Fuzzy Inference with Schemes for Guaranteeing Convexity and Symmetricity in Consequences Based on α-Cuts

Author(s):  
Kiyohiko Uehara ◽  
◽  
Takumi Koyama ◽  
Kaoru Hirota ◽  

A fuzzy inference method is proposed on the basis of α-cuts, which can mathematically prove to deduce consequences in both convex and symmetric forms under the required conditions, studied here, when fuzzy sets in the consequent parts of fuzzy rules are all convex and symmetric. The inference method can reflect the distribution forms of fuzzy sets in consequent parts of fuzzy rules, guaranteeing the convexity in deduced consequences. It also has a control scheme for the fuzziness and specificity in deduced consequences. The controllability provides a way to suppress excessive fuzziness increase and specificity decrease in deduced consequences. Simulation studies show that the proposed method can deduce consequences in convex and symmetric forms under the required conditions. It is also demonstrated that the distribution forms of consequent parts are reflected to deduced consequences. Moreover, it is found that the fuzziness and specificity of deduced consequences can be effectively controlled in the simulations.

Author(s):  
Kiyohiko Uehara ◽  
◽  
Shun Sato ◽  
Kaoru Hirota ◽  

An inference method is proposed for sparse fuzzy rules on the basis of interpolations at a number of points determined by α-cuts of given facts. The proposed method can perform nonlinear mapping even with sparse rule bases when each given fact activates a number of fuzzy rules which represent nonlinear relations. The operations for the nonlinear mapping are exactly the same as for the case when given facts activate no fuzzy rules due to the sparseness of rule bases. Such nonlinear mapping cannot be provided by conventional methods for sparse fuzzy rules. In evaluating the proposed method, mean square errors are adopted to indicate difference between deduced consequences and fuzzy sets transformed by nonlinear fuzzy-valued functions to be represented with sparse fuzzy rules. Simulation results show that the proposed method can follow the nonlinear fuzzy-valued functions. The proposed method contributes to both reducing the number of fuzzy rules and providing nonlinear mapping with sparse rule bases.


Author(s):  
Kiyohiko Uehara ◽  
◽  
Kaoru Hirota ◽  

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.


Author(s):  
KAI MENG TAY ◽  
CHEE PENG LIM

An important and difficult issue in designing a Fuzzy Inference System (FIS) is the specification of fuzzy sets and fuzzy rules. In this paper, two useful qualitative properties of the FIS model, i.e., the monotonicity and sub-additivity properties, are studied. The monotonic sufficient conditions of the FIS model with Gaussian membership functions are further analyzed. The aim is to incorporate the sufficient conditions into the FIS modeling process, which serves as a simple (which can be easily understood by domain users), easy-to-use (which can be easily applied to or can be a part of the FIS model), and yet reliable (which has a sound mathematical foundation) method to preserve the monotonicity property of the FIS model. Another aim of this paper is to demonstrate how these additional qualitative information can be exploited and extended to be part of the FIS designing procedure (i.e., for fuzzy sets and fuzzy rules design) via the sufficient conditions (which act as a set of useful governing equations for designing the FIS model). The proposed approach is able to avoid the "trial and error" procedure in obtaining a monotonic FIS model. To assess the applicability of the proposed approach, two practical problems are examined. The first is an FIS-based model for water level control, while the second is an FIS-based Risk Priority Number (RPN) model in Failure Mode and Effect Analysis (FMEA). To further illustrate the importance of the sufficient conditions as the governing equations, an analysis on the consequences of violating the sufficient conditions of the FIS-based RPN model is presented.


2015 ◽  
Vol 25 (3) ◽  
pp. 377-396
Author(s):  
N. Sozhamadevi ◽  
S. Sathiyamoorthy

Abstract A new type Fuzzy Inference System is proposed, a Probabilistic Fuzzy Inference system which model and minimizes the effects of statistical uncertainties. The blend of two different concepts, degree of truth and probability of truth in a unique framework leads to this new concept. This combination is carried out both in Fuzzy sets and Fuzzy rules, which gives rise to Probabilistic Fuzzy Sets and Probabilistic Fuzzy Rules. Introducing these probabilistic elements, a distinctive probabilistic fuzzy inference system is developed and this involves fuzzification, inference and output processing. This integrated approach accounts for all of the uncertainty like rule uncertainties and measurement uncertainties present in the systems and has led to the design which performs optimally after training. In this paper a Probabilistic Fuzzy Inference System is applied for modeling and control of a highly nonlinear, unstable system and also proved its effectiveness.


Author(s):  
Kiyohiko Uehara ◽  
◽  
Kaoru Hirota ◽  

A connection admission control (CAC) method is proposed for asynchronous transfer mode (ATM) networks by applying the fuzzy inference and learning algorithm of neural networks. In order to guarantee the allowed cell loss ratio (CLR) in CAC, the upper bound of CLR must be used as the criterion for judging whether an incoming call can be accepted or not. For estimating the upper bound of CLR from observed CLR data, fuzzy inference, based on a weighted mean of fuzzy sets, is adopted. This inference method can effectively estimate the possibility distribution of CLR by applying the error back-propagation algorithm with the proposed energy functions in learning and provide the upper bound of CLR efficiently from the distribution. A self-compensation mechanism for estimation errors is also provided, which is simple enough to work in real time by taking advantage of the fuzzy inference method adopted. Fuzzy rules in the area with no observed data are generated by extrapolation from adjacent fuzzy rules in the area with observed data. This increases the multiplex gain, thereby guaranteeing the allowed CLR as much as possible. The simulation results show the feasibility of the proposed CAC method.


METIK JURNAL ◽  
2020 ◽  
Vol 4 (2) ◽  
pp. 76-82
Author(s):  
Dominggus Norvindes Dellas ◽  
Ika Purnamasari ◽  
Nanda Arista Rizki

The decision-making process using a fuzzy inference system (FIS) logic can use one of the methods called the Tsukamoto method. The process carried out in this method is the same as the fuzzy method in general, namely the formation of fuzzy sets, the fuzzification process, defuzzification, and measuring the accuracy of the result. The purpose of this study was to apply the Tsukamoto method to predict the yield of oil palm production at PT. Waru Kaltim Plantation. Based on the analysis using the Tsukamoto method, 36 fuzzy rules were obtained for each data from February 2013 to December 2015. The prediction results of palm oil production in 2013 did not change, except for May and August. In February, March, June, and August 2014 the level of production is constant, and almost throughout 2015, there was constant. The predicted MAPE for oil palm production was 31,522%, or in the fairly good category.


This work presents the comparison study between neural super-twisting sliding mode control (NSTSM) and adaptive-network-based fuzzy inference system-STSM (ANFIS-STSM) algorithm of the doubly fed induction generator (DFIG) controlled by direct power control (DPC). The mathematical model of the three-phase DFIG has been described. The descriptions of the DPC strategy, NSTSM and the ANFIS-STSM algorithm have been presented. The DPC strategy with NSTSM and ANFIS-STSM has been described. The simulation studies of the DPC strategy with intelligent STSM algorithms have been performed, and the results of these studies are presented and discussed.


This work presents the comparison study between neural super-twisting sliding mode control (NSTSM) and adaptive-network-based fuzzy inference system-STSM (ANFIS-STSM) algorithm of the doubly fed induction generator (DFIG) controlled by direct power control (DPC). The mathematical model of the three-phase DFIG has been described. The descriptions of the DPC strategy, NSTSM and the ANFIS-STSM algorithm have been presented. The DPC strategy with NSTSM and ANFIS-STSM has been described. The simulation studies of the DPC strategy with intelligent STSM algorithms have been performed, and the results of these studies are presented and discussed


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