Jerry Mendel - Profile on Academia.edu (original) (raw)

Papers by Jerry Mendel

In this paper, we present solutions to Zadeh's challenge problem on calculating linguistic probab... more In this paper, we present solutions to Zadeh's challenge problem on calculating linguistic probabilities. First, we argue that Zadeh's solution to this problem via the Generalized Extension Principle is very difficult to implement. Then, we use a syllogism based on the entailment principle to interpret the problem so that it can be solved by calculation of pessimistic (lower) and optimistic (upper) probabilities via Linguistic Weighted Averages. We use a pessimistic and an optimistic compatibility measure to calculate such probabilities. Then, we choose vocabularies for heights and linguistic probabilities that are involved in the problem statement. The vocabularies are modeled using interval type-2 fuzzy sets. We calculate optimistic (upper) and pessimistic (lower) probabilities, which naturally would be interval type-2 fuzzy sets. Finally, we map the pessimistic and optimistic probabilities into linguistic probabilities present in the vocabularies, so that the results can be comprehended by a human. We investigate viable alternatives for the pessimistic and optimistic compatibility measures, and also solve a similar problem with a different hypothesis.

IEEE Transactions on Fuzzy Systems, Apr 1, 2020

This paper provides a novel and better understanding of the performance potential of a nonsinglet... more This paper provides a novel and better understanding of the performance potential of a nonsingleton (NS) fuzzy system over a singleton (S) fuzzy system. It is done by extending sculpting the state space works from S to NS fuzzification and demonstrating uncertainties about measurements, modeled by NS fuzzification: first, fire more rules more often, manifested by a reduction (increase) in the sizes of first-order rule partitions for those partitions associated with the firing of a smaller (larger) number of rulesthe coarse sculpting of the state space; second, this may lead to an increase or decrease in the number of type-1 (T1) and interval type-2 (IT2) first-order rule partitions, which now contain rule pairs that can never occur for S fuzzification-a new rule crossover phenomenon-discovered using partition theory; and third, it may lead to a decrease, the same number, or an increase in the number of second-order rule partitions, all of which are system dependentthe fine sculpting of the state space. The authors' conjecture is that it is the additional control of the coarse sculpting of the state space, accomplished by prefiltering and the max-min (or max-product) composition, which provides an NS T1 or IT2 fuzzy system with the potential to outperform an S T1 or IT2 system when measurements are uncertain.

This paper provides an answer to the question that the type-2 fuzzy logic community is now asking... more This paper provides an answer to the question that the type-2 fuzzy logic community is now asking: "What comes after interval type-2 fuzzy logic systems (IT2 FLSs)?" It demonstrates, through a geometrical understanding of the type-reduced set, that logical next steps in the progression from type-1 to interval type-2 to type-2 FLSs are quasi-T2 FLSs, either an interconnection of a T1 FLS and an IT2 FLS, or an interconnection of two IT2 FLSs, in which both FLSs are designed simultaneously. The quasi-T2 FLSs overcome the computational difficulties that are associated with set theoretic operations and type-reduction (TR) for general T2 FSs and FLSs, because all set theoretic operations can be performed as in existing T1 or IT2 FLSs, and because TR for an IT2 FLS can be performed using existing KM Algorithms.

International Journal of Applied Mathematics and Computer Science, 2002

Per-C. The Per-C includes an encoder, a type-2 rulebased fuzzy logic system, and a decoder. It le... more Per-C. The Per-C includes an encoder, a type-2 rulebased 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.

Signal Processing, Jun 1, 2000

In this paper we focus on model-based statistical signal processing and how some problems that ar... more In this paper we focus on model-based statistical signal processing and how some problems that are associated with it can be solved using fuzzy logic. We explain how uncertainty (which is prevalent in statistical signal processing applications) can be handled within the framework of fuzzy logic. Type-1 singleton and non-singleton fuzzy logic systems (FLSs) are reviewed. Type-2 FLSs, which are relatively new, and are very appropriate for signal processing problems, because they can handle linguistic and numerical uncertainties, are overviewed in some detail. The output of a type-2 FLS is a type-2 fuzzy set. Using a new operation called type-reduction, the type-2 set can be reduced to a type-1 set } the type-reduced set } which plays the role of a con"dence interval for linguistic uncertainties. No such result can be obtained for a type-1 FLS. We demonstrate, by means of examples, that a type-2 FLS can outperform a type-1 FLS for one-step prediction of a Mackey}Glass chaotic time series whose measurements are corrupted by additive noise, and equalization of a nonlinear time-varying channel. 2000 Elsevier Science B.V. All rights reserved. In diesem Artikel setzen wir den Schwerpunkt auf modellbasierte statistische Signalverarbeitung und zeigen MoK glichkeiten zur LoK sung von Problemen dieses Umfeldes mit Hilfe der Fuzzy Logik auf. Wir erlaK utern, wie Entscheidungsunsicherheit (die in saK mtlichen Anwendunger der statistischen Signalverarbeitung vorherrscht) im Rahmen der Fuzzy Logik behandelt werden kann. ZunaK chst werden Typ-1 Singleton und Nicht-Singleton Fuzzy Logik Systeme (FLS) besprochen. Typ-2 FLS, die relativ neu sind, werden etwas detaillierter behandelt. Sie eignen sich sehr zur LoK sung von Signalverarbeitungsproblemen, da sie linguistische und numerische Unsicherheit handhaben koK nnen. Die Ausgabe eines Typ-2 FLS stellt die Typ-2 Fuzzy-Menge dar. Mit Hilfe einer neuen, als Typ-Reduktion bezeichneten Operation, kann die Typ-2 Menge auf eine Typ-1 Menge } die Typ-reduzierte Menge } uK berfuK hrt werden. Sie entspricht einem Kon"denzintervall fuK r linguistische Unsicherheit. Kein derartiges Resultat kann fuK r eine Typ-1 FLS abgeleitet werden. Anhand von Beispielen zeigen wir, da{ eine Typ-2 FLS eiher Typ-1 FLS zum einen als Einschritt-PraK diktion uK berlegen sein kann, wenn, sie auf eine chaotische Mackey}Glass Zeitreihe angwandt wird, deren Me{werte durch additives Rauschen gestoK rt sind oder wenn sie zum anderen bei der Entzerrung eines nichtlinearen zeitvarianten Kanals angewandt wird. 2000 Elsevier Science B.V. All rights reserved. Dans cet article, nous nous concentrons sur le traitement statisque de signaux a`base de mode`les et sur la fac7 on dont certains proble`mes qui lui sont associeH s peuvent e( tre reH solus en utilisant de la logique #oue. Nous expliquons comment

arXiv (Cornell University), Jul 2, 2019

Interval type-2 (IT2) fuzzy systems have become increasingly popular in the last 20 years. They h... more Interval type-2 (IT2) fuzzy systems have become increasingly popular in the last 20 years. They have demonstrated superior performance in many applications. However, the operation of an IT2 fuzzy system is more complex than that of its type-1 counterpart. There are many questions to be answered in designing an IT2 fuzzy system: Should singleton or non-singleton fuzzifier be used? How many membership functions (MFs) should be used for each input? Should Gaussian or piecewise linear MFs be used? Should Mamdani or Takagi-Sugeno-Kang (TSK) inference be used? Should minimum or product t-norm be used? Should type-reduction be used or not? How to optimize the IT2 fuzzy system? These questions may look overwhelming and confusing to IT2 beginners. In this paper we recommend some representative starting choices for an IT2 fuzzy system design, which hopefully will make IT2 fuzzy systems more accessible to IT2 fuzzy system designers.

arXiv (Cornell University), Jun 1, 2019

There have been different strategies to improve the performance of a machine learning model, e.g.... more There have been different strategies to improve the performance of a machine learning model, e.g., increasing the depth, width, and/or nonlinearity of the model, and using ensemble learning to aggregate multiple base/weak learners in parallel or in series. This paper proposes a novel strategy called patch learning (PL) for this problem. It consists of three steps: 1) train an initial global model using all training data; 2) identify from the initial global model the patches which contribute the most to the learning error, and train a (local) patch model for each such patch; and, 3) update the global model using training data that do not fall into any patch. To use a PL model, we first determine if the input falls into any patch. If yes, then the corresponding patch model is used to compute the output. Otherwise, the global model is used. We explain in detail how PL can be implemented using fuzzy systems. Five regression problems on 1D/2D/3D curve fitting, nonlinear system identification, and chaotic time-series prediction, verified its effectiveness. To our knowledge, the PL idea has not appeared in the literature before, and it opens up a promising new line of research in machine learning.

Granular computing, Dec 18, 2015

This article compares three methods [Interval Approach (IA), Enhanced Interval Approach (EIA) and... more This article compares three methods [Interval Approach (IA), Enhanced Interval Approach (EIA) and Hao-Mendel Approach (HMA)] for estimating (synthesizing) an interval type-2 fuzzy set (IT2 FS) model for a word, beginning with data that are collected from a group of subjects, or from a single subject. It summarizes the stages for each of the methods in tables so it is possible to compare the steps of each stage side-by-side. It also demonstrates, by means of an example of three words, that using more information contained in the collected data intervals is equivalent to reducing the uncertainty in the IT2 FS model. It recommends the HMA because it uses more information contained in the collected data intervals than does the IA or the EIA, and because it is the only method to-date that leads to normal IT2 FSs. Such fuzzy sets are easier to compute with than are non-normal IT2 FSs.

Adaptive Cumulant-Based Estimation of ARMA Parameters

ABSTRACT

IEEE Transactions on Acoustics, Speech, and Signal Processing, Jul 1, 1990

Several algorithms are developed to estimate the parameters of a causal nonminimum phase ARMA(p, ... more Several algorithms are developed to estimate the parameters of a causal nonminimum phase ARMA(p, q) system which is excited by an unobservable independent identically distributed (i.i.d.) non-Gaussian process; the output is contaminated by additive colored Gaussian noise of unknown power spectral density. First we present a fiindamental result pertaining to the identifiability of AR parameters, based on the Yule-Walker type equations drawn from a (specific) set of (p + 1) 1-D slices of the kth (k > 2) order output cumulant. Next, we develop several MA parameter estimation algorithms: one method uses q 1-D slices of the output cumulant; a second method uses only two 1-D cumulant slices. These methods do not involve computation of the residual (i.e., AR compensated) time series or polynomial factorization. Multidimensional versions of the various algorithms are also presented. A simulation study demonstrating the effectiveness of our algorithms is included.

Adaptive, learning, and pattern recognition systems: Theory and applications

IEEE Transactions on Automatic Control, 1972

Copyright© 1970, by Academic Press, Inc. all rights reserved. no part of this book may be reprodu... more Copyright© 1970, by Academic Press, Inc. all rights reserved. no part of this book may be reproduced in any form, by photostat, microfilm, retrieval system, or any other means, without written permission from the publishers. ACADEMIC PRESS, INC. Ill Fifth Avenue, New York, New York ...

IEEE Transactions on Fuzzy Systems, Sep 1, 2020

There have been different strategies to improve the performance of a machine learning model, e.g.... more There have been different strategies to improve the performance of a machine learning model, e.g., increasing the depth, width, and/or nonlinearity of the model, and using ensemble learning to aggregate multiple base/weak learners in parallel or in series. This article proposes a novel strategy called patch learning (PL) for this problem. It consists of three steps: first, train an initial global model using all training data; second, identify from the initial global model the patches that contribute the most to the learning error, and train a (local) patch model for each such patch; and, third, update the global model using training data that do not fall into any patch. To use a PL model, we first determine if the input falls into any patch. If yes, then the corresponding patch model is used to compute the output. Otherwise, the global model is used. We explain in detail how PL can be implemented using fuzzy systems. Five regression problems on one-dimensional (1-D)/2-D/3-D curve fitting, nonlinear system identification, and chaotic time-series prediction, verified its effectiveness. To our knowledge, the PL idea has not appeared in the literature before, and it opens up a promising new line of research in machine learning.

Fuzzy Logic, Type-2 and Uncertainty

SpringerReference, Aug 29, 2011

ABSTRACT

Maximum-Likelihood Seismic Deconvolution

IEEE Transactions on Geoscience and Remote Sensing, 1983

ABSTRACT

Type-1 Fuzzy Systems: Design Methods and Applications

This chapter focuses first on what exactly “design of a type-1 fuzzy system” means, and then prov... more This chapter focuses first on what exactly “design of a type-1 fuzzy system” means, and then provides a tabular way for making the choices that are needed in order to fully specify a type-1 fuzzy system, and introduces two approaches to design, the partially dependent approach and the totally independent approach. It then describes six design methods for designing a type-1 fuzzy system, namely: one-pass, least squares, derivative-based, SVD-QR, derivative-free and iterative. It then introduces and covers three case studies (forecasting of time series, knowledge mining using surveys, and fuzzy logic control, all of which are reexamined in Chap. 10), as well as the applications of forecasting of compressed video traffic, and rule-based classification of video traffic. Twelve examples are used to illustrate the chapter’s important concepts.

Type-2 Fuzzy Logic Systems : Type

Type-reduction in a type-2 fuzzy logic system (FLS) is an “extended” version of the defuzzificati... more Type-reduction in a type-2 fuzzy logic system (FLS) is an “extended” version of the defuzzification operation in a type-1 FLS. In this paper, we briefly review the structure of a type-2 FLS and describe type-reduction in detail. We focus on a center-of-sets type-reducer, and provide some examples to illustrate it. We also provide some practical approximations to type-reduction computations for certain type-2 membership functions.

Realization of a suboptimal controller by off-line training techniques

IEEE Transactions on Automatic Control, 1967

State space models of lossless layered media

IEEE Transactions on Automatic Control, 1977

: This paper develops time-domain state space models for lossless layered media which are describ... more : This paper develops time-domain state space models for lossless layered media which are described by the wave equation and boundary conditions. Our models are for non-equal one-way travel times; hence, they are more general than existing models of layered media which are usually for layers of equal one-way travel times. Full state models, which involve 2K states for a K-layer media system, as well as half-state models, which involve only K states are developed and related. Certain transfer functions, which appear in the geophysics literature in connection with models of layered media with equal travel times, are generalized to the situation of non equal travel times. Our state space models represent a new class of equations, causal functional equations, some of whose properties and approaches to simulation are discussed.

Critical Thinking About Explainable AI (XAI) for Rule-Based Fuzzy Systems

IEEE Transactions on Fuzzy Systems, 2021

This article is about explainable artificial intelligence (XAI) for rule-based fuzzy systems [tha... more This article is about explainable artificial intelligence (XAI) for rule-based fuzzy systems [that can be expressed generically, as <inline-formula><tex-math notation="LaTeX">$y({{\bf x}}) = f({{\bf x}})$</tex-math></inline-formula>]. It explains why it is <italic>not valid</italic> to explain the output of Mamdani or Takagi–Sugeno–Kang rule-based fuzzy systems using IF-THEN rules, and why it <italic>is valid</italic> to explain the output of such rule-based fuzzy systems as an <italic>association</italic> of the compound antecedents of a small subset of the original larger set of rules, using a phrase such as “these linguistic antecedents are <italic>symptomatic</italic> of this output.” Importantly, it provides a novel multi-step approach to obtain such a small subset of rules for three kinds of fuzzy systems, and illustrates it by means of a very comprehensive example. It also explains why the choice for antecedent membership function shapes may be more critical for XAI than before XAI, why linguistic approximation and similarity are essential for XAI, and, it provides a way to estimate the quality of the explanations.

In this paper, we present solutions to Zadeh's challenge problem on calculating linguistic probab... more In this paper, we present solutions to Zadeh's challenge problem on calculating linguistic probabilities. First, we argue that Zadeh's solution to this problem via the Generalized Extension Principle is very difficult to implement. Then, we use a syllogism based on the entailment principle to interpret the problem so that it can be solved by calculation of pessimistic (lower) and optimistic (upper) probabilities via Linguistic Weighted Averages. We use a pessimistic and an optimistic compatibility measure to calculate such probabilities. Then, we choose vocabularies for heights and linguistic probabilities that are involved in the problem statement. The vocabularies are modeled using interval type-2 fuzzy sets. We calculate optimistic (upper) and pessimistic (lower) probabilities, which naturally would be interval type-2 fuzzy sets. Finally, we map the pessimistic and optimistic probabilities into linguistic probabilities present in the vocabularies, so that the results can be comprehended by a human. We investigate viable alternatives for the pessimistic and optimistic compatibility measures, and also solve a similar problem with a different hypothesis.

IEEE Transactions on Fuzzy Systems, Apr 1, 2020

This paper provides a novel and better understanding of the performance potential of a nonsinglet... more This paper provides a novel and better understanding of the performance potential of a nonsingleton (NS) fuzzy system over a singleton (S) fuzzy system. It is done by extending sculpting the state space works from S to NS fuzzification and demonstrating uncertainties about measurements, modeled by NS fuzzification: first, fire more rules more often, manifested by a reduction (increase) in the sizes of first-order rule partitions for those partitions associated with the firing of a smaller (larger) number of rulesthe coarse sculpting of the state space; second, this may lead to an increase or decrease in the number of type-1 (T1) and interval type-2 (IT2) first-order rule partitions, which now contain rule pairs that can never occur for S fuzzification-a new rule crossover phenomenon-discovered using partition theory; and third, it may lead to a decrease, the same number, or an increase in the number of second-order rule partitions, all of which are system dependentthe fine sculpting of the state space. The authors' conjecture is that it is the additional control of the coarse sculpting of the state space, accomplished by prefiltering and the max-min (or max-product) composition, which provides an NS T1 or IT2 fuzzy system with the potential to outperform an S T1 or IT2 system when measurements are uncertain.

This paper provides an answer to the question that the type-2 fuzzy logic community is now asking... more This paper provides an answer to the question that the type-2 fuzzy logic community is now asking: "What comes after interval type-2 fuzzy logic systems (IT2 FLSs)?" It demonstrates, through a geometrical understanding of the type-reduced set, that logical next steps in the progression from type-1 to interval type-2 to type-2 FLSs are quasi-T2 FLSs, either an interconnection of a T1 FLS and an IT2 FLS, or an interconnection of two IT2 FLSs, in which both FLSs are designed simultaneously. The quasi-T2 FLSs overcome the computational difficulties that are associated with set theoretic operations and type-reduction (TR) for general T2 FSs and FLSs, because all set theoretic operations can be performed as in existing T1 or IT2 FLSs, and because TR for an IT2 FLS can be performed using existing KM Algorithms.

International Journal of Applied Mathematics and Computer Science, 2002

Per-C. The Per-C includes an encoder, a type-2 rulebased fuzzy logic system, and a decoder. It le... more Per-C. The Per-C includes an encoder, a type-2 rulebased 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.

Signal Processing, Jun 1, 2000

In this paper we focus on model-based statistical signal processing and how some problems that ar... more In this paper we focus on model-based statistical signal processing and how some problems that are associated with it can be solved using fuzzy logic. We explain how uncertainty (which is prevalent in statistical signal processing applications) can be handled within the framework of fuzzy logic. Type-1 singleton and non-singleton fuzzy logic systems (FLSs) are reviewed. Type-2 FLSs, which are relatively new, and are very appropriate for signal processing problems, because they can handle linguistic and numerical uncertainties, are overviewed in some detail. The output of a type-2 FLS is a type-2 fuzzy set. Using a new operation called type-reduction, the type-2 set can be reduced to a type-1 set } the type-reduced set } which plays the role of a con"dence interval for linguistic uncertainties. No such result can be obtained for a type-1 FLS. We demonstrate, by means of examples, that a type-2 FLS can outperform a type-1 FLS for one-step prediction of a Mackey}Glass chaotic time series whose measurements are corrupted by additive noise, and equalization of a nonlinear time-varying channel. 2000 Elsevier Science B.V. All rights reserved. In diesem Artikel setzen wir den Schwerpunkt auf modellbasierte statistische Signalverarbeitung und zeigen MoK glichkeiten zur LoK sung von Problemen dieses Umfeldes mit Hilfe der Fuzzy Logik auf. Wir erlaK utern, wie Entscheidungsunsicherheit (die in saK mtlichen Anwendunger der statistischen Signalverarbeitung vorherrscht) im Rahmen der Fuzzy Logik behandelt werden kann. ZunaK chst werden Typ-1 Singleton und Nicht-Singleton Fuzzy Logik Systeme (FLS) besprochen. Typ-2 FLS, die relativ neu sind, werden etwas detaillierter behandelt. Sie eignen sich sehr zur LoK sung von Signalverarbeitungsproblemen, da sie linguistische und numerische Unsicherheit handhaben koK nnen. Die Ausgabe eines Typ-2 FLS stellt die Typ-2 Fuzzy-Menge dar. Mit Hilfe einer neuen, als Typ-Reduktion bezeichneten Operation, kann die Typ-2 Menge auf eine Typ-1 Menge } die Typ-reduzierte Menge } uK berfuK hrt werden. Sie entspricht einem Kon"denzintervall fuK r linguistische Unsicherheit. Kein derartiges Resultat kann fuK r eine Typ-1 FLS abgeleitet werden. Anhand von Beispielen zeigen wir, da{ eine Typ-2 FLS eiher Typ-1 FLS zum einen als Einschritt-PraK diktion uK berlegen sein kann, wenn, sie auf eine chaotische Mackey}Glass Zeitreihe angwandt wird, deren Me{werte durch additives Rauschen gestoK rt sind oder wenn sie zum anderen bei der Entzerrung eines nichtlinearen zeitvarianten Kanals angewandt wird. 2000 Elsevier Science B.V. All rights reserved. Dans cet article, nous nous concentrons sur le traitement statisque de signaux a`base de mode`les et sur la fac7 on dont certains proble`mes qui lui sont associeH s peuvent e( tre reH solus en utilisant de la logique #oue. Nous expliquons comment

arXiv (Cornell University), Jul 2, 2019

Interval type-2 (IT2) fuzzy systems have become increasingly popular in the last 20 years. They h... more Interval type-2 (IT2) fuzzy systems have become increasingly popular in the last 20 years. They have demonstrated superior performance in many applications. However, the operation of an IT2 fuzzy system is more complex than that of its type-1 counterpart. There are many questions to be answered in designing an IT2 fuzzy system: Should singleton or non-singleton fuzzifier be used? How many membership functions (MFs) should be used for each input? Should Gaussian or piecewise linear MFs be used? Should Mamdani or Takagi-Sugeno-Kang (TSK) inference be used? Should minimum or product t-norm be used? Should type-reduction be used or not? How to optimize the IT2 fuzzy system? These questions may look overwhelming and confusing to IT2 beginners. In this paper we recommend some representative starting choices for an IT2 fuzzy system design, which hopefully will make IT2 fuzzy systems more accessible to IT2 fuzzy system designers.

arXiv (Cornell University), Jun 1, 2019

There have been different strategies to improve the performance of a machine learning model, e.g.... more There have been different strategies to improve the performance of a machine learning model, e.g., increasing the depth, width, and/or nonlinearity of the model, and using ensemble learning to aggregate multiple base/weak learners in parallel or in series. This paper proposes a novel strategy called patch learning (PL) for this problem. It consists of three steps: 1) train an initial global model using all training data; 2) identify from the initial global model the patches which contribute the most to the learning error, and train a (local) patch model for each such patch; and, 3) update the global model using training data that do not fall into any patch. To use a PL model, we first determine if the input falls into any patch. If yes, then the corresponding patch model is used to compute the output. Otherwise, the global model is used. We explain in detail how PL can be implemented using fuzzy systems. Five regression problems on 1D/2D/3D curve fitting, nonlinear system identification, and chaotic time-series prediction, verified its effectiveness. To our knowledge, the PL idea has not appeared in the literature before, and it opens up a promising new line of research in machine learning.

Granular computing, Dec 18, 2015

This article compares three methods [Interval Approach (IA), Enhanced Interval Approach (EIA) and... more This article compares three methods [Interval Approach (IA), Enhanced Interval Approach (EIA) and Hao-Mendel Approach (HMA)] for estimating (synthesizing) an interval type-2 fuzzy set (IT2 FS) model for a word, beginning with data that are collected from a group of subjects, or from a single subject. It summarizes the stages for each of the methods in tables so it is possible to compare the steps of each stage side-by-side. It also demonstrates, by means of an example of three words, that using more information contained in the collected data intervals is equivalent to reducing the uncertainty in the IT2 FS model. It recommends the HMA because it uses more information contained in the collected data intervals than does the IA or the EIA, and because it is the only method to-date that leads to normal IT2 FSs. Such fuzzy sets are easier to compute with than are non-normal IT2 FSs.

Adaptive Cumulant-Based Estimation of ARMA Parameters

ABSTRACT

IEEE Transactions on Acoustics, Speech, and Signal Processing, Jul 1, 1990

Several algorithms are developed to estimate the parameters of a causal nonminimum phase ARMA(p, ... more Several algorithms are developed to estimate the parameters of a causal nonminimum phase ARMA(p, q) system which is excited by an unobservable independent identically distributed (i.i.d.) non-Gaussian process; the output is contaminated by additive colored Gaussian noise of unknown power spectral density. First we present a fiindamental result pertaining to the identifiability of AR parameters, based on the Yule-Walker type equations drawn from a (specific) set of (p + 1) 1-D slices of the kth (k > 2) order output cumulant. Next, we develop several MA parameter estimation algorithms: one method uses q 1-D slices of the output cumulant; a second method uses only two 1-D cumulant slices. These methods do not involve computation of the residual (i.e., AR compensated) time series or polynomial factorization. Multidimensional versions of the various algorithms are also presented. A simulation study demonstrating the effectiveness of our algorithms is included.

Adaptive, learning, and pattern recognition systems: Theory and applications

IEEE Transactions on Automatic Control, 1972

Copyright© 1970, by Academic Press, Inc. all rights reserved. no part of this book may be reprodu... more Copyright© 1970, by Academic Press, Inc. all rights reserved. no part of this book may be reproduced in any form, by photostat, microfilm, retrieval system, or any other means, without written permission from the publishers. ACADEMIC PRESS, INC. Ill Fifth Avenue, New York, New York ...

IEEE Transactions on Fuzzy Systems, Sep 1, 2020

There have been different strategies to improve the performance of a machine learning model, e.g.... more There have been different strategies to improve the performance of a machine learning model, e.g., increasing the depth, width, and/or nonlinearity of the model, and using ensemble learning to aggregate multiple base/weak learners in parallel or in series. This article proposes a novel strategy called patch learning (PL) for this problem. It consists of three steps: first, train an initial global model using all training data; second, identify from the initial global model the patches that contribute the most to the learning error, and train a (local) patch model for each such patch; and, third, update the global model using training data that do not fall into any patch. To use a PL model, we first determine if the input falls into any patch. If yes, then the corresponding patch model is used to compute the output. Otherwise, the global model is used. We explain in detail how PL can be implemented using fuzzy systems. Five regression problems on one-dimensional (1-D)/2-D/3-D curve fitting, nonlinear system identification, and chaotic time-series prediction, verified its effectiveness. To our knowledge, the PL idea has not appeared in the literature before, and it opens up a promising new line of research in machine learning.

Fuzzy Logic, Type-2 and Uncertainty

SpringerReference, Aug 29, 2011

ABSTRACT

Maximum-Likelihood Seismic Deconvolution

IEEE Transactions on Geoscience and Remote Sensing, 1983

ABSTRACT

Type-1 Fuzzy Systems: Design Methods and Applications

This chapter focuses first on what exactly “design of a type-1 fuzzy system” means, and then prov... more This chapter focuses first on what exactly “design of a type-1 fuzzy system” means, and then provides a tabular way for making the choices that are needed in order to fully specify a type-1 fuzzy system, and introduces two approaches to design, the partially dependent approach and the totally independent approach. It then describes six design methods for designing a type-1 fuzzy system, namely: one-pass, least squares, derivative-based, SVD-QR, derivative-free and iterative. It then introduces and covers three case studies (forecasting of time series, knowledge mining using surveys, and fuzzy logic control, all of which are reexamined in Chap. 10), as well as the applications of forecasting of compressed video traffic, and rule-based classification of video traffic. Twelve examples are used to illustrate the chapter’s important concepts.

Type-2 Fuzzy Logic Systems : Type

Type-reduction in a type-2 fuzzy logic system (FLS) is an “extended” version of the defuzzificati... more Type-reduction in a type-2 fuzzy logic system (FLS) is an “extended” version of the defuzzification operation in a type-1 FLS. In this paper, we briefly review the structure of a type-2 FLS and describe type-reduction in detail. We focus on a center-of-sets type-reducer, and provide some examples to illustrate it. We also provide some practical approximations to type-reduction computations for certain type-2 membership functions.

Realization of a suboptimal controller by off-line training techniques

IEEE Transactions on Automatic Control, 1967

State space models of lossless layered media

IEEE Transactions on Automatic Control, 1977

: This paper develops time-domain state space models for lossless layered media which are describ... more : This paper develops time-domain state space models for lossless layered media which are described by the wave equation and boundary conditions. Our models are for non-equal one-way travel times; hence, they are more general than existing models of layered media which are usually for layers of equal one-way travel times. Full state models, which involve 2K states for a K-layer media system, as well as half-state models, which involve only K states are developed and related. Certain transfer functions, which appear in the geophysics literature in connection with models of layered media with equal travel times, are generalized to the situation of non equal travel times. Our state space models represent a new class of equations, causal functional equations, some of whose properties and approaches to simulation are discussed.

Critical Thinking About Explainable AI (XAI) for Rule-Based Fuzzy Systems

IEEE Transactions on Fuzzy Systems, 2021

This article is about explainable artificial intelligence (XAI) for rule-based fuzzy systems [tha... more This article is about explainable artificial intelligence (XAI) for rule-based fuzzy systems [that can be expressed generically, as <inline-formula><tex-math notation="LaTeX">$y({{\bf x}}) = f({{\bf x}})$</tex-math></inline-formula>]. It explains why it is <italic>not valid</italic> to explain the output of Mamdani or Takagi–Sugeno–Kang rule-based fuzzy systems using IF-THEN rules, and why it <italic>is valid</italic> to explain the output of such rule-based fuzzy systems as an <italic>association</italic> of the compound antecedents of a small subset of the original larger set of rules, using a phrase such as “these linguistic antecedents are <italic>symptomatic</italic> of this output.” Importantly, it provides a novel multi-step approach to obtain such a small subset of rules for three kinds of fuzzy systems, and illustrates it by means of a very comprehensive example. It also explains why the choice for antecedent membership function shapes may be more critical for XAI than before XAI, why linguistic approximation and similarity are essential for XAI, and, it provides a way to estimate the quality of the explanations.