The term Soft Computing (SC) represents the combination of emerging problem-solving technologies such as Fuzzy Logic (FL), Probabilistic Reasoning (PR), Neural Networks (NNs), and Genetic Algorithms (GAs). Each of these technologies provide us with complementary reasoning and searching methods to solve complex, real-world problems. After a brief description of each of these technologies, we will analyze some of their most useful combinations, such as the use of FL to control GAs and NNs parameters; the application of GAs to evolve NNs (topologies or weights) or to tune FL controllers; and the implementation of FL controllers as NNs tuned by backpropagation-type algorithms.

We present an approach to determine the similarity of classes which utilizes fuzzy and incomplete terminological knowledge together with schema knowledge. We clearly distinguish between semantic similarity determining the degree of resemblance according to real world semantics, and structural correspondence explaining how classes can actually be interrelated. To compute the semantic similarity we introduce the notion of semantic relevance and apply fuzzy set theory to reason about both terminological knowledge and schema knowledge. 1 Introduction The identification of similar or corresponding concepts forms one of the main steps when investigating different world models and relating them to each other. Apart from its long tradition in document retrieval, this issue has also been investigated in more structured frameworks such as schema independent query formulation, e.g., [Mot90], or database integration, where for a survey you may look at [SL90]. As argued in [GPN91], there should b...

this paper we investigate some logics whose set of truth values is the real interval [0; 1] and we concentrate our attention to logics having a conjunction whose truth function t(x; y) is a t-norm, and having a corresponding residuated implication (or, as Pavelka [14] observes, the conjunction and the implication form an adjoint couple); i.e., if i(x; y) is the truth function of the implication then

There has been a growing interest and activity in the area ofmultiple criteria decision making (MCDM), especially in the last 20 years. Modeling and optimization methods have been developed in both crisp and fuzzy environments. The overwhelming majority of approaches for finding best compromise solutions to MCDM problems do not make use of the interdependences among the objectives. However, as has been pointed out by [Car90, Car92], in modeling real world problems (especially in management sciences) we often encounter MCDM problems with interdependent objectives. It is our intention in this paper to introduce measures of interdependences between the objectives, in order to provide for a better understanding of the decision problem, and to find e#ective and more correct solutions to MCDM problems. Keywords: MCDM, e#ective solution, interdependence, triangular norm. # The final version of this paper appeared in: Computers

New reasoning techniques for dealing with uncertainty in expert systems have been embedded in RUM, a Reasoning with Uncertainty Module. RUM is an integrated software tool based on a frame system (KEE) that is implemented in an object oriented language. RUM's capabilities are subdivided into three layers: representation, inference, and control. The representation layer is based on frame-like data struc tures that capture the uncertainty information used in the inference layer and the uncertainty mete-information used in the control layer. Linguistic probabilities are used to describe the lower and upper bounds of the certainty mea sure attached to a well formed formula. The source and the conditions under which the information was obtained represent the non-numerical meta-information. The inference layer provides the uncertainty calculi with which to perform the intersection, detachment, union, and pooling of information. Five uncertainty calculi, based on their underlying Triangular norms, are used in this layer. The control layer uses the meta-information to select the appropriate calculus for each context and to resolve even tual ignorance or conflict in the information. This layer enables the programmer to declaratively express the local (context dependent) meta-knowledge that will substitute for the global assumptions traditionally used in uncertain reasoning. RUM has been tested in a sequence of experiments in both naval and aerial situation assessment, consisting of correlating reports and tracks, locating and classifying platforms, and identifying intents and threats. I.

In multiple objective programs [MOP], application functions are established to measure the degree of fulfillment of the decision maker’s requirements (achievement of goals,nearness to an ideal point,satisfaction,etc.) about the objective functions (see e.g.[7,24]) and are extensively used in the process of

Many different formal techniques, both numerical and symbolic, have been developed over the past two decades for dealing with incomplete and uncertain information. In this paper we review some of the most important of these formalisms, describing how they work, and in what ways they differ from one another. We also consider heterogeneous approaches which incorporate two or more approximate reasoning mechanisms within a single reasoning system. These have been proposed to address limitations in the use of individual formalisms.

Multiple Crtiple Decision Making (MCDM) shows signs of becoming a matur: field. Ther ar four quite distinct families of methods:(i) theoutr91 ing, (ii) the value and utilitytheor based, (iii) the multiple objectivepr68: ming, and (iv) gr): decision and negotiationtheor based methods. Fuzzy MCDM has basically been developed along the same lines, although with the help of fuzzy settheor a number of innovations have been made possible; the most impor:1 t methods arr17 ed and a novelappr68 h - inter57 endence in MCDM - is intr duced. 1

The capacity to robustly detect humans in video is a critical component of automated visual surveillance systems. This paper describes a bilattice based logical reasoning approach that exploits contextual information and knowledge about interactions between humans, and augments it with the output of different low level detectors for human detection. Detections from low level parts-based detectors are treated as logical facts and used to reason explicitly about the presence or absence of humans in the scene. Positive and negative information from different sources, as well as uncertainties from detections and logical rules, are integrated within the bilattice framework. This approach also generates proofs or justifications for each hypothesis it proposes. These justifications (or lack thereof) are further employed by the system to explain and validate, or reject potential hypotheses. This allows the system to explicitly reason about complex interactions between humans and handle occlusions. These proofs are also available to the end user as an explanation of why the system thinks a particular hypothesis is actually a human. We employ a boosted cascade of gradient histograms based detector to detect individual body parts. We have applied this framework to analyze the presence of humans in static images from different datasets. 1.

: In this paper, we introduce seminormed and semiconormed fuzzy integrals associated with confidence measures. These confidence measures have a field of sets as their domain, and a complete lattice as their codomain. In introducing these integrals, the analogy with the classical introduction of Legesgue integrals is explored and exploited. It is amongst other things shown that our integrals are the most general integrals that satisfy a number of natural basic properties. In this way, our dual classes of fuzzy integrals constitute a significant generalization of Sugeno's fuzzy integrals. A large number of important general properties of these integrals is studied. Furthermore, and most importantly, the combination of seminormed fuzzy integrals and possibility measures on the one hand, and semiconormed fuzzy integrals and necessity measures on the other hand, is extensively studied. It is shown that these combinations are very natural, and have properties which are analogous to the combi...