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Combining Experimentation and Theory

A Hommage to Abe Mamdani

herausgegeben von: Enric Trillas, Piero P. Bonissone, Luis Magdalena, Janusz Kacprzyk

Verlag: Springer Berlin Heidelberg

Buchreihe : Studies in Fuzziness and Soft Computing

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

The unexpected and premature passing away of Professor Ebrahim H. "Abe" Mamdani on January, 22, 2010, was a big shock to the scientific community, to all his friends and colleagues around the world, and to his close relatives. Professor Mamdani was a remarkable figure in the academic world, as he contributed to so many areas of science and technology. Of great relevance are his latest thoughts and ideas on the study of language and its handling by computers.

The fuzzy logic community is particularly indebted to Abe Mamdani (1941-2010) who, in 1975, in his famous paper An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller, jointly written with his student Sedrak Assilian, introduced the novel idea of fuzzy control. This was an elegant engineering approach to the modeling and control of complex processes for which mathematical models were unknown or too difficult to build, yet they could effectively and efficiently be controlled by human operators. This ground-breaking idea has found innumerable applications and can be considered as one of the main factors for the proliferation and adoption of fuzzy logic technology.

Professor Mamdani's own life and vital experience are illustrative of his “never surrendering” attitude while facing adversaries, which is normal for a person proposing any novel solution, and represent a great example for everybody. His subtle sense of humor, his joy for life, and his will to critically help people, especially young people, were characteristics deeply appreciated by all the people who enjoyed and benefited from his friendship and advice.

This book constitutes a posthumous homage to Abe Mamdani. It is a collection of original papers related in some way to his works, ideas and vision, and especially written by researchers directly acquainted with him or with his work. The underlying goal of this book will be fulfilled if, in the very spirit of Mamdani's legacy, the papers will trigger a scientific or philosophical debate on the issues covered, or contribute to a cross-fertilization of ideas in the various fields.

Inhaltsverzeichnis

Frontmatter

Correspondence between an Experimentalist and a Theoretician

Abstract

Between October and December, 2009, the two authors of this correspondence exchanged a series of emails expressing their thoughts on topics related with science, formal logic, language, mathematical modeling, etc. Since the last email is dated in December, the 24th, and unfortunately the first author passed away at January, the 22nd, 2010, not only the correspondence is unfinished but it will remain so forever.

Ebrahim H. Mamdani, E. Trillas

Days Spent with Professor Ebrahim H. Mamdani

Abstract

In our very early days of fuzzy sets and logic, I had an opportunity to spend some time with Professor Ebrahim Mamdani. Therefore, it is my privilege to tell something about him. In this small article I would like to tell a story concerned with the dawn of the fuzzy control age, about something having happened with and also having been influenced by Professor Mamdani from 1975 to 1987.

Michio Sugeno

Soft Computing as a Tool, Six Years Later

Abstract

After a brief expression of my personal gratitude for the inspiring mentorship received from Professors Lotfi Zadeh and Abe Mamdani, I review some of the 70’s seminal papers that lead to Prof Mamdani’s innovation in fuzzy control (FC). Then, I discuss the concurrent development of FC and expert system applications, which took place in the 80’s, noting the similarity stemming from their common use of knowledge bases (KB) developed via rapid prototyping. FC and expert systems also shared a common difficulty: avoiding KB obsolescence over time which was caused by the dynamic environment in which they were deployed. For FC, the lack of automation in their design and maintenance process changed in the 90’s, when Soft Computing (SC) offered a broader computational paradigm for developing intelligent systems, by adding a search and learning component to the fuzzy logic reasoning component. These SC components allowed researchers to automate the fine-tuning of fuzzy systems. In a 2004 position paper, Prof. Mamdani and I made some initial remarks regarding the use and misuse of SC as a tool. In the last six years we have seen an evolution of SC, with a clearer role for their use in capturing knowledge to embed in object-level models, and meta-knowledge to guide the design and upkeep of these models. I illustrate this concept with three real-world examples in insurance risk management, fleet asset selection, and power plant management.

Piero P. Bonissone

Abe Mamdani: A Pioneer of Soft Artificial Intelligence

Abstract

By means of a careful analysis of early papers by Zadeh on fuzzy rules, we suggest an explanation of why Mamdani came up with his way of modelling fuzzy control rules. And then we recall the semantics of fuzzy rules so as to position Mamdani,s rules in possibility theory. We also explain the links between (probabilistic) conditionals, as well as association rules, and Mamdani’s rules. Finally, we comment on Mamdani’s constant taste for applied Artificial Intelligence (AI), while the whole field of fuzzy rule-based systems he created, and viewed as part of AI, eventually moved away from it.

Didier Dubois, Henri Prade

An Essay on the Interpretability of Mamdani Systems

Abstract

Mamdani Systems are very well known in the area of Fuzzy Control, where they have been, they are, and they will continue to be successfully used. Efforts to linguistically interpret Mamdani Systems as a method for inference in fuzzy logic have faced the difficulty of interpreting the output of such systems before defuzzification, which consists of an aggregation of normally truncated fuzzy sets. The present chapter offers a metasemantic approach to alleviate this problem.

Claudio Moraga

A Historical Review of Mamdani-Type Genetic Fuzzy Systems

Abstract

The need for trading off interpretability and accuracy is intrinsic to the use of fuzzy systems. The fuzzy modeling scientific community has proposed many different design techniques dealing with the interpretability-accuracy tradeoff. In particular, the use of genetic fuzzy systems has been widely extended thanks to their inherent flexibility and their capability to jointly consider different optimization criteria. The current contribution constitutes a brief review on some of the existing genetic fuzzy system approaches relying on Mamdani-type fuzzy rule-based systems to obtain interpretable linguistic fuzzy models with a good accuracy.

Oscar Cordón

Fuzzy Control for Knowledge-Based Interpolation

Abstract

Fuzzy control accounts for the biggest industrial success of fuzzy logic. We review an interpretation of Mamdani’s heuristic control approach. It can be seen as knowledge-based interpolation based on input-output points of a vaguely known function.We reexamine two real-world control problems that have been fortunately solved based on this interpretation.

Christian Moewes, Rudolf Kruse

Linguistic Fuzzy Rules in Data Mining: Follow-Up Mamdani Fuzzy Modeling Principle

Abstract

From the definition of fuzzy sets by Zadeh in 1965, fuzzy logic has become a significant area of interest for researchers on artificial intelligence. In particular, Professor Mamdani was the pioneer who investigated the use of fuzzy logic for interpreting the human derived control rules, and therefore his work was considered a milestone application of this theory.

In this work, we aim to carry out an overview of the principles of fuzzy modeling given by Mamdani and its application to different areas of data mining that can be exploited such as classification, association rule mining or subgroup discovery, among others. Specifically, we present a case of study on classification with highly imbalanced data-sets in which linguistic fuzzy rule based systems have shown to achieve a good behaviour among other techniques such as decision trees.

A. Fernández, F. Herrera

Fuzzy Rules in Data Mining: From Fuzzy Associations to Gradual Dependencies

Abstract

Fuzzy rules, doubtlessly one of the most powerful tools of fuzzy logic, have not only been used successfully in established application areas like control engineering and approximate reasoning, but more recently also in the field of data mining. In this chapter, we provide a synthesis of different approaches to fuzzy association analysis, that is, the data-driven extraction of interesting patterns expressed in the form of fuzzy rules. In this regard, we highlight a specific advantage of a fuzzy in comparison to a conventional approach, namely an increased expressiveness that allows for representing patterns of interest in a more distinctive way. Therefore, we specifically focus on the modeling of a less common type of pattern, namely gradual dependencies between attributes in a data set.

Eyke Hüllermeier

Mascot Robot System Based on Fuzzy Control Technology

Abstract

A mascot robot system based on fuzzy inference is developed for casual information recommendation in a home environment. The system is an Internet-based intelligent robotic environment that assists human by information retrieval and presenting recommendation with casual communication. It consists of five eye robots that present friendly mentality expression, speech recognition modules, an information recommendation engine that recommends information to human by taking into account the current situation, and a server that supervises the whole system. In addition, a fuzzy logic based multi-modal gesture recognition system is added based on, where both web camera images and hand motion data (given by a 3D acceleration sensor put on human wrists) are used to notify the emotion of humans to robots in real time. These components are networked and integrated hierarchically based on RT (Robot Technology) middleware. The subjective estimation using psychological scale has been conducted for 11 subjects. Since the results of the subjective estimation shows 3.08 and 2.62, the validity of the fuzzy interpersonal motions expression has been confirmed. The proposed mascot robot system provides informative support to human through casual communication in a home environment.

Kaoru Hirota, Yoichi Yamazaki, Fangyan Dong

From Fuzzy Rule-Based Systems to Granular Fuzzy Rule-Based Systems: A Study in Granular Computing

Abstract

In the study, we introduce a concept of granular fuzzy rule-based systems, offer a motivation behind its emergence and elaborate on ensuing algorithmic developments. It is shown that the granularity of the fuzzy rules is directly associated with a reduction (compression) process in which the number of rules becomes reduced in order to enhance the readability (transparency) of the resulting rule base. The retained rules are made more abstract (general) by admitting a granular form of the fuzzy sets forming their antecedents. In other words, while the original rules read as “if A_i then B_i” their reduced subset comes in the form “if G(A_i) then B_i” with G(.) denoting a certain granular extension of the original fuzzy set (which can be realized e.g., in the form of interval-valued fuzzy sets, fuzzy sets of type-2 or rough – fuzzy sets). It is shown that the optimization of the reduced set of rules is realized through an optimal distribution of information granularity among fuzzy sets forming the conditions of the reduced rules. In particular, it is shown that the distribution of information granularity, being regarded as an important design asset, is realized through a minimization of a certain objective function quantifying how well the granular fuzzy set formed by the reduced rule set represents (covers) all rules. In the sequel, we introduce an idea of a granular representation of results of inferences realized in fuzzy rule-based systems.

Witold Pedrycz

Interval Type-2 Mamdani Fuzzy Systems for Intelligent Control

Abstract

Fuzzy information processing in type-2 fuzzy systems has been implemented in most cases based on the Karnik and Mendel (KM) and Wu-Mendel (WM) approaches. However, both of these approaches are time consuming for most real-world applications, in particular for control problems. For this reason, a more efficient method based on evolutionary algorithms has been proposed by Castillo and Melin (CM). This method is based on directly obtaining the type reduced results by using an evolutionnary algorithm (EA). The basic idea is that with an EA the upper and lower membership functions in the output can be obtained directly based on experimental data for a particular problem. A comparative study (in control applications) of the three methods, based on accuracy and efficiency is presented, and the CM is shown to outperform both the KM and WM methods in efficiency while accuracy is comparable.

Oscar Castillo

Image Processing and Pattern Recognition with Mamdani Interval Type-2 Fuzzy Inference Systems

Abstract

Interval type-2 fuzzy systems can be of great help in image processing and pattern recognition applications. In particular, edge detection is a process usually applied to image sets before the training phase in recognition systems. This preprocessing step helps to extract the most important shapes in an image, ignoring the homogeneous regions and remarking the real objective to classify or recognize. Many traditional and fuzzy edge detectors can be used, but it’s very difficult to demonstrate which one is better before the recognition results. In this work we present an experiment where several edge detectors were used to preprocess the same image sets. Each resultant image set was used as training data for neural network recognition system, and the recognition rates were compared. The goal of this experiment is to find the better edge detector that can be used as training data on a neural network for image recognition.

Patricia Melin

Bipolar Queries: Some Inspirations from Intention and Preference Modeling

Abstract

The concept of a bipolar query, meant as a database query that involves both mandatory and optional conditions is discussed from the point of view of flexible database querying and modeling of more sophisticated user’s intentions and preferences. Aggregation of the matching degrees against the negative and positive conditions to derive an overall matching degree is considered taking as the point of departure the Lacroix and Lavency approach [25] for bipolar queries. It is shown that the use of a multiple valued logic based formalism for the representation of positive and negative desires in the context of intention modeling proposed by Casali, Godo and Sierra [8, 7] can be employed to extend the approach to bipolar queries. Both the approaches have roots in the seminal Dubois and Prade’s view of bipolarity in the possibilistic setting (cf. for a comprehensive review Dubois and Prade [17]).

Janusz Kacprzyk, Sławomir Zadrożny

Evolving Linguistic Fuzzy Models from Data Streams

Abstract

This work outlines a new approach for online learning from imprecise data, namely, fuzzy set based evolving modeling (FBeM) approach. FBeM is an adaptive modeling framework that uses fuzzy granular objects to enclose uncertainty in the data. The FBeM algorithm is data flow driven and supports learning on an instance-per-instance recursive basis by developing and refining fuzzy models on-demand. Structurally, FBeM models combineMamdani and functional fuzzy systems to output granular and singular approximations of nonstationary functions. In general, approximand functions can be time series, decision boundaries between classes, and control and regression functions. Linguistic description of the behavior of the system over time is provided by information granules and associated rules. An application example on a reactive control problem, underlining the complementarity of Mamdani and functional parts of the model, illustrates the usefulness of the approach. More specifically, the problem concerns sensor-based robot navigation and localization. In addition to precise singular output values, granular output values provide effective robust obstacle avoidance navigation.

Daniel Leite, Fernando Gomide

A Quantitative View on Quasi Fuzzy Numbers

Abstract

In this paper we generalize the principles of possibilistic mean value, variance, covariance and correlation of fuzzy numbers to a more general class of fuzzy subsets of the real line: to quasi fuzzy numbers.

Christer Carlsson, Robert Fullér, József Mezei

Similarity and Implication between Fuzzy Sets

Abstract

The pioneering work of Mamdani and Assilian [9] was the first practical application of a number of concepts from fuzzy-set theory [12] and fuzzy logic [15] to the solution of a family of important control problems. Inspired by ongoing developments in artificial intelligence [7], this work reported on the successful application of fuzzyset based generalizations of conventional logic, such as Zadeh’s compositional rule of inference [14], to the inferential derivation of measures of control adequacy.

Enrique H. Ruspini

From Leibniz’s Shinning Theorem to the Synthesis of Rules through Mamdani-Larsen Conditionals

Abstract

This paper deals with the problem of synthesizing by conjunction a finite set of rules \(\mu_{i} \longrightarrow(1\leq i \leq n)\) into a single one \(\mu_{1} . \mu{2}...\mu{n} \longrightarrow \sigma_{1} . \sigma{2}...\sigma{n}\), and depending on the conditional’s representation. It is proven that, among the usual five types of fuzzy conditionals, the problem is only solved by the Mamdani-Larsen’s type min-conditionals.

Enric Trillas, Claudi Alsina

On the Paradoxical Success of Mamdani’s Minimum-Based Inference

Abstract

Mamdani’s inference has an incredible success, especially in areas such as decision making and control. Yet, it is well known that it uses a min-based implication that does not verify classical boolean logic requirements.

This contribution aims at, in the one hand, exploring Mamdani’s choice from a practical point of view, and in the other hand, explaining the success of Mamdani’s inference from a logical perspective, by introducing a simple variant of the Generalized Modus Ponens (GMP) that uses standard fuzzy implications.

In addition, this new formulation opens the way for new methods of inference that have the same benefits as Mamdani’s.

Marcin Detyniecki, Benjamin Moubêche, Bernadette Bouchon-Meunier

Enhancing Quality of Experience in Public Collections

Abstract

A visit to a public collection is potentially one of the most effective and entertaining ways of knowledge acquisition open to the viewing public. Such collections are nevertheless coming under increased pressure, due to competition from alternative forms of ‘edutainment’ and ‘digital convergence’, to improve the Quality of Experience given to visitors. This paper reports on the convergence of elements of pervasive and adaptive computing, in the construction and implementation of an interactive museum exhibit, which uses fuzzy inference from user behaviour to personalise the exhibit’s behavioural response. We describe a usability experiment which shows that the technological enrichment of conventional environments and artefacts, together with intelligent decision-making, can have a positive impact on Quality of Experience.

Jeremy Pitt, Arvind Bhusate

Metaphors for Linguistic Description of Data

Abstract

In this paper, we propose a formal representation of the meaning of sentences involving conceptual metaphors in the context of the research line of Computing with Words and Perceptions. Conceptual metaphors are mappings between conceptual domains that are common in everyday natural language usage. They are not just a matter of lexico-grammar stratum but of representation and processing in the semantic stratum of language. Here, the Granular Linguistic Model of a Phenomenon is presented as a computational paradigm for representing the meaning of metaphorical sentences, with an application devoted to generate linguistic descriptions of data. The obtained results provide an approach to assign a fuzzy fulfilment degree to linguistic expressions with a more complex semantic and lexico-grammar structure than usually handled in Fuzzy Logic.

Gracian Triviño, Daniel Sánchez

Using Dempster-Shafer Structures to Provide Probabilistic Outputs in Fuzzy Systems Modeling

Abstract

Our interest is in providing a capability to include probabilistic outputs in fuzzy systems modeling. To accomplish this we use Dempster-Shafer belief structures. We first discuss some basic ideas from the Dempster-Shafer theory of evidence. We then describe Mamdani’s paradigm for fuzzy systems modeling which provided the pioneering framework for the many applications of fuzzy logic control. We then show how to use the Dempster-Shafer belief structure to provide machinery for including randomness in the fuzzy systems modeling process. We show how to this can be used to include various types of uncertainties including additive noise in the fuzzy systems modeling process. We next describe the Takagi-Sugeno approach to fuzzy systems modeling. Finally we use the Dempster-Shafer belief structure to enable the inclusion of probabilistic aspects in the output of the Takagi-Sugeno model.

Ronald R. Yager, Dimitar P. Filev

The Experimenter and the Theoretician – Linguistic Synthesis to Tell Machines What to Do

Abstract

There is a traditional division of labor in scientific reseach: on the one hand we have theoretical investigations and on the other hand we have experimental examinations. This bifurcation of scientific labor can be delineated back to the ancient world and this tradition became manifest in the 17th century when modern science established mathematics as the proper tool to describe scientific theories and when observation and experiments became the framework for empirical science. During the 18th and 19th century with Newton’s physics and Laplace’s causal determinism, mathematics became the distinguished language to describe scientific theories in physics and astronomy and later in the other sciences. In the 20th century this development reached a partitioning in theoretical and experimental sciences, e.g. in physics and chemistry, and sometimes in other fields, too. Also in the applied sciences, especially in engineering, the role of mathematics started to increase in these areas, too. Along with this development several types of engineers turned up, more or less geared to mathematics or to experiments.

Rudolf Seising

Concepts, Theories, and Applications: The Role of “Experimentation” (and “Context”) for Formalizing New Ideas along Innovative Avenues

Abstract

The main aim of this paper is to present a few general ideas preliminary to an assessment of the role that a correct interchange between the elaboration of new theories and an open minded experimentation can have in the development of new fields of investigation. Although many of the reflections and remarks that follow will be of a very broad type, the reference background of all the paper will be, in general, the composite field of information sciences and, more specifically, the innovative concepts and approaches introduced by fuzzy sets theory. Abe Mamdani’s work can certainly be considered as an outstanding example of the way in which these innovations arose and, subsequently, flourished.

Settimo Termini

Imperfect Causality: Combining Experimentation and Theory

Abstract

This paper is a journey around causality, imperfect causality, causal models and experiments for testing hypothesis about what causality is, with special attention to imperfect causality. Causal relations are compared with logic relations and analogies and differences are highlighted. Classical properties of causality are described and one characteristic more is added: causes, effects and the cause-effect links usually are qualified by different degrees of strength. Causal sentences automatically recovered from texts show this. In daily life, imperfect causality has an extensive role in causal decision-making. Bayes Nets offer an appropriate model to characterize causality in terms of conditional probabilities, explaining not only how choices are made but also how to learn new causal squemes based on the previously specified. Psychological experiments seem to support this view. But Bayes Nets have an Achilles hell: if the names labeling nodes are vague in meaning, the probability cannot be specified in an exact way. Fuzzy logic offers models to deals with vagueness in language. Kosko fuzzy cognitive maps provide the classical way to address fuzzy causalility. Other less relevant models to manage imperfect causality are proposed, but fuzzy people still lacks of a comprehensive batterie of examples to test those models about how fuzzy causality works. We provide a program that retrieves causal and conditional causal sentences from texts and authomatically depicts a graph representing causal concepts as well as the links between them, including fuzzy quantifiers and semantic hedges modifying nodes and links. Get these mechanisms can provide a benchmark to test hyphotesis about what is fuzzy causality, contributing to improve the current models.

Alejandro Sobrino

A Reflection on Fuzzy Conditionals

Abstract

This chapter is just a reflection on some theoretical aspects dealing with the representation in fuzzy terms of imprecise linguistic rules. Namely, it deals with the functions able to represent ‘rules’, or fuzzy conditionals, whose election at each case not only depends on the problem’s context, but on the kind of reasoning intended for its use. Some results on the suitability of Mamdani-Larsen type conditionals are presented.

Enric Trillas, Itziar García-Honrado

Fuzzy vs. Likert Scale in Statistics

Abstract

Likert scales or associated codings are often used in connection with opinions/valuations/ratings, and especially with questionnaires with a pre-specified response format.A guideline to design questionnaires allowing free fuzzy-numbered response format is now given, the fuzzy numbers scale being very rich and expressive and enabling to describe in a friendly way the usual answers in this context. A review of some techniques for the statistical analysis of the obtained responses is enclosed and a real-life example is used to illustrate the application.

María Ángeles Gil, Gil González-Rodríguez

Backmatter

Titel: Combining Experimentation and Theory
herausgegeben von: Enric Trillas
Piero P. Bonissone
Luis Magdalena
Janusz Kacprzyk
Verlag: Springer Berlin Heidelberg
Electronic ISBN: 978-3-642-24666-1
Print ISBN: 978-3-642-24665-4
DOI: https://doi.org/10.1007/978-3-642-24666-1

Springer Professional

Über dieses Buch

Inhaltsverzeichnis

Frontmatter

Correspondence between an Experimentalist and a Theoretician

Days Spent with Professor Ebrahim H. Mamdani

Soft Computing as a Tool, Six Years Later

Abe Mamdani: A Pioneer of Soft Artificial Intelligence

An Essay on the Interpretability of Mamdani Systems

A Historical Review of Mamdani-Type Genetic Fuzzy Systems

Fuzzy Control for Knowledge-Based Interpolation

Linguistic Fuzzy Rules in Data Mining: Follow-Up Mamdani Fuzzy Modeling Principle

Fuzzy Rules in Data Mining: From Fuzzy Associations to Gradual Dependencies

Mascot Robot System Based on Fuzzy Control Technology

From Fuzzy Rule-Based Systems to Granular Fuzzy Rule-Based Systems: A Study in Granular Computing

Interval Type-2 Mamdani Fuzzy Systems for Intelligent Control

Image Processing and Pattern Recognition with Mamdani Interval Type-2 Fuzzy Inference Systems

Bipolar Queries: Some Inspirations from Intention and Preference Modeling

Evolving Linguistic Fuzzy Models from Data Streams

A Quantitative View on Quasi Fuzzy Numbers

Similarity and Implication between Fuzzy Sets

From Leibniz’s Shinning Theorem to the Synthesis of Rules through Mamdani-Larsen Conditionals

On the Paradoxical Success of Mamdani’s Minimum-Based Inference

Enhancing Quality of Experience in Public Collections

Metaphors for Linguistic Description of Data

Using Dempster-Shafer Structures to Provide Probabilistic Outputs in Fuzzy Systems Modeling

The Experimenter and the Theoretician – Linguistic Synthesis to Tell Machines What to Do

Concepts, Theories, and Applications: The Role of “Experimentation” (and “Context”) for Formalizing New Ideas along Innovative Avenues

Imperfect Causality: Combining Experimentation and Theory

A Reflection on Fuzzy Conditionals

Fuzzy vs. Likert Scale in Statistics

Backmatter

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