We shall continue to discuss further properties of null-additive fuzzy measure on metric spaces following the previous results. Under the null-additivity condition, some properties of the inner/outer regularity and the regularity of fuzzy measure are shown. Also the strong regularity of fuzzy measure is discussed on complete separable metric spaces. As an application of strong regularity, we pr...

Fuzzy measure and fuzzy integral theory is an outgrowth of classical measure theory and has found applications in image processing and information fusion. This paper presents the review of a study on the development of a machinery fault diagnosis application of fuzzy measures and fuzzy integrals. Fuzzy measures and fuzzy integrals take into account the index of importance of criteria and intera...

uncertainty inherent in the financial market was usually consid- ered to be random. however, randomness is only one special type of uncer- tainty and appropriate when describing objective information. for describing subjective information it is preferred to assume that uncertainty is fuzzy. this paper defines the expected payoof trading strategies in a fuzzy financial market within the framewor...

Data envelopment analysis (DEA) mainly utilizes envelopment technology to replace production function in microeconomics. The input and output of decision making units (DMUs) are projected into the attributes to evaluate or measure their performance. However, if the inputs and outputs are linguistically termed or are fuzzy-numbered, conventional DEA can not easily measure the performance. Theref...

The well known fuzzy measures, λ-measure and P-measure, have only one formulaic solution. A multivalent fuzzy measure with infinitely many solutions based on Pmeasure was proposed by our previous work, called completed L-measure. In this paper, a further improved fuzzy measure, called extensional completed L-measure, is proposed. This new fuzzy measure is proved that it is not only an extension...

This study proposes a mathematical and morphological erosion calculation through defuzzification of the fuzzy set measure corresponding to the fuzzy integral by reducing detecting areas required for matching through areal labeling and filtering and applying the template matching uses edges to the detecting areas. It defines a λ-fuzzy set measure in application and all subsets of defuzzification...

The aim of this paper is to define a convergence in measure m, where m an intuitionistic fuzzy state. We prove version weak law large numbers for sequence independent observables, too.

Abstract In this work we introduce and study some concepts relatively to fuzzy σ–algebra such as measure, countably additive, complete measure extension of measure. Moreover, present their basic properties examples them. addition, it is shown that the linear combination a too. Finally, relationships between proposed have been introduced.