Inference Based on α-Cut and Generalized Mean in Representing Fuzzy-Valued Functions

Uehara, Kiyoji; Koyama, Takumi; Hirota, Kaoru

doi:10.20965/jaciii.2010.p0581

J. Adv. Comput. Intell. Intell. Inform.

2010

DOI: 10.20965/jaciii.2010.p0581

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Inference Based on α-Cut and Generalized Mean in Representing Fuzzy-Valued Functions

Kiyoji Uehara¹,

Takumi Koyama²,

Kaoru Hirota³

Abstract: It is mathematically proved that inference based on α-cuts and generalized mean (α-GEMII) deduces consequences converging to fuzzy sets mapped by linear fuzzy-valued functions, to be represented with α-GEMII, as the number of fuzzy rules increases. The proof indicates that α-GEMII satisfies axiomatic properties and can contribute to presenting interpretability in designing fuzzy systems in the rule base. Such properties do not hold in conventional methods based on the compositional rule of inference. Simulatio… Show more

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Cited by 3 publications

References 22 publications

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Inference with Fuzzy Rule Interpolation at an Infinite Number of Activating Points

Uehara¹,

Hirota²

2015

J. Adv. Comput. Intell. Intell. Inform.

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An inference method for sparse fuzzy rules is proposed which interpolates fuzzy rules at an infinite number of activating points and deduces consequences based on α-GEMII (α-level-set and generalized-mean-based inference). The activating points, proposed in this paper, are determined so as to activate interpolated fuzzy rules by each given fact. The proposed method is named α-GEMINAS (α-GEMII-based inference with fuzzy rule interpolation at an infinite number of activating points). α-GEMINAS solves the problem in infinite-level interpolation where fuzzy rules are interpolated at the least upper and greatest lower bounds of an infinite number of α-cuts of each given fact. The infinite-level interpolation can nonlinearly transform the shapes of given membership functions to those of deduced ones in accordance even with sparse fuzzy rules under some conditions. These conditions are, however, strict from a practical viewpoint. α-GEMINAS can deduce consequences without these conditions and provide nonlinear mapping comparable with infinite-level interpolation. Simulation results demonstrate these properties of α-GEMINAS. Thereby, it is found that α-GEMINAS is practical and applicable to a wide variety of fields.

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Inference with Fuzzy Rule Interpolation at an Infinite Number of Activating Points

Uehara¹,

Hirota²

2015

J. Adv. Comput. Intell. Intell. Inform.

View full text Add to dashboard Cite

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Fuzzy Inference: Its Past and Prospects

Uehara¹,

Hirota²

2017

J. Adv. Comput. Intell. Intell. Inform.

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Fuzzy inference in the past and its future prospects are described to further promote research in the field: First, the basic methods of fuzzy inference are introduced. Then, the progress of fuzzy inference is reviewed, showing its remarkable achievements, especially in industries. A consideration of fuzzy inference is presented from operational viewpoints. It provides a key to creating fuzzy-inference methods in the future. The growing research area of fuzzy inference is also introduced in order to discuss a current direction, reflecting the consideration mentioned above. Moreover, some future prospects on fuzzy inference are presented, which are expected to stimulate research.

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Fuzzy Inference Based on α-Cuts and Generalized Mean: Relations Between the Methods in its Family and their Unified Platform

Uehara¹,

Hirota²

2017

JACIII

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This paper clarifies the relations in properties and structures between fuzzy inference methods based on α-cuts and the generalized mean. The group of the inference methods is named the α-GEM (α-cut and generalized-mean-based inference) family. A unified platform is proposed for the inference methods in the α-GEM family by the effective use of the above-mentioned relations. For the unified platform, a criterion is made clear to uniquely determine the value of a parameter in fuzzy-constraint propagation control for facts given by singletons. Moreover, conditions are derived to make the inference methods in the α-GEM family equivalent to singleton-consequent-type fuzzy inference which has been successfully applied to a wide variety of fields. Thereby, the unified platform can contribute to the construction of an inference engine for both the methods in the α-GEM family and singleton-consequent-type fuzzy inference. Such scheme of the inference engine provides an effective way to make these inference methods transformed into each other in learning for selecting the inference methods as well as for optimizing fuzzy rules.

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Inference Based on α-Cut and Generalized Mean in Representing Fuzzy-Valued Functions

Cited by 3 publications

References 22 publications

Inference with Fuzzy Rule Interpolation at an Infinite Number of Activating Points

Inference with Fuzzy Rule Interpolation at an Infinite Number of Activating Points

Fuzzy Inference: Its Past and Prospects

Fuzzy Inference Based on α-Cuts and Generalized Mean: Relations Between the Methods in its Family and their Unified Platform

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