Iranian journal of fuzzy systems
Volume:1 Issue: 1, 2004

The appearance of the first issue of the Iranian Journal of Fuzzy Systems, or IJFS for short, is an important event—an event which reflects substantial research activity in Iran aimed at advancing the frontiers of fuzzy logic, soft computing and their applications. On perusing the contents of the first issue, one cannot but be highly impressed by the quality of reported research, its wide range and its up-to-dateness. The contributors, the editors and the editorial board deserve congratulations on launching IJFS; we should like to extend to all our best wishes for further successes. It is a centuries-old tradition to base scientific theories on Aristotelian logic—a logical system whose centerpiece is the principle of the excluded-middle: truth is bivalent, meaning that every proposition, p, is either true or false, with no shades of truth allowed. But as we move further into the age of computation and automated reasoning, it becomes increasingly apparent that bivalence is in fundamental conflict with reality. In the real world, truth is pervasively a matter of degree, and partiality is the norm rather than exception. It is this reality that underlies the conceptual structure of fuzzy logic. In fuzzy logic, everything is, or is allowed to be, a matter of degree. What is undeniably true is that bivalent-logic-based scientific theories have led to brilliant successes that are visible to all. We have conquered space, we have built incredibly fast computers, we have the Internet, and we can communicate via mobile telephones. But alongside the brilliant successes, we see instances of significant failures and slow progress. We cannot construct robots that can compete with children in agility; we cannot write programs which can summarize a book; and we cannot automate driving a car in city traffic. What is the reason for successes, on one hand, and failures on the other? Humans have a remarkable capability to perform a wide variety of physical and mental tasks, e.g., driving a car in city traffic, without any measurements and any computations. In performing such tasks, humans employ perceptions—perceptions of time, distance, speed, shape and other attributes of physical and mental objects. Perceptions are intrinsically imprecise, reflecting the bounded ability of sensory organs, and ultimately the brain, to resolve detail and store information. A concomitant of imprecision of perceptions is that bivalent-logic-based systems are inherently limited in their capability to operate on perception-based information. It is this limitation of conventional bivalent-logic-based approaches that underlies the lack of significant progress in problem-areas in which perceptions play an important role. Fuzzy logic abandons bivalence. In so doing, fuzzy logic opens the door to exploration of new directions in the advancement of machine intelligence and systems analysis. The role model for fuzzy logic is the human mind. From a system-theoretic point of view, fuzzy logic is linked to all of the important aspects of systems theory-modeling, identification, analysis, synthesis stability, filtering, and estimation. In particular, interest in stability theory of fuzzy control systems has grown markedly in recent years. Alongside the growth in theory, industrial, consumer, financial, medical and other applications of fuzzy systems have proliferated in Japan, Europe, the United States, China and many other countries. There are still some who view fuzzy set theory and fuzzy logic with a skeptical eye, but the initial widespread resistance to the basic ideas of fuzzy set theory and fuzzy logic has been relegated to history. A key component of the theory of fuzzy systems is the calculus of fuzzy if-then rules. This tool is the basis for the linguistic approach—an approach which provides an alternative to the conventional numerically-based approaches to systems design and analysis. An important aspect of the linguistic approach is that it obviates the need for precise mathematical models of control and decision processes. The linguistic approach is associated with an extensive literature and is likely to be an object of considerable attention in IJFS. The Iranian Journal of Fuzzy Systems should play an important role as a forum for presentation of new ideas and new applications. We should like to extend to Dr. Mashinchi and Borzooei our special congratulations for pioneering the Journal and for contributing so much and in so many ways to the advancement of the theory of fuzzy systems and its applications.

In recent years there has been a remarkable increase in research activity connected with fuzzy thinking in Iran and its neighboring countries, and these countries have hosted several international conferences in many fields related to fuzzy sets and systems. We have been encouraged to launch this new journal by friends around the world, some of whom have been kind enough to respond to our appeal for invited papers. We would like to express our immense gratitude to all of them as well as to the members of the editorial board and all our colleagues who have agreed to act as referees for the journal. As always, Professor Lotfi Zadeh has been a beacon of light and we owe him very special thanks. This issue of the journal is dedicated to the late Professor V. Tahani of the Isfahan University of Technology, both a friend and much esteemed colleague who, after a protracted fight with cancer, passed away in September 2000, much too young.

The paper analyses issues leading to errors in graphic object classifiers. The distance measures suggested in literature and used as a basis in traditional, fuzzy, and Neuro-Fuzzy classifiers are found to be not suitable for classification of non-stylized or fuzzy objects in which the features of classes are much more difficult to recognize because of significant uncertainties in their location and gray-levels. The authors suggest a Neuro-Fuzzy graphic object classifier with modified distance measure that gives better performance indices than systems based on traditional ordinary and cumulative distance measures. The simulation has shown that the quality of recognition significantly improves when using the suggested method.

While sophisticated analytical methods like Morgenstern-Price or finite element methods are available for more realistic analysis of stability of slopes, assessment of the exact values of soil parameters is practically impossible. Uncertainty in the soil parameters arises from two different sources: scatter in data and systematic error inherent in the estimate of soil properties. Hence, stability of a slope should be expressed using a factor of safety accompanied by a reliability index. In this paper, theory of fuzzy sets is used to deal with the uncertain nature of soil parameters and the inaccuracy involved in the analysis simultaneously. Soil parameters are defined using suitable fuzzy sets and the uncertainty inherent in the value of factor of safety is assessed accordingly. It is believed that this approach accounts for the uncertainty in soil parameters more realistically compared to the conventional probabilistic approaches reported in the literature. A computer program is developed that carries out the large amount of calculations required for evaluating the fuzzy factor of safety based on the concept of domain interval analysis. An aggregated fuzzy reliability index (AFRI) is defined and assigned to the calculated factor of safety. The proposed method is applied to a case study and the results are discussed in details. Results from sensitivity analysis describe where the exploration effort or quality control should be concentrated. The advantage of the proposed method lies in its fast calculation speed as well as its ease of data acquisition from experts'' opinion through fuzzy sets.

The pioneer work of image compression/reconstruction based on fuzzy relational equations (ICF) and the related works are introduced. The ICF regards an original image as a fuzzy relation by embedding the brightness level into [0,1]. The compression/reconstruction of ICF correspond to the composition/solving inverse problem formulated on fuzzy relational equations. Optimizations of ICF can be consequently deduced based on fuzzy relational calculus, i.e., computation time reduction/improvement of reconstructed image quality are correspond to a fast solving method/finding an approximate solution of fuzzy relational equations, respectively. Through the experiments using test images extracted from Standard Image DataBAse (SIDBA), the effectiveness of the ICF and its optimizations are shown.. Optimizations of ICF can be consequently deduced based on fuzzy relational calculus, i.e., computation time reduction/improvement of reconstructed image quality are correspond to a fast solving method/finding an approximate solution of fuzzy relational equations, respectively. Through the experiments using test images extracted from Standard Image DataBAse (SIDBA), the effectiveness of the ICF and its optimizations are shown.

In applications there occur different forms of uncertainty. The two most important types are randomness (stochastic variability) and imprecision (fuzziness). In modelling, the dominating concept to describe uncertainty is using stochastic models which are based on probability. However, fuzziness is not stochastic in nature and therefore it is not considered in probabilistic models. Since many years the description and analysis of fuzziness is subject of intensive research. These research activities do not only deal with the fuzziness of observed data, but also with imprecision of informations. Especially methods of standard statistical analysis were generalized to the situation of fuzzy observations. The present paper contains an overview about the presentation of fuzzy information and the generalization of some basic classical statistical concepts to the situation of fuzzy data.

The notion of strong arcs in a fuzzy graph was introduced by Bhutani and Rosenfeld in [1] and fuzzy end nodes in the subsequent paper [2] using the concept of strong arcs. In Mordeson and Yao [7], the notion of ``degrees'' for concepts fuzzified from graph theory were defined and studied. In this note, we discuss degrees for fuzzy end nodes and study further some properties of fuzzy end nodes and fuzzy cut nodes.

The intuitionistic fuzzification of (strong, weak, s-weak) hyper BCK-ideals is introduced, and related properties are investigated. Characterizations of an intuitionistic fuzzy hyper BCK-ideal are established. Using a collection of hyper BCK-ideals with some conditions, an intuitionistic fuzzy hyper BCK-ideal is built.

In this paper, countable compactness and the Lindelof property are defined for L-fuzzy sets, where L is a complete de Morgan algebra. They don''t rely on the structure of the basis lattice L and no distributivity is required in $L$. A fuzzy compact L-set is countably compact and has the Lindelof property. An L-set having the Lindelof property is countably compact if and only if it is fuzzy compact. Many characterizations of countable compactness and the Lindelof property are presented by means of open L-sets and closed L-sets when L is a completely distributive de Morgan algebra.