX ͕͓A* ‫ؠ‬ R* ‫ؠ‬ B*͔ Ϫ ͑y, x͒∧A͑x, ␤͖͒ ϭ ∨ xʦProjX͑A͒ A͑x, ␤͒ ϭ O Proof of(6).If A ϭ A, then Proj L ( A) ϭ A. The conclusion is obvious.…”

mentioning

confidence: 91%

Fuzzy reasoning based on generalized fuzzy If-Then rules

Liu

Ruan

et al. 2002

Int. J. Intell. Syst.

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“…Using this approach significantly reduces the number of rules in the knowledge base while maintaining a relatively high level of compliance when mapping the input variables. The concept of fuzzy models was originally created for the needs of fuzzy logic control (FLC) and was derived from control theory based on mathematical models of the open-loop process to be controlled [29]. Their essence boils down to the realisation of the following inference: one or more crisp numerical values appear on the system input, and an inference engine using a knowledge model sets the value of one or more output values, which are also crisp numerical values.…”

Section: Problem Formulationmentioning

confidence: 99%

Knowledge-based methods for cost estimation of metal casts

Macioł

2016

Int J Adv Manuf Technol

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The aim of the research presented in this paper was to verify the hypothesis that the problem of estimating the variable costs of metal casts can be solved by using knowledge-based systems. The estimation of variable costs determines the adequate pricing of products, which is a crucial marketing problem in enterprises. The problem of estimating the direct costs is especially important in companies whose participation in the market is defined as versatile manufacturing. This problem was the target of many studies presented in this paper. The assumptions that the direct costs of a metal cast are dependent on the physical features of the cast and the most effective method of cost estimation is an intuitive qualitative technique based on a rule-based system were considered. The nature of the relationships between the casts' features and the direct costs of production could be effectively formed by experts as reasoning rules. In this paper, the results of experiments conducted on the basis of the example of the production program of a foundry that manufactures water-system fittings is presented. Three methods of knowledge-definition and reasoning techniques were examined: the classical method of crisp reasoning, fuzzy reasoning with the Mamdani's method, and fuzzy reasoning with the Takagi-Sugeno model. Proper experiments were conducted. The results of the experiments confirmed the hypothesis, which allows the assessment of different reasoning methods.A. Maciol

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“…Since 1973, a series of fuzzy reasoning theories and methods have been proposed from various points of views. 1,3,4,7,21,22,23,25,26 There has been no concern until now about fuzzy reasoning methods directly based on Zadeh's extension principle 6,14 in all these research works about fuzzy reasoning. It is well known that Zadeh's extension principle plays a very important role in fuzzy set theory.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy reasoning based on the extension principle

Kerre

Ruan

et al. 2001

Int. J. Intell. Syst.

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Ž. According to the operation of decomposition also known as representation theorem Ž . Negoita CV, Ralescu, DA. Kybernetes 1975;4:169᎐174 in fuzzy set theory, the whole fuzziness of an object can be characterized by a sequence of local crisp properties of that object. Hence, any fuzzy reasoning could also be implemented by using a similar idea, i.e., a sequence of precise reasoning. More precisely, we could translate a fuzzy relation ''If A Ž then B'' of the Generalized Modus Ponens Rule the most common and widely used interpretation of a fuzzy rule, A, B, are fuzzy sets in a universe of discourse X, and of . Ž . discourse Y, respectively into a corresponding precise relation between a subset of P X Ž . and a subset of P Y , and then extend this corresponding precise relation to two kinds of transformations between all L-type fuzzy subsets of X and those of Y by using Zadeh's extension principle, where L denotes a complete lattice. In this way, we provide an alternative approach to the existing compositional rule of inference, which performs fuzzy reasoning based on the extension principle. The approach does not depend on the choice of fuzzy implication operator nor on the choice of a t-norm. The detailed reasoning methods, applied in particular to the Generalized Modus Ponens and the Generalized Modus Tollens, are established and their properties are further investigated in this paper. ᮊ

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Reasoning system with fuzzy uncertainty

Cited by 6 publications

References 17 publications

Fuzzy reasoning based on generalized fuzzy If-Then rules

Fuzzy reasoning based on generalized fuzzy If-Then rules

Knowledge-based methods for cost estimation of metal casts

Fuzzy reasoning based on the extension principle

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