2. Fuzzy stochastic processes First we give some mathematical notations regarding fuzzy numbers. Let (Ω,M, P ) be a probability space, where M is a σ-field and P is a non-atomic probability measure. R denotes the set of all real numbers, and let C(R) be the set of all non-empty bounded closed intervals. A ‘fuzzy number’ is denoted by its membership function ã : R → [0, 1] which is normal, upper...

We introduce the concepts of fuzzy (r, s)-regular open sets and fuzzy almost (r, s)-continuous mappings on the intuitionistic fuzzy topological spaces in Šostak’s sense. Also we investigate the equivalent conditions of the fuzzy almost (r, s)-continuity.

See the abstract for Chapter D1. Relatively early in neural network research there emerged an interest in analyzing and designing layered, feedforward networks augmented by some formalism stemming from the theory of fuzzy sets. One of B2.3 the first approaches was the fuzzification of the binary McCulloch–Pitts neuron (Lee and Lee 1975). B1.2 Then, several researchers looked at a typical feedfo...

Abs t rac t : This paper presents a review of d i f f e r e n t approximate reasoning techniques which have been proposed for dea l ing w i t h uncer ta in or imprecise knowledge ,espec i a l ly in expert systems based on product i o n ru le methodology. Theore t i ca l approaches such as Bayesian i n fe rence ,Sha fe r ' s b e l i e f theory or Zadeh's p o s s i b i l i t y theory as wel l as ...

In many real life situations e g when making an environmental decision it is important to be able to predict long term consequences of di erent decisions Very often these predictions must be done in the situation where the only available information consists of expert rules which are formulated by words from natural language One possible way to transform these expert words into numerical simula...

A 3-layer back propagation network is used to implement a pattern association task which learns mappings that are analogous to the present and past tense forms of English verbs, i.e., arbitrary, identity, vowel change, and suffixation mappings. The degree of correspondence between connectionist models of tasks of this type (Rumelhart & McClelland, 1986; 1987) and children’s acquisition of infle...

K e y w o r d s S o f t c o m p u t i n g , Fuzzy sets, Membership functions, Natural disaster risk. 1. I N T R O D U C T I O N Recently, the world has witnessed scary natural disasters with fatal results. Forest fires and floods are major global issues with a huge environmental impact on a global scale. All of the Mediterranean countries, Australia, and U.S.A. face a serious forest fire proble...