Fuzzy Arithmetic and Extension Principle

Fuzzy arithmetic is an extensively used instrument for dealing with uncertainty in a computationally competent method, recently and much better in the upcoming years. This thesis aims to investigate the basic properties of fuzzy arithmetic as its title implies. The properties of fuzzy arithmetic definitions, examples are discussed. Here we investigates the properties of fuzzy sets, properties of fuzzy number, performing arithmetic operations on fuzzy number, properties of L-R fuzzy number, performing operations on L-R fuzzy number, properties of fuzzy interval and properties of L-R fuzzy interval. Also, the extension principle and fuzzy arithmetic operations using extension principle are investigated. The fuzzy equation is solved by using the method o

Orthogonal bases of Hermitean monogenic polynomials : an explicit construction in complex dimension 2

In this contribution we construct an orthogonal basis of Hermitean monogenic polynomials for the specific case of two complex variables. The approach combines group representation theory, see [5], with a Fischer decomposition for the kernels of each of the considered Dirac operators, see [4], and a Cauchy-Kovalevskaya extension principle, see [3]

A short survey of normative properties of possibility distributions

In 2001 Carlsson and Full´er [1] introduced the possibilistic mean value, variance and covariance of fuzzy numbers. In 2003 Full´er and Majlender [4] introduced the notations of crisp weighted possibilistic mean value, variance and covariance of fuzzy numbers, which are consistent with the extension principle. In 2003 Carlsson, Full´er and Majlender [2] proved the possibilisticCauc hy-Schwartz inequality. Drawing heavily on [1, 2, 3, 4, 5] we will summarize some normative properties of possibility distributions

Unitary Extension Principle for Nonuniform Wavelet Frames in L2(R)L^2(\mathbb{R})

We study the construction of nonuniform tight wavelet frames for the Lebesgue space $L^2(\mathbb{R})$, where the related translation set is not necessary a group. The main purpose of this paper is to prove the unitary extension principle (UEP) and the oblique extension principle (OEP) for construction of multi-generated nonuniform tight wavelet frames for $L^2(\mathbb{R})$. Some examples are also given to illustrate the results

Approximate Reasoning with Fuzzy Booleans

This paper introduces, in analogy to the concept of fuzzy numbers, the concept of fuzzy booleans, and examines approximate reasoning with the compositional rule of inference using fuzzy booleans. It is shown that each set of fuzzy rules is equivalent to a set of fuzzy rules with singleton crisp antecedents; in case of fuzzy booleans this set contains only two rules. It is shown that Zadeh's extension principle is equivalent to the compositional rule of inference using a complete set of fuzzy rules with singleton crisp antecedents. The results are applied to describe the use of approximate reasoning with fuzzy booleans to object-oriented design methods