In this paper  we give newresults on the best approximation  in the Hausdorff topological vectorspace and  consider relationship  with orthogonality. Also we determined under  what conditions the map $P_{K,f}$ is upper semicontinous.

Necessary and sufficient conditions under which two fuzzy sets (in the most general, poset valued setting) with the same domain have equal families of cut sets are given. The corresponding equivalence relation on the related fuzzy power set is investigated. Rela­ tionship of poset valued fuzzy sets and fuzzy sets for which the co-domain is Dedekind-MacNeille completion of that posets is deduced.

Well log data are routinely used for stratigraphic interpretation of the earth’s subsurface. This paper investigates using a co-evolutionary fuzzy system to generate a well log interpreter that can automatically process well log data and interpret reservoir permeability. The methodology consists of 3 steps: 1) transform well log data into fuzzy symbols which maintain the character of the origin...

Considering the increasing interest in fuzzy theory and possible applications,the concept of fuzzy metric space concept has been introduced by severalauthors from different perspectives. This paper interprets the theory in termsof metrics evaluated on fuzzy numbers and defines a strong Hausdorff topology.We study interrelationships between this theory and other fuzzy theories suchas intuitionis...

An orthogonality space is a set X together with symmetric and irreflexive binary relation ⊥, called the relation. A block partition of maximal mutually orthogonal elements X, decomposition collection subsets each which complement union others. (X,⊥) normal if any gives rise to unique space. The one-dimensional subspaces Hilbert equipped usual provides motivating example. Together maps that are,...

Fuzzy co-clustering extends co-clustering by assigning membership functions to both the objects and the features, and is helpful to improve clustering accurarcy of biomedical data. In this paper, we introduce a new fuzzy co-clustering algorithm based on information bottleneck named ibFCC. The ibFCC formulates an objective function which includes a distance function that employs information bott...