E. Helly’s theorem asserts that any bounded sequence of monotone real functions contains a pointwise convergent subsequence. We reprove this theorem in a generalized version in terms of monotone functions on linearly ordered sets. We show that the cardinal number responsible for this generalization is exactly the splitting number. We also show that a positive answer to a problem of S. Saks is o...

In the field of multicriteria decision analysis, the most distinctive characteristic of the monotone measure, or called the nonadditive measure, the fuzzy measure, the capacity, is that it can adequately and flexibly describe the interactions between the decision criteria. Traditionally, the interaction described with the monotone measure can be measured by the various kinds of the probabilisti...

The responses of single neurons in the primary and secondary auditory cortex of cat were recorded during the presentation of sequences consisting of five tones of different frequencies. Discharges to tones within these sequences usually (84%) exhibited a dependence on the 'direction' of the sequence (ascending, descending, or mixed frequencies). For sequences consisting of 5 tones of identical ...

It has been shown that the class of fuzzy sets a quasilinear space structure. In addition, various norms are defined on this class, and it is given normed with these norms. study, we first developed algebraic structure F ℝ n ...

Let \yA be a sequence of functions, y. e TlseSE where S is a nonempty subset of the /-dimensional Euclidean space and 77 is an ordered vector space with positive cone X . If y, £"sfji,i sufficient conditions are given that \y A have a subsequence \hA such that for each t e S the sequence {A.(i)| is monotone for k sufficiendy large, depending on i. If each E is an ordered topological vector spac...

The concept of difference sequence spaces have been given by M.Et.and Colak . In this paper, we defined Spaces ∆_v^r (l_∞ ) ,∆_v^r (c) and (c_0 their α- duals or Köthe – Töeplitz dual also discuss about some topological property these spaces. Further, checked perfectness properties like monotone solidness also.

In this paper we define the sequence space wF f ; p;D ð Þ which is called the space of strongly Dp-Cesàro summable sequences with modulus f. Furthermore the fuzzy D-statistically pre-Cauchy sequence is defined and the necessary and sufficient conditions are given for a sequence of fuzzy numbers to be fuzzy D-statistically preCauchy and to be fuzzy D-statistically convergent. Also some relations...

This paper considers reconngurations of polygons, where each polygon edge is a rigid link, no two of which can cross during the motion. We prove that one can reconngure any monotone polygon into a convex polygon; a polygon is monotone if any vertical line intersects the interior at a (possibly empty) interval. Our algorithm computes in O(n 2) time a sequence of O(n 2) moves, each of which rotat...

In this paper the concept of strongly (λM )p − Cesáro summability of a sequence of fuzzy numbers and strongly λM− statistically convergent sequences of fuzzy numbers is introduced. Keywords—Fuzzy numbers, statistical convergence, Orlicz space, entire sequence.