In paper the fuzzy linear system d x C x A ~ ~ ~   where A and C are crisp matrices and n m  d~ is a LR fuzzy numbers vector, is investigated in detail. We generalize the definition and arithmetic operations of LR fuzzy numbers and convert the dual fuzzy linear system to two crisp systems of linear equations. Then the minimal fuzzy solution of the original fuzzy system is obtained by solving...

Since the surveys described in our last report (Crisp, 1958) on the distribution in north-west Europe of the immigrant Australasian barnacle, Elminius modestus Darwin, the species has become much commoner along the western coasts and has finally spread to Ireland (Beard, 1957). In this report we present the results of surveys made in 1958-9 along the eastern side of the Irish Channel and in the...

The deserts of the world are hottest places, very less rainfall, almost clear skies throughout the year. These deserts receive highest direct normal irradiance which is most suitable for concentrating solar power plants. With the technological developments and their innovations in concentrating solar power, thermal storage and hybridization/ back up, the sunniest countries expects that CSP shou...

We use a combination of three techniques for the speciication of processes, data and time: CSP, Object-Z and Duration Calculus. Whereas the combination of CSP and Object-Z is well established by the work of C. Fischer 2, 3], the integration with Duration Calculus is new. The combination is used to specify parts of a novel case study on radio controlled railway crossings.

It is well known that the linear extension majority (LEM) relation of a poset of size n ≥ 9 can contain cycles. In this paper we are interested in obtaining minimum cutting levels αm such that the crisp relation obtained from the mutual rank probability relation by setting to 0 its elements smaller than or equal to αm, and to 1 its other elements, is free from cycles of length m. In a first par...

In 1965, Zadeh [30] introduced a concept of a fuzzy set as the generalization of a crisp set. Also, in 1971, he introduced a fuzzy relation naturally, as a generalization of a crisp relation in [31]. Nel [27] introduced the notion of a topological universe which implies concrete quasitopos [1]. Every topological universe satisfies all the properties of a topos except one condition on the subobj...

In this paper we focus on linear fuzzy programming problems. The linear fuzzy programming problems will contain fuzzy constraints with a crisp objective function, crisp constraints with a fuzzy objective function, or fuzzy constraints with a fuzzy objective function. We propose here optimizing fuzzy constraints and objectives that consist of a triplet and are much like triangular fuzzy numbers,...

The support of a set A is the crisp subset of A with nonzero membership grades. Similarly, the core of a set A is the crisp subset of A with membership grade equal to one. So, supp(A) = {x|μA(x) > 0} and core(A) = {x|μA(x) = 1}. (1.1.4) The α-cut Aα of a set A is the crisp subset of A with membership grades of at least α. So, Aα = α-cut(A) = {x|μA(x) ≥ α}. (1.1.5) Note that core(A) = 1-cut(A). ...

In this work we propose an approach to encode real objects represented by feature vectors into fuzzy concepts. A system is designed, whose main component is an adaptive fuzzy encoder which learns object membership degrees to fuzzy concepts from a set of objects and the expert’s crisp assignment to a concept. To properly use the expert’s crisp choices, the learning is performed with the help of ...

This article introduces interior and closure operators with inclusion degree considered within a crisp or fuzzy topological framework. First, inclusion degree is introduced in an extension of the interior and closure operators in crisp topology. This idea is then introduced in fuzzy topology by incorporating a relaxed version of fuzzy subsethood. The introduction of inclusion degree leads to a ...