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, gai sequence.

In the era of huge datasets, the top-k search becomes an effective way to decrease the search time of top-k objects. The original top-k search requires a monotone combination function and lists of objects ordered by attribute values. Our approach of the top-k search is motivated by complex user preferences over product catalogues. Such user preferences are composed of the local user preferences...

This paper considers the generation of some interpretable fuzzy rules for assigning an amino acid sequence into the appropriate protein superfamily. Since the main objective of this classifier is the interpretability of rules, we have used the distribution of amino acids in the sequences of proteins as features. These features are the occurrence probabilities of six exchange groups in the seque...

Many AI/Machine learning problems require adaptively selecting a sequence of items, each selected item might provide some feedback that is valuable for making better selections in the future, with goal maximizing an adaptive submodular function. Most existing studies this field focus on either monotone case or non-monotone case. Specifically, if utility function and submodular, Golovin Krause (...

Recently the author defined a sequence of blowups for each variety in positive characteristic, called F-blowups. Our purpose is to prove that the sequence is monotone if the variety has only F-pure singularities. As a corollary, we also obtain some result on the stability of the sequence.

In this paper we present three algorithms that solve three combinatorial optimization problems related to each other. One of them is the patience sorting game, invented as a practical method of sorting real decks of cards. The second problem is computing the longest monotone increasing subsequence of the given sequence of n positive integers in the range 1, . . . , n. The third problem is to en...

In this paper we present three algorithms that solve three combinatorial optimization problems related to each other. One of them is the patience sorting game, invented as a practical method of sorting real decks of cards. The second problem is computing the longest monotone increasing subsequence of the given sequence of n positive integers in the range 1; : : : ; n. The third problem is to en...

Given a sequence of n independent random variables with common continuous distribution, we propose a simple adaptive online policy that selects a monotone increasing subsequence. We show that the expected number of monotone increasing selections made by such policy is within O(logn) of optimal. Our construction provides a direct and natural way for proving the O(logn)-optimality gap. An earlier...

Given a monotone graphical property Q, how large should d(n) be to ensure that if (Hn) is any sequence of graphs satisfying |Hn| = n and (Hn)¿d(n), then almost every induced subgraph of Hn has property Q? We prove essentially best possible results for the following monotone properties: (i) k-connected for :xed k, (ii) Hamiltonian. c © 2002 Elsevier Science B.V. All rights reserved.