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

Papers by Jerry Mendel

Research paper thumbnail of Adaptive Cumulant-Based Estimation of ARMA Parameters

ABSTRACT

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Research paper thumbnail of ARMA parameter estimation using only output cumulants

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

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Research paper thumbnail of 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 ...

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Research paper thumbnail of Some modeling problems in reflection seismology

IEEE ASSP magazine, 1986

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Research paper thumbnail of Patch Learning

IEEE Transactions on Fuzzy Systems, Sep 1, 2020

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Research paper thumbnail of Fuzzy Logic, Type-2 and Uncertainty

SpringerReference, Aug 29, 2011

ABSTRACT

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Research paper thumbnail of Maximum-Likelihood Seismic Deconvolution

IEEE Transactions on Geoscience and Remote Sensing, 1983

ABSTRACT

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Research paper thumbnail of 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.

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Research paper thumbnail of 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.

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Research paper thumbnail of Realization of a suboptimal controller by off-line training techniques

IEEE Transactions on Automatic Control, 1967

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Research paper thumbnail of 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.

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Research paper thumbnail of 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.

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Research paper thumbnail of Maclaurin series expansion complexity-reduced center of sets type-reduction + defuzzification for interval type-2 fuzzy systems

2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2016

This paper provides a mathematical analysis that shows how the crisp output of an IT2 FLS that is... more This paper provides a mathematical analysis that shows how the crisp output of an IT2 FLS that is obtained by using the Begian-Melek-Mendel (BMM) formula compares to the one obtained by using center-of-sets type-reduction followed by defuzzification (COS TR + D). This is made possible by reformulating the structural solutions of the two optimization problems that are associated with COS TR, and then expanding each of them using a Maclaurin series expansion. As a result of doing this, we show that BMM is the zero-order approximation to COS TR + D. Additionally, by retaining the zero-order and first-order terms from the Maclaurin series expansions, we provide a new Enhanced BMM, one that is non-iterative, has a closed form and is much faster than using the EKM algorithms for COS TR. Although the Enhanced BMM formula is slower than BMM, we demonstrate, by means of extensive simulations, that it is from 5% to 50% more accurate than is BMM for achieving the same numerical solution that is obtained from COS TR + D; and, it is at least 94% faster than when EKM is used for COS TR +D, which makes the Extended BMM a very strong candidate for use in real time applications of IT2 FLSs.

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Research paper thumbnail of Multicriteria decision making based on intuitionistic fuzzy prioritized arithmetic mean

International Journal of Intelligent Systems, 2018

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Research paper thumbnail of Intuitionistic Fuzzy Hybrid Weighted Arithmetic Mean and Its Application in Decision Making

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2019

Atanassov’s intuitionistic fuzzy sets (AIFSs), characterized by a membership function, a non-memb... more Atanassov’s intuitionistic fuzzy sets (AIFSs), characterized by a membership function, a non-membership function, and a hesitancy function, is a generalization of a fuzzy set. There are various intuitionistic fuzzy hybrid weighted aggregation operators to deal with multi-attribute decision making problems which consider the importance degrees of the arguments and their ordered positions simultaneously. However, these existing hybrid weighed aggregation operators are not monotone with respect to the total order on intuitionistic fuzzy values (AIFVs), which is undesirable. Based on the Łukasiewicz triangular norm, we propose an intuitionistic fuzzy hybrid weighted arithmetic mean, which is monotone with respect to the total order on AIFVs, and therefore is a true generalization of such operations. We give an example that a company intends to select a project manager to illustrate the validity and applicability of the proposed aggregation operator. Moreover, we extend this kind of hybr...

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Research paper thumbnail of Applications of State Variable Technology in Reflection Seismology for Oil and Gas Exploration

IFAC Proceedings Volumes, 1981

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Research paper thumbnail of A Predictive Model for Improving the Efficiency of Frac Jobs

SPE Western Regional Meeting, 2015

This paper presents a new method for forecasting post-fracturing responses in a tight oil reservo... more This paper presents a new method for forecasting post-fracturing responses in a tight oil reservoir using historical hydraulic fracturing data. The methodology is based on a nonlinear regression method called Variable Structure Regression (VSR). Data for 80 frac jobs were used to calibrate and predict responses. Information per fracturing job included feet of perforation, number of perforations per stage, number of stages, pad volume, slurry volume and sand volume. Information for a set of hydraulically fractured vertical wells was used to test the proposed technique. The VSR method establishes the optimal nonlinear dependencies of variables to predict the cumulative liquid production after fracturing. This method determines the relationships between fracturing parameters and post-fracturing productions in the form of linguistic terms, thereby providing a physical understanding of the process. The exact mathematical structure of these linguistic terms and the number of terms are est...

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Research paper thumbnail of Computing With Words (CWW): role of fuzzy, probability and measurement concepts, and operations

The goal of this panel at IEEE World Computational Intelligence Congress in Brisbane, Australia w... more The goal of this panel at IEEE World Computational Intelligence Congress in Brisbane, Australia was to discuss the fundamental concepts that underline a new area of computing with words initiated by L. Zadeh. The panel was held on June 10 with six panelists: Gleb Beliakov (Deakin University, Australia), Bernadette Bouchon Meunier (University of Paris, France), Janusz Kacprzyk (Polish Academy of Sciences, Poland), Boris Kovalerchuk (moderator, Central Washington University, USA), Vladik Kreinovich (moderator, University of Texas, USA), and Jerry Mendel (University of Southern California, USA).

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Research paper thumbnail of On clarifying some definitions and notations used for type-2 fuzzy sets as well as some recommended changes

Information Sciences, 2016

This paper is about some important changes in type-2 fuzzy set (T2 FS) definitions and notations ... more This paper is about some important changes in type-2 fuzzy set (T2 FS) definitions and notations that have occurred during the past 16 years. It summarizes the evolution of how the primary membersh...

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Research paper thumbnail of Correction to “new fast optimal white-noise estimators for deconvolution”

IEEE transactions on geoscience electronics, Jul 1, 1977

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Research paper thumbnail of Adaptive Cumulant-Based Estimation of ARMA Parameters

ABSTRACT

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Research paper thumbnail of ARMA parameter estimation using only output cumulants

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

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Research paper thumbnail of 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 ...

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Research paper thumbnail of Some modeling problems in reflection seismology

IEEE ASSP magazine, 1986

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Patch Learning

IEEE Transactions on Fuzzy Systems, Sep 1, 2020

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Fuzzy Logic, Type-2 and Uncertainty

SpringerReference, Aug 29, 2011

ABSTRACT

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Research paper thumbnail of Maximum-Likelihood Seismic Deconvolution

IEEE Transactions on Geoscience and Remote Sensing, 1983

ABSTRACT

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Research paper thumbnail of 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.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of 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.

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Research paper thumbnail of Realization of a suboptimal controller by off-line training techniques

IEEE Transactions on Automatic Control, 1967

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Research paper thumbnail of 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.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of 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.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Maclaurin series expansion complexity-reduced center of sets type-reduction + defuzzification for interval type-2 fuzzy systems

2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2016

This paper provides a mathematical analysis that shows how the crisp output of an IT2 FLS that is... more This paper provides a mathematical analysis that shows how the crisp output of an IT2 FLS that is obtained by using the Begian-Melek-Mendel (BMM) formula compares to the one obtained by using center-of-sets type-reduction followed by defuzzification (COS TR + D). This is made possible by reformulating the structural solutions of the two optimization problems that are associated with COS TR, and then expanding each of them using a Maclaurin series expansion. As a result of doing this, we show that BMM is the zero-order approximation to COS TR + D. Additionally, by retaining the zero-order and first-order terms from the Maclaurin series expansions, we provide a new Enhanced BMM, one that is non-iterative, has a closed form and is much faster than using the EKM algorithms for COS TR. Although the Enhanced BMM formula is slower than BMM, we demonstrate, by means of extensive simulations, that it is from 5% to 50% more accurate than is BMM for achieving the same numerical solution that is obtained from COS TR + D; and, it is at least 94% faster than when EKM is used for COS TR +D, which makes the Extended BMM a very strong candidate for use in real time applications of IT2 FLSs.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Multicriteria decision making based on intuitionistic fuzzy prioritized arithmetic mean

International Journal of Intelligent Systems, 2018

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Intuitionistic Fuzzy Hybrid Weighted Arithmetic Mean and Its Application in Decision Making

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2019

Atanassov’s intuitionistic fuzzy sets (AIFSs), characterized by a membership function, a non-memb... more Atanassov’s intuitionistic fuzzy sets (AIFSs), characterized by a membership function, a non-membership function, and a hesitancy function, is a generalization of a fuzzy set. There are various intuitionistic fuzzy hybrid weighted aggregation operators to deal with multi-attribute decision making problems which consider the importance degrees of the arguments and their ordered positions simultaneously. However, these existing hybrid weighed aggregation operators are not monotone with respect to the total order on intuitionistic fuzzy values (AIFVs), which is undesirable. Based on the Łukasiewicz triangular norm, we propose an intuitionistic fuzzy hybrid weighted arithmetic mean, which is monotone with respect to the total order on AIFVs, and therefore is a true generalization of such operations. We give an example that a company intends to select a project manager to illustrate the validity and applicability of the proposed aggregation operator. Moreover, we extend this kind of hybr...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Applications of State Variable Technology in Reflection Seismology for Oil and Gas Exploration

IFAC Proceedings Volumes, 1981

Bookmarks Related papers MentionsView impact

Research paper thumbnail of A Predictive Model for Improving the Efficiency of Frac Jobs

SPE Western Regional Meeting, 2015

This paper presents a new method for forecasting post-fracturing responses in a tight oil reservo... more This paper presents a new method for forecasting post-fracturing responses in a tight oil reservoir using historical hydraulic fracturing data. The methodology is based on a nonlinear regression method called Variable Structure Regression (VSR). Data for 80 frac jobs were used to calibrate and predict responses. Information per fracturing job included feet of perforation, number of perforations per stage, number of stages, pad volume, slurry volume and sand volume. Information for a set of hydraulically fractured vertical wells was used to test the proposed technique. The VSR method establishes the optimal nonlinear dependencies of variables to predict the cumulative liquid production after fracturing. This method determines the relationships between fracturing parameters and post-fracturing productions in the form of linguistic terms, thereby providing a physical understanding of the process. The exact mathematical structure of these linguistic terms and the number of terms are est...

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Computing With Words (CWW): role of fuzzy, probability and measurement concepts, and operations

The goal of this panel at IEEE World Computational Intelligence Congress in Brisbane, Australia w... more The goal of this panel at IEEE World Computational Intelligence Congress in Brisbane, Australia was to discuss the fundamental concepts that underline a new area of computing with words initiated by L. Zadeh. The panel was held on June 10 with six panelists: Gleb Beliakov (Deakin University, Australia), Bernadette Bouchon Meunier (University of Paris, France), Janusz Kacprzyk (Polish Academy of Sciences, Poland), Boris Kovalerchuk (moderator, Central Washington University, USA), Vladik Kreinovich (moderator, University of Texas, USA), and Jerry Mendel (University of Southern California, USA).

Bookmarks Related papers MentionsView impact

Research paper thumbnail of On clarifying some definitions and notations used for type-2 fuzzy sets as well as some recommended changes

Information Sciences, 2016

This paper is about some important changes in type-2 fuzzy set (T2 FS) definitions and notations ... more This paper is about some important changes in type-2 fuzzy set (T2 FS) definitions and notations that have occurred during the past 16 years. It summarizes the evolution of how the primary membersh...

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Research paper thumbnail of Correction to “new fast optimal white-noise estimators for deconvolution”

IEEE transactions on geoscience electronics, Jul 1, 1977

Bookmarks Related papers MentionsView impact