We provide a new approach to the Hutchinson-Barnsley theory for idempotent measures first presented in Mazurenko and Zarichnyi (2018) [24]. The main feature developed here is metrization of space using embedding fuzzy sets. metric obtained induces topology stronger than canonical pointwise convergence topology. A key result existence bijection between sets conjugation Markov operator an IFS on ...

In this paper, we propose the new concept of optimal solution for fuzzy variational problems based on the possibility and necessity measures. Inspired by the well–known embedding theorem, we can transform the fuzzy variational problem into a bi–objective variational problem. Then the optimal solutions of fuzzy variational problem can be obtained by solving its corresponding biobjective variatio...

This paper proposes a new fuzzy similarity measure to calculate the degree of similarity of generalized fuzzy numbers (GFN’s).The fuzzy similarity measure is developed by integrating the concept of centre of gravity (COG) points and fuzzy difference of distance of points of fuzzy numbers. A fuzzy description for difference of distances between fuzzy numbers in its turn exploits appropriate simi...

measurement systems analysis (msa) has been applied in different aspect of industrial assessments to evaluate various types of quantitative and qualitative measures. qualification of a measurement system depends on two important features: accuracy and precision. since the capability of each quality system is severely related to the capability of its measurement system, the weakness of the two ...

In a unified knowledge representation, data, information and knowledge are all represented in a single formalism as “items”. A unified knowledge representation is extended here to include two types of fuzzy measures of knowledge integrity. These integrity measures define a graduated integrity region for data, information and knowledge. This fuzzy region contains knowledge of increasingly questi...

In this article we present three similarity measures between simplified neutrosophic hesitant fuzzy sets, which contain the concept of single valued neutrosophic hesitant fuzzy sets and interval valued neutrosophic hesitant fuzzy sets, based on the extension of Jaccard similarity measure, Dice similarity measure and Cosine similarity in the vector space. Then based on these three defined simila...