The unavoidable imprecision of measurements of continuous physical quantities can be modelled by using the concept of fuzzy numbers and fuzzy vectors. Concerning a quantitative usage of such data the classical concept of relative frequencies for real data has to be extended to so-called fuzzy relative frequencies for fuzzy data, whereby the fuzzy relative frequency of a set is a fuzzy number. A...

in this paper we classify fuzzy subgroups of a rank-3 abelian group $g = mathbb{z}_{p^n} + mathbb{z}_p + mathbb{z}_p$ for any fixed prime $p$ and any positive integer $n$, using a natural equivalence relation given in cite{mur:01}. we present and prove explicit polynomial formulae for the number of (i) subgroups, (ii) maximal chains of subgroups, (iii) distinct fuzzy subgroups, (iv) non-isomorp...

In this paper we present a Petri-net-based approach to consider anticipated faults in real-time distributed systems. The proposed approach is based on Fuzzy Time G-Nets which is the integration of two Petri Nets extensions: Fuzzy Time Petri Net (timing Petri net extension) and G-Nets (Petri net extended with object oriented concepts). We also show that Fuzzy Time G-Nets can be used to represent...

We introduce the concept of interval-valued fuzzy congruences on a semigroup S and we obtain some important results: First, for any interval-valued fuzzy congruence R on a group G, the interval-valued congruence class Re is an interval-valued fuzzy normal subgroup of G. Second, for any interval-valued fuzzy congruence R on a groupoid S, we show that a binary operation ∗ an S/R is well-defined a...

In this paper we present a Petri-net-based approach to consider fault tolerance aspects in a modiied control track vehicle system. The proposed approach is based on Fuzzy Time G-Nets which is the integration of two Petri Nets extensions: Fuzzy Time Petri Net (timing Petri net extension) and G-Nets (Petri net extended with object oriented concepts). We also show how to model such system by means...

The aim of this paper is to study induced (quasi-)uniformities in Kramosil and Michalek's fuzzy metric spaces. Firstly, $I$-uniformity in the sense of J. Guti'{e}rrez  Garc'{i}a and $I$-neighborhood system in the sense of H"{o}hle and u{S}ostak are induced by the given fuzzy metric. It is shown that the fuzzy metric and the induced $I$-uniformity will generate the same $I$-neighborhood system. ...

The chromatic sum of a graph G, ∑ (G), is introduced in the dissertation of Kubicka [3]. It is defined as the smallest possible total over all vertices that can occur among all colorings of G using natural numbers for the colors. It is known that computing the chromatic sum of an arbitrary graph is an NP-complete problem. The vertex-strength of the graph G, denoted by s(G), is the smallest inte...

Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Aim of this article is to find the maximum and minimum solution of the fuzzy neutrosophic soft relational equations xA=b and Ax=b, where x and b are fuzzy neutrosophic soft vector and A is a fuzzy neutrosophic soft matrix. Wheneve...

A fuzzy graph (f-graph) is a pair G : (σ, μ) where σ is a fuzzy subset of a set S and μ is a fuzzy relation on σ. A fuzzy graph H : (τ, υ) is called a partial fuzzy subgraph of G : (σ, μ) if τ (u) ≤ σ(u) for every u and υ (u, v) ≤ μ(u, v) for every u and v . In particular we call a partial fuzzy subgraph H : (τ, υ) a fuzzy subgraph of G : (σ, μ ) if τ (u) = σ(u) for every u in τ * and υ (u, v) ...

In the literature, there are a lot of methods concerning the problem of ordering the interval numbers k , ~ ] , [y,g], ... (', ') or the fuzzy ones A, B , ... (see 4, and for a n overview of methods). All of these methods can be classified a s belonging t o two different approaches. (i) Ordering t h e crisp or the fuzzy intervals using binary order relations: [ c , ~ ] 4 [ y , ~ ] , A 5 B, .......