During the last two decades, Group for intelligent systems at Mathematical faculty in Belgrade has developed several theorem provers for different kind of formal systems. Lately, we have turned our attention to fuzzy logic and development of the corresponding theorem prover. The first step is to find the suitable axiomatization, i.e., the formalization of fuzzy logic that is sound, complete and...

A fuzzy knowledge-based network is developed based on the linguistic rules extracted from a fuzzy decision tree. A scheme for automatic linguistic discretization of continuous attributes, based on quantiles, is formulated. A novel concept for measuring the goodness of a decision tree, in terms of its compactness (size) and efficient performance, is introduced. Linguistic rules are quantitativel...

A hybrid approach to fuzzy supervised learning is presented. It is based on a genetic-neuro learning algorithm. The mixed-genetic coding adopted involves only the premises of the fuzzy rules. The conclusions are derived through a least-squares solution of an over-determined system using the singular value decomposition (SVD) algorithm. The paper presents the results obtained with C++ software c...

Bijayalaxmi Panda, Soumya Sahoo, Sovan Kumar Patnaik Abstract— Cluster analysis is one of the major techniques in pattern recognition, which is basically considered as one of the unsupervised learning technique. We can apply clustering techniques in various areas like clustering medicine, business, engineering systems and image processing, etc.,The traditional hard clustering methods restrict t...

Algorithms based on minimization of compactness and of fuzziness are developed whereby it is possible to obtain both fuzzy and nonfuzzy (thresholded) versions of an ill-defined image. The incorporation of fuzziness in the spatial domain, i.e., in describing the geometry of regions, makes it possible to provide more meaningful results than by considering fuzziness in grey level alone. The effect...

in this paper the concepts of fuzzifying β − irresolute functions and fuzzifying β − compactspaces are characterized in terms of fuzzifying β − open sets and some of their properties are discussed.

In this paper we consider a dominating Finsler metric on a complete Riemannian manifold. First we prove that the energy integral of the Finsler metric satisfies the Palais-Smale condition, and ask for the number of geodesics with endpoints in two given submanifolds. Using Lusternik-Schnirelman theory of critical points we obtain some multiplicity results for the number of Finsler-geodesics betw...

Given a manifold M and a proper sub-bundle ∆ ⊂ TM , we study homotopy properties of the horizontal base-point free loop space Λ, i.e. the space of absolutely continuous maps γ : S → M whose velocities are constrained to ∆ (for example: legendrian knots in a contact manifold). A key technical ingredient for our study is the proof that the base-point map F : Λ → M (the map associating to every lo...