An ilttempt is made here to delnonslrale tile way of implemenllng the concept of fuzzy geometry in image proeessing/"Ilalysls prohlems. Some new measures "re also provided in lhis eontexL Four ,Jigorilhllls ,Ire described for objeet/baekgroulld classification and skeleton extraction in both fuzzy and nonfuZ7.y (crisp) forms. Their effectiveness is demollsl r;'lc<! Oil various lypes of images. T...

Our reasoning is clearly fuzzy, so why is crisp logic so often adequate? We explain this phenomenon by showing that in the presence of noise, an arbitrary continuous (e.g., fuzzy) system can be well described by its discrete analog. However, as the description gets more accurate, the continuous description becomes necessary. 1 Formulation of the Problem Fuzzy logic is needed. Our reasoning is c...

Two recently developed methods for extraction of crisp logical rules from neural networks trained with backpropagation algorithm are compared. Both methods impose constraints on the structure of the network by adding regularization terms to the error function. Networks with minimal number of connections are created, leading to a small number of crisp logical rules. The two methods are compared ...

A voting model semantics for fuzzy sets is assumed with the corresponding ideas of mass assignment theory. The use of fuzzy sets in this way will provide better interpolation, greater knowledge compression, less dependence on the effects of noisy data than if only crisp sets were used. We will see how easy and useful it is to use successful inference methods such as decision trees, probabilisti...

The design methodology used in the design of the CRISP Microprocessor is described. CRISP is a high performance 32-bit microprocessor using 172,163 transistors in a 1.75μ CMOS technology. A top down approach was taken in the design of the machine, using tools ranging from instruction set interpreters to detailed device modelling. In addition to a discussion of the tools, this paper describes th...

One of the main challenges of fuzzy community detection problems is to be able to measure the quality of a fuzzy partition. In this paper, we present an alternative way of measure the quality of a fuzzy community detection output based on n-dimensional grouping and overlapping functions that generalize the classical modularity for crisp community detection problems and also for crisp overlappin...

Crisp bread, as a new type of bread, had a stronger hardness, fracturability and a finer texture compared with the tradition hard bread. The objective of this study was to test whether Sodium Stearoyl Lactylate could change the microstructure of dough and improve the texture of crisp bread. Two probes used were P/2 and P/2N and these graphs were calculated by several means. Results of these cal...

In order to overcome weaknesses of the conventional crisp neural network and the fuzzy-operation-oriented neural network, we have developed a general fuzzy-reasoning-oriented fuzzy neural network called a Crisp-Fuzzy Neural Network (CFNN) which is capable of extracting high-level knowledge such as fuzzy IF-THEN rules from either crisp data or fuzzy data. A CFNN can eeectively compress a 5 5 fuz...