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

2017 ◽  
Vol 21 (4) ◽  
pp. 597-615
Author(s):  
Kiyohiko Uehara ◽  
Kaoru Hirota ◽  
◽  
Keyword(s):  
Fuzzy Inference ◽  
Constraint Propagation ◽  
Inference Engine ◽  
Fuzzy Rules ◽  
Fuzzy Constraint ◽  
Generalized Mean ◽  
Effective Use ◽  
Inference Methods

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.

Multi-Level Control of Fuzzy-Constraint Propagation via Evaluations with Linguistic Truth Values in Generalized-Mean-Based Inference

2016 ◽  
Vol 20 (2) ◽  
pp. 355-377 ◽  
Author(s):  
Kiyohiko Uehara ◽  
◽  
Kaoru Hirota ◽  
Keyword(s):  
Fuzzy Sets ◽  
Level Set ◽  
Constraint Propagation ◽  
Fuzzy Rules ◽  
Truth Values ◽  
Fuzzy Constraints ◽  
Control Scheme ◽  
Fuzzy Constraint ◽  
Generalized Mean ◽  
Α Level

A method is proposed for fuzzy inference which can propagate convex fuzzy-constraints from given facts to consequences in various forms by applying a number of fuzzy rules, particularly when asymmetric fuzzy sets are used for given facts and/or fuzzy rules. The conventionalmethod, α-GEMS (α-level-set and generalized-mean-based inference in synergy with composition), cannot be performed with asymmetric fuzzy sets; it can be conducted only with symmetric fuzzy sets. In order to cope with asymmetric fuzzy sets as well as symmetric ones, a control scheme is proposed for the fuzzy-constraint propagation, which is α-cut based and can be performed independently at each level of α. It suppresses an excessive specificity decrease in consequences, particularly stemming from the asymmetricity. Thereby, the fuzzy constraints of given facts are reflected to those of consequences, to a feasible extent. The theoretical aspects of the control scheme are also presented, wherein the specificity of the support sets of consequences is evaluated via linguistic truth values (LTVs). The proposed method is named α-GEMST (α-level-set and generalized-meanbased inference in synergy with composition via LTV control) in order to differentiate it from α-GEMS. Simulation results show that α-GEMST can be properly performed, particularly with asymmetric fuzzy sets. α-GEMST is expected to be applied to the modeling of given systems with various fuzzy input-output relations.

Multi-Level Control of Fuzzy-Constraint Propagation in Inference Based on α-Cuts and Generalized Mean

2013 ◽  
Vol 17 (4) ◽  
pp. 647-662 ◽  
Author(s):  
Kiyohiko Uehara ◽  
◽  
Kaoru Hirota ◽  
Keyword(s):  
Fuzzy Sets ◽  
Level Set ◽  
Constraint Propagation ◽  
Fuzzy Rules ◽  
Nonlinear Mapping ◽  
Fuzzy Input ◽  
Fuzzy Constraint ◽  
Multi Level ◽  
Generalized Mean ◽  
Α Level

An inference method is proposed, which can perform nonlinear mapping between convex fuzzy sets and present a scheme of various fuzzy-constraint propagation from given facts to deduced consequences. The basis of nonlinear mapping is provided by α-GEMII (α-level-set and generalized-mean-based inference) whereas the control of fuzzy-constraint propagation is based on the compositional rule of inference (CRI). The fuzzy-constraint propagation is controlled at the multi-level of α in its α-cut-based operations. The proposed method is named α-GEMS (α-level-set and generalized-mean-based inference in synergy with composition). Although α-GEMII can perform the nonlinear mapping according to a number of fuzzy rules in parallel, it has limitations in the control of fuzzy-constraint propagation and therefore has difficulty in constructing models of various given systems. In contrast, CRI-based inference can rather easily control fuzzy-constraint propagation with high understandability especially when a single fuzzy rule is used. It is difficult, however, to perform nonlinear mapping between convex fuzzy sets by using a number of fuzzy rules in parallel. α-GEMS can solve both of these problems. Simulation results show that α-GEMS is performed well in the nonlinear mapping and fuzzy-constraint propagation. α-GEMS is expected to be applied to modeling of given systems with various fuzzy input-output relations.

Inference with Governing Schemes for Propagation of Fuzzy Convex Constraints Based on α-Cuts

2009 ◽  
Vol 13 (3) ◽  
pp. 321-330 ◽  
Author(s):  
Kiyohiko Uehara ◽  
◽  
Takumi Koyama ◽  
Kaoru Hirota ◽  
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Constraint Propagation ◽  
Convex Constraints ◽  
Inference Method ◽  
Self Tuning ◽  
Fuzzy Constraint ◽  
Generalized Mean

A governing scheme is proposed for fuzzy constraint propagation from given facts to consequences in convex forms, which is applied to the inference method based on α-cuts and generalized mean. The governing is performed by self-tuning which can reflect the distribution forms of fuzzy sets in consequent parts to the forms of deduced consequences. Thereby, the proposed scheme can solve the problems in the conventional inference based on the compositional rule of inference that deduces fuzzy sets with excessive fuzziness increase and specificity decrease. In simulations, it is confirmed that the proposed scheme can effectively perform the constraint propagation from given facts to consequences in convex forms while reflecting fuzzy-set distributions in consequent parts. It is also demonstrated that consequences are deduced without excessively large fuzziness and small specificity.

Fuzzy Inference Methods Employing T-norm with Threshold and Their Implementation

2003 ◽  
Vol 7 (3) ◽  
pp. 362-369 ◽  
Author(s):  
Bui Cong Cuong ◽  
◽  
Nguyen Hoang Phuong ◽  
Ho Khanh Le ◽  
Bui Truong Son ◽  
...  
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Inference ◽  
Inference Engine ◽  
Fuzzy Inference Engine ◽  
Reasoning Systems ◽  
Different Types ◽  
The Many ◽  
Inference Methods

The fuzzy inference engine is an important part of reasoning systems. Among the many different types of inference, MATLAB is a powerful tool including many useful toolboxes, one of which is the Fuzzy Logic Toolbox. To improve toolbox capacity, we programmed and installed several new inference methods.

scholarly journals Classification with Fuzzification Optimization Combining Fuzzy Information Systems and Type-2 Fuzzy Inference

2021 ◽  
Vol 11 (8) ◽  
pp. 3484
Author(s):  
Martin Tabakov ◽  
Adrian Chlopowiec ◽  
Adam Chlopowiec ◽  
Adam Dlubak
Keyword(s):  
Fuzzy Inference ◽  
Real Data ◽  
Fuzzy Rules ◽  
Fuzzy Information ◽  
Benchmark Data ◽  
System A ◽  
Footprint Of Uncertainty ◽  
Interval Type ◽  
Derived Rules

In this research, we introduce a classification procedure based on rule induction and fuzzy reasoning. The classifier generalizes attribute information to handle uncertainty, which often occurs in real data. To induce fuzzy rules, we define the corresponding fuzzy information system. A transformation of the derived rules into interval type-2 fuzzy rules is provided as well. The fuzzification applied is optimized with respect to the footprint of uncertainty of the corresponding type-2 fuzzy sets. The classification process is related to a Mamdani type fuzzy inference. The method proposed was evaluated by the F-score measure on benchmark data.

scholarly journals Aplikasi Pengambilan Keputusan dengan Metode Tsukamoto pada Penentuan Tingkat Kepuasan pelanggan

CAUCHY ◽  
2015 ◽  
Vol 4 (1) ◽  
pp. 10 ◽  
Author(s):  
Venny Riana Riana Agustin ◽  
Wahyu Henky Irawan
Keyword(s):  
Decision Making ◽  
Fuzzy Logic ◽  
Fuzzy Inference ◽  
Weighted Average ◽  
Fuzzy Rules ◽  
Quality Of Services ◽  
Inference System ◽  
A Value ◽  
Fuzzy Logic Analysis

Tsukamoto method is one method of fuzzy inference system on fuzzy logic for decision making. Steps of the decision making in this method, namely fuzzyfication (process changing the input into kabur), the establishment of fuzzy rules, fuzzy logic analysis, defuzzyfication (affirmation), as well as the conclusion and interpretation of the results. The results from this research are steps of the decision making in Tsukamoto method, namely fuzzyfication (process changing the input into kabur), the establishment of fuzzy rules by the general form IF a is A THEN B is B, fuzzy logic analysis to get alpha in every rule, defuzzyfication (affirmation) by weighted average method, as well as the conclusion and interpretation of the results. On customers at the case, in value of 16 the quality of services, the value of 17 the quality of goods, and value of 16 a price, a value of the results is 45,29063 and the level is low satisfaction

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