Foreword

I feel honored by the dedication of the Special Issue of IJCCC to me. I should like to express my deep appreciation to the distinguished Co-Editors and my good friends, Professors Balas, Dzitac and Teodorescu, and to distinguished contributors, for honoring me. The subjects which are addressed in the Special Issue are on the frontiers of fuzzy logic. The Foreword gives me an opportunity to share with the readers of the Journal my recent thoughts regarding a subject which I have been pondering about for many years - fuzzy logic and natural languages. The first step toward linking fuzzy logic and natural languages was my 1973 paper," Outline of a New Approach to the Analysis of Complex Systems and Decision Processes." Two key concepts were introduced in that paper. First, the concept of a linguistic variable - a variable which takes words as values; and second, the concept of a fuzzy if- then rule - a rule in which the antecedent and consequent involve linguistic variables. Today, close to forty years later, these concepts are widely used in most applications of fuzzy logic. The second step was my 1978 paper, "PRUF - a Meaning Representation Language for Natural Languages." This paper laid the foundation for a series of papers in the eighties in which a fairly complete theory of fuzzy - logic-based semantics of natural languages was developed. My theory did not attract many followers either within the fuzzy logic community or within the linguistics and philosophy of languages communities. There is a reason. The fuzzy logic community is largely a community of engineers, computer scientists and mathematicians - a community which has always shied away from semantics of natural languages. Symmetrically, the linguistics and philosophy of languages communities have shied away from fuzzy logic. In the early nineties, a thought that began to crystallize in my mind was that in most of the applications of fuzzy logic linguistic concepts play an important, if not very visible role. It is this thought that motivated the concept of Computing with Words (CW or CWW), introduced in my 1996 paper "Fuzzy Logic = Computing with Words." In essence, Computing with Words is a system of computation in which the objects of computation are words, phrases and propositions drawn from a natural language. The same can be said about Natural Language Processing (NLP.) In fact, CW and NLP have little in common and have altogether different agendas. In large measure, CW is concerned with solution of computational problems which are stated in a natural language. Simple example. Given: Probably John is tall. What is the probability that John is short? What is the probability that John is very short? What is the probability that John is not very tall? A less simple example. Given: Usually Robert leaves office at about 5 pm. Typically it takes Robert about an hour to get home from work. What is the probability that Robert is home at 6:l5 pm.? What should be noted is that CW is the only system of computation which has the capability to deal with problems of this kind. The problem-solving capability of CW rests on two key ideas. First, employment of so-called restriction-based semantics (RS) for translation of a natural language into a mathematical language in which the concept of a restriction plays a pivotal role; and second, employment of a calculus of restrictions - a calculus which is centered on the Extension Principle of fuzzy logic. What is thought-provoking is that neither traditional mathematics nor standard probability theory has the capability to deal with computational problems which are stated in a natural language. Not having this capability, it is traditional to dismiss such problems as ill-posed. In this perspective, perhaps the most remarkable contribution of CW is that it opens the door to empowering of mathematics with a fascinating capability - the capability to construct mathematical solutions of computational problems which are stated in a natural language. The basic importance of this capability derives from the fact that much of human knowledge, and especially world knowledge, is described in natural language. In conclusion, only recently did I begin to realize that the formalism of CW suggests a new and challenging direction in mathematics - mathematical solution of computational problems which are stated in a natural language. For mathematics, this is an unexplored territory

Examples of Artificial Perceptions in Optical Character Recognition and Iris Recognition

This paper assumes the hypothesis that human learning is perception based, and consequently, the learning process and perceptions should not be represented and investigated independently or modeled in different simulation spaces. In order to keep the analogy between the artificial and human learning, the former is assumed here as being based on the artificial perception. Hence, instead of choosing to apply or develop a Computational Theory of (human) Perceptions, we choose to mirror the human perceptions in a numeric (computational) space as artificial perceptions and to analyze the interdependence between artificial learning and artificial perception in the same numeric space, using one of the simplest tools of Artificial Intelligence and Soft Computing, namely the perceptrons. As practical applications, we choose to work around two examples: Optical Character Recognition and Iris Recognition. In both cases a simple Turing test shows that artificial perceptions of the difference between two characters and between two irides are fuzzy, whereas the corresponding human perceptions are, in fact, crisp.Comment: 5th Int. Conf. on Soft Computing and Applications (Szeged, HU), 22-24 Aug 201

A quantitative approach to topology for fuzzy regions

There has been lots of research in the field of fuzzy spatial data and the topology of fuzzy spatial objects. In this contribution, an extension to the 9-intersection model is presented, to allow for the relative position of overlapping fuzzy regions to be determined. The topology will be determined by means of a. new intersection matrix, and a set of numbers, expressing the similarity between the topology of the given regions and a number of predefined cases. The approach is not merely a conceptual idea, but has been built on our representation model and can as such be immediately applied

An artificial immune system for fuzzy-rule induction in data mining

This work proposes a classification-rule discovery algorithm integrating artificial immune systems and fuzzy systems. The algorithm consists of two parts: a sequential covering procedure and a rule evolution procedure. Each antibody (candidate solution) corresponds to a classification rule. The classification of new examples (antigens) considers not only the fitness of a fuzzy rule based on the entire training set, but also the affinity between the rule and the new example. This affinity must be greater than a threshold in order for the fuzzy rule to be activated, and it is proposed an adaptive procedure for computing this threshold for each rule. This paper reports results for the proposed algorithm in several data sets. Results are analyzed with respect to both predictive accuracy and rule set simplicity, and are compared with C4.5rules, a very popular data mining algorithm

Using level-2 fuzzy sets to combine uncertainty and imprecision in fuzzy regions

In many applications, spatial data need to be considered but are prone to uncertainty or imprecision. A fuzzy region - a fuzzy set over a two dimensional domain - allows the representation of such imperfect spatial data. In the original model, points of the fuzzy region where treated independently, making it impossible to model regions where groups of points should be considered as one basic element or subregion. A first extension overcame this, but required points within a group to have the same membership grade. In this contribution, we will extend this further, allowing a fuzzy region to contain subregions in which not all points have the same membership grades. The concept can be used as an underlying model in spatial applications, e.g. websites showing maps and requiring representation of imprecise features or websites with routing functions needing to handle concepts as walking distance or closeby

Tensor Algebra: A Combinatorial Approach to the Projective Geometry of Figures

This paper explores the combinatorial aspects of symmetric and antisymmetric forms represented in tensor algebra. The development of geometric perspective gained from tensor algebra has resulted in the discovery of a novel projection operator for the Chow form of a curve in P3 with applications to computer vision