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.

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 ...

vendor selection is dominantly considered to be a multi attribute decision making (madm) problem, since the decision maker needs to evaluate suppliers simultaneously in different and even contrastive evaluation criteria. one shortcoming of madm methods is that they only compare alternatives with each other, and there is no comparison with the requirements of the buying company. a very efficient...

The existing Data Envelopment Analysis models for evaluating the relative eciency of a set of decision making units by using various inputs to produce various outputs are limited to crisp data in crisp production possibility set. In this paper, rst of all the production possibility set is extended to the fuzzy production possibility set by extension principle in constant return to scale, and th...

Since the world is full of indeterminacy, the neutrosophics found their place into contemporary research. The fundamental concepts of neutrosophic set, introduced by Smarandache in [30, 31, 32] and Salama et al. in [4-29]. In Geographical information systems (GIS) there is a need to model spatial regions with indeterminate boundary and under indeterminacy. In this paper the structure of some cl...

This paper presents a novel type-2 Fuzzy logic System to define the Shape of a facial component with the crisp output. The Fuzzy model, designed in this paper, takes crisp value of width and height of a facial component and produces the crisp value of Shape for different facial components. The Fuzzy model is designed using Matlab 6.5 and Visual Basic 6.0 and tested with the facial components ex...

We describe the use of weighted linked pyramids for soft region segmentation of colour images. In many digital images definitive region boundaries can not be determined, casting doubt on the reasonableness of a conventional crisp segmentation. We propose that soft segmentation gives a more natural region segmentation of digital images than conventional crisp segmentation. Weighted linked pyrami...