In highly competitive industrial market, the concept of failure analysis is an unavoidable fact in complex industrial systems. Reliability of such systems not only depends on the reliability of each element of these systems, but also depends on occurrence of sequence of failures. In this paper, a novel approach to sequential failure analysis is proposed which is based upon fuzzy logic and the c...

Recently various generalizations or extensions of the now “classical” Wiener number1 have become of interest, both as regards new individual numbers2-7 and as regards sequences of numbers.8-12 Of particular interest here are those numbers of Tratch et al.2 and of Randić,3 their manner of interrelation, their formulas for trees as extended to general cycle-containing graphs, and their extension ...

Abstract A tournament on a graph is an orientation of its edges. The score sequence lists the in-degrees in non-decreasing order. Works by Winston and Kleitman (J Comb Theory Ser 35(2):208–230, 1983) Kim Pittel 92(2):197–206, 2000) showed that number $$S_n$$ S n sequenc...

In this study, we first define the concept of inverse and direct system in category of fuzzy modules. We investigate whether or not limit of inverse (direct) system of exact sequences of fuzzy modules is exact. Later, we show that direct system limit of exact sequences of fuzzy modules is exact. Generally, limit of inverse system of exact sequences is not exact. Then we define the notion ← (1) ...

in a previous work, we introduced particular fuzzy numbers anddiscussed some of their properties. in this paper we use the comparison methodintroduced by dorohonceanu and marin[5] to compare between these fuzzynumbers.

In this work, a new concept of upper dense sequence in interval (0,1] is introduced. There are infinitely many upper dense sequences in interval (0,1]. Using any upper dense sequence, a new decomposition theorem for fuzzy sets is established and proved. Then, using a chosen upper dense sequence as one of the necessary reference systems, infinitely many total orderings on the set of all fuzzy nu...