Scientia Iranica
Volume:18 Issue: 3, 2011

In a historical context, we first review the development of fuzzy system models from “Fuzzy Rule Bases” proposed by Zadeh (1975) [1], with versions of Sugeno–Yasukawa (1993) [2] and Tagaki–Sugeno (1985) [3]. Secondly, we review the development of the “Fuzzy C-Regression Model” (FCRM), proposed by Hathaway and Bezdek (1993) [4], as well as “Combined FCM, and FCRM Algorithms, proposed by Höppner and Klawonn (2003) [5]. Thirdly, we review “Fuzzy Functions”, proposed by Türkşen (2008) [6] and further developed by Celikyilmaz and Türkşen (2008–2009) [7], [8] and [9] in a variety of versions. An experimental assessment of various models are discussed in this writing.

The viewpoint of this paper is based on the hypothesis that human expert know-how is represented and stored in natural fuzzy linguistic terms. Know-how is obtained by the summarization of numerous experiences over a long period of time and expressed with a set of fuzzy IF-THEN rules. This paper describes the electronic circuits, both in current and voltage modes including semiconductor chips that were developed from 1980–1997, and dedicated to fuzzy information processing. A set of fuzzy IF-THEN rules with a fuzzy inference engine has a good ability to describe complicated systems that are nonlinear, time-varying, multivariable, chaotic, unpredictable, etc. The focus of this paper lies not only on a fuzzy inference engine and defuzzifier, but also on a fuzzy memory device, fuzzy PLA, a grade-controllable membership function circuit and time-sweeping mode fuzzy computer hardware. Distinctive features of a fuzzy logic controller are presented by employing benchmark tests, such as an inverted pendulum, wine glass stabilization and mouse stabilization. These experimental results show that fuzzy logic control is effective, even in cases where the mathematical model is not available.

To improve the exploration and exploitation abilities of the standard Gravitational Search Algorithm (GSA), a novel operator called “Disruption”, originating from astrophysics, is proposed. The disruption operator is inspired by nature and, with the least computation, has improved the ability of GSA to further explore and exploit the search space. The proposed improved GSA has been evaluated on 23 nonlinear benchmark functions and compared with standard GSA, the genetic algorithm and particle swarm optimization. The obtained results confirm the high performance of the proposed method in solving various nonlinear functions.

This article provides very personal reflections on some of the important contributions made by Lotfi A. Zadeh that have made impacts upon my own research. Upon reflection, I found that his work-fuzzy and non-fuzzy-have influenced much of my career.

Investigation of the chaotic behavior of traffic streams at urban intersections due to signals has involved researchers in endeavoring to predict a smooth traffic flow model for stabilizing traffic congestion and avoid unnecessary delays. In this paper, we study a hybrid adaptive model, based on a combination of coloured Petri nets, fuzzy logic and learning automata, to efficiently control traffic signals. We show that in comparison with results found in the literature, vehicle delay time is significantly reduced using the proposed method.

The contribution of Lotfi Zadeh to the development of fuzzy logic goes far beyond the introduction of the seminal concept of a fuzzy set, and has multiple facets. This article, as a small tribute to the corpus of ideas, notions and results brought together over almost five decades by Zadeh, singles out and illustrates two of his most stimulating, thought-provoking and fruitful creations: fuzzy rules, on the one hand, and possibility theory, on the other. Indeed, the modeling of conditional statements of the form, “if x is A, then y is B”, plays a crucial role in any attempt at formalizing human reasoning. Starting from the expression of different forms of fuzzy rules that have been identified in the setting of possibility theory, we study their counterparts in the extensions of possibilistic logic. A distinction between rules and meta-rules is especially emphasized in the representational setting of possibility theory. It amounts to viewing rules as pieces of knowledge that contribute to the partial specification of a unique epistemic state, while meta-rules characterize constraints between specified epistemic states, as in possibilistic answer set programming.

Zadeh is one of the most impressive thinkers of the current time. An engineer by formation, although the range of his scientific interests is very broad, this paper only refers to his work towards reaching computation, mimicking ordinary reasoning, expressed in natural language, namely, with the introduction of fuzzy sets, fuzzy logic, and soft computing, as well as more recently, computing with words and perceptions.

Breast cancer is one of the leading causes of female mortality in the world, and early detection is an important means of reducing the mortality rate. The presence of microcalcification clusters has been considered as a very important indicator of malignant types of breast cancer, and its detection is important to prevent and treat the disease. This paper presents an effective approach, in order to detect microcalcification clusters in digitized mammograms, based on the synergy of image processing and partitional (hard and fuzzy) clustering techniques. Mathematical morphology has been used for image processing, and is used in this work as a first step, with the purpose of enhancing the contrast of microcalcifications. Image segmentation is an important task in the field of image processing, in order to identify regions with the same features. In the second step, we use image segmentation, using three partitional, hard and fuzzy clustering algorithms, such as k-Means, Fuzzy c-Means and Possibilistic Fuzzy c-Means, in order to make a comparison of the advantages and drawbacks offered by these algorithms, and which should help to improve the detection of microcalcification clusters in digitized mammograms.

In this paper, we provide a new perspective on the issues of mentation and cognition and its mathematical formulation using fuzzy logic approach.

In this paper, we highlight one of the brightest concepts launched by L. Zadeh, namely, the extension principle. Due to this principle, every one-to-one correspondence and, more generally, every one-to-many correspondence can be extended to fuzzy sets, i.e. sets without precise boundaries.

The purpose of this paper is to present Lotfi Zadeh’s influence on mathematics. Mathematics rests on the foundation of logic and set theory. L.A. Zadeh’s seminal paper on fuzzy sets laid the groundwork for fuzzy logic and thus the foundation of fuzzy mathematics.

In system modeling, knowledge management comes vividly into the picture when dealing with a collection of models. These models, being considered as sources of knowledge, are engaged in some collective pursuits of collaboration and consensus formation. We show the use of information granules in these processes by elaborating on their conceptual role. It is revealed that information granules are used to facilitate processes of collaboration and consensus building. Such granular constructs, referred to as granular models, can also emerge as a part of higher order models to reflect and quantify the diversity of the sources of knowledge involved in knowledge management. Several detailed algorithmic schemes are presented, along with related computational aspects associated with Granular Computing. It is also shown how the construction of information granules, through the use of the principle of justifiable granularity, becomes advantageous in the realization of granular models. This study builds upon seminal concepts established in L.A. Zadeh’s Rosetta Stone paper devoted to information granulation.

This paper outlines the inspiration received by the author from the Zadeh–MacFarlane–Jamshidi trio in his pursuit concerning the theory and Application of fuzzy logic. Beginning with Zadeh’s pioneering work, a hierarchical control system was developed, in collaboration with MacFarlane, for application in robotic manipulators. Subsequently, the work was extended to an analytical basis for controller tuning using fuzzy decision making. On the prompting of Jamshidi to address the issue of knowledge-base simplification, theorems were developed related to decoupling a fuzzy rule base. These developments provided a theoretical basis for applying single-context decision making to a problem governed by the knowledge base of coupled fuzzy rules. The developed theorems establish an analytical equivalence between the decisions made from a coupled set of fuzzy rules and an uncoupled set of fuzzy rules concerning the same problem domain. These developments have been applied to supervisory control of an industrial fish cutting machine. The paper presents the pertinent theory and illustrative examples.

Conventional approaches to optimization generally utilize a point-based search to scan domains of complex functions. These optimization algorithms, as a result, face a perpetual search that is never concluded with certainty, since the search space can never be completely scanned. In contrast, the proposed approach benefits from a granular view to scan the whole of the domain space. Such perspective can yield an efficient tool for analysis of complex functions, especially when proof is required. In contrast to conventional granular techniques that usually compute with certain granules, this scheme exploits uncertain granules, in addition to certain ones, to improve computational efficiency. To efficiently navigate the search space, Zadeh’s extension principle, along with several heuristics, is introduced to estimate and reduce the likeliness of inaccuracy. Function analysis is then converted to a question–answering process. This method is general and can be applied to all types of functions whether linear or nonlinear, analytical or non-analytical and continuous or discrete. Several examples and a MATLAB toolbox are provided to illustrate the real-world applicability and computational efficiency of the approach.

A fuzzy set theoretic approach for handling preference uncertainty within the paradigm of the Graph Model for Conflict Resolution is employed for systematically carrying out the strategic investigation of a conflict over the proposed export of water in bulk quantities. Following an overview of the literature regarding fuzzy preferences and their applications in decision making, the graph model is restructured to incorporate fuzzy preferences into calculations of stability. Nash and sequential stability definitions, which reflect human behavior in conflict, are modified to accommodate fuzzy preferences. The conflict over the potential large-scale export of water from Lake Gisborne, located in Canada’s Newfoundland and Labrador province, is modeled, assuming that one of the four Decision Makers (DMs) in the dispute has fuzzy or uncertain preferences, while the preferences of the remaining DMs are crisp. The strategic insights gained by varying the satisficing behavior of the DM with fuzzy preferences are discussed.

This paper presents an introduction to the analysis and synthesis of sampled-data (discrete-time) systems, i.e. systems in which some or all signals can change values only at discrete values of time. The description of these systems is presented using state-space concepts. Following an introduction to linear discrete-time systems including systems where two or more samplers operate at different frequencies, here is a brief introduction to non-linear systems including the study of stability using the Second Method of Lyapunov. The latter part of the paper describes pulse-width modulated discrete systems. The final section considers the synthesis of systems designed to reach equilibrium states in the minimum number of sampling periods. The concepts discussed in the paper are illustrated with a large number of examples.

This paper describes a biometric personal authentication method, using a pair of right and left sole pressure distribution changes, while walking. This system acquires sole pressure distribution changes via a mat type load distribution sensor, and does personal authentication. We employ twelve features based on the shape of a footprint, and twenty seven features based on weight movement for sole pressure data. Fuzzy if-then rules for each registered person are introduced, within which, their parameters are statistically determined in the learning process. We calculate the fuzzy degree of a pair of right and left sole pressure data for any registered person, and identify the walking person as the person with the highest fuzzy degree; the fuzzy degree being higher than a threshold. We employed 90 volunteers and authenticated them. We evaluate the proposed fuzzy method by five hold cross validation on which low false rejection and false acceptance rates are achieved. Thus, this fuzzy logic approach is precise for this biometric system.

During the past few years, research in the field of cooperative control of swarms of robots and especially UAV has continuously increased. In order to develop research in the field of swarms of UAV, this paper identifies three problems: the development of a testbed for UAV, the implementation of an ad hoc network and a protocol based on network control, and a consensus control algorithm for cooperative control of UAV. The testbed currently enables us to perform waypoint navigation using a Global Positioning System (GPS). The protocol communication designed for the ad hoc network has proved to be reliable for our application and can be expanded to be used with different numbers of agents. The algorithm of consensus control has been analyzed and tested in simulation. Future work will allow implementing the consensus control as a centralized or distributed control.

Uncertainty is generally defined as ‘that which is not precisely known’. This definition permits the identification of different kinds of uncertainty arising from different sources and activities, most of which go unnoticed in analysis. In this paper, the evolution of uncertainty through time begins from a historical perspective and concludes with a new perspective based upon making inferences. The evolution of uncertainty, in terms of analytical progress, begins with assessing probabilities and concludes with models and methods for assessing the ‘total uncertainty’ within an application. Both evolutionary tracks are briefly described in the context of physical science and engineering applications; however, nothing presented precludes application to other fields, e.g. economics, social sciences, medicine and business. As we honor his 90th birthday, Zadeh’s fuzzy sets and logic play a prominent role in both evolutions. Uncertainty assessment involves how to identify, classify, characterize, quantify, and combine uncertainties within an application, with the expressed goal of understanding how to manage uncertainties. Managing uncertainties is important, because uncertainties directly affect decision and policy making. Assessment and quantification of uncertainties are generally defined and outlined. Mathematical developments are not provided and in some cases are still under or in need of development.

scarcely seems possible that Professor Lotfi Zadeh is 90 years old, and that I have known him for 49 years. Since 1961, every time I meet him, he never seems to age in his “uniform” of black dress pants and hounds-tooth checkered sports coat. Of course, he himself has humorously and self-deprecatingly characterized that “once you sank to the lowest point, you cannot age anymore”. I prefer to think of him as ageless and forever generous, especially with young scholars.

Gupta is Professor (Emeritus), and holds the Distinguished Chair, at the College of Engineering, and is Director of the Intelligent Systems Research Laboratory at the University of Saskatchewan. Dr. Gupta’s current research interests are in the areas of Neuro-Vision Systems, Neuro-Control Systems, Integration of Fuzzy-Neural Systems, Neuronal Morphology of Biological Vision Systems, Intelligent and Cognitive Robotic Systems, Cognitive Information, New Paradigms in Information Processing, Chaos in Neural Systems, and Fuzzy-Neural Logic in Law. He is also developing some new architecture of Computational Neural Networks and Computational Fuzzy Neural Networks for application to Advanced Robotics, Aerospace, Medical, Industrial, Business Systems and Law. His interests also lie in: Signal and Image Processing with Applications to Medical Systems. Dr Gupta is a Fellow of IEEE, IFSA and SPIE.