We extend the notion of immunity to closed sets and to Π1 classes in particular in two ways: immunity meaning the corresponding tree has no infinite computable subset, and tree-immunity meaning it has no infinite computable subtree. We separate these notions from each other and that of being special, and show separating classes for computably inseparable c.e. sets are immune and perfect thin cl...

We explore a notion of fuzzy T -neighbourhood spaces, for any continuous triangular norm T , and we present on this notion a uni6ed treatment. Our theory, on one hand, generalizes the theory of Lowen (Fuzzy Sets and Systems 7 (1982) 65) from T =Min to arbitrary T , which has been the progenitor of this work, and on the other hand it is strongly related to the theory of L-neighbourhoods of H; oh...

The development and maintenance of software reliability enjoys a high priority in the evolution of modern computer technology. Over the last three decades or so, a tremendous amount of research has gone into the theory and practice of producing reliable software. Given the many subjective factors that in3uence software reliability, it is surprising that very little of this research has been dir...

Contrapositive symmetry (CPS) is a tautology in classical logic. In fuzzy logic, not all fuzzy implications have CPS with respect to a given strong negation. Given a fuzzy implication J , towards imparting contrapositive symmetry to J with respect to a strong negation N two techniques, viz., upper and lower contrapositivisation, have been proposed by Bandler and Kohout [Semantics of implication...

The comparison of protein structures is an important problem in bioinformatics. As a protein biological role is derived from its three dimensional native state, the comparison of a new protein structure (with unknown function) with other protein structures (with known biological activity) can shed light into the biological role of the former. Consequently, advances in the comparison (and cluste...

Words mean different things to different people, and so are uncertain. We, therefore, need a fuzzy set model for a word that has the potential to capture their uncertainties. In this paper I propose that an interval type-2 fuzzy set (IT2 FS) be used as a FS model of a word, because it is characterized by its footprint of uncertainty (FOU), and therefore has the potential to capture word uncerta...

‎Let $X$ be a real normed  space, then  $C(subseteq X)$  is  functionally  convex  (briefly, $F$-convex), if  $T(C)subseteq Bbb R $ is  convex for all bounded linear transformations $Tin B(X,R)$; and $K(subseteq X)$  is  functionally   closed (briefly, $F$-closed), if  $T(K)subseteq Bbb R $ is  closed  for all bounded linear transformations $Tin B(X,R)$. We improve the    Krein-Milman theorem  ...

in this paper, rstly we have introduced to entropy of sequences of fuzzy sets and given sometheorems about it. secondly, the waves p and t which appears in electrocardiograms weretransferred to fuzzy sets, by using denition of entropy for sequences of fuzzy sets, and somenumerical values were obtained for sequences of waves p and t. thus any person can makea medical predictions for some cardiac...

in this paper, by means of fuzzy approaches, an accurate method is introduced for edging of color photographs. the difference between our method with other similar methods is the use of a morphological operation to think or thick the obtained edges. in this proposed method, a 3×3 window is dragged on the photo. for each block, 12 point sets will be defined, each including two non-overlapping po...