As a natural extension of the fuzzy variable, bifuzzy variable is defined as mapping from credibility space to collection variables, which an appropriate tool model two-fold phenomena. In order enrich its theoretical foundation, this paper explores some important measures for regular most commonly used type variables. Firstly, we introduce variables’ mean chance measure and properties, includin...

This paper considers fuzzifying topologies, a special case of I-fuzzy topologies (bifuzzy topologies), introduced by Ying [25]. It investigates topological notions defined by means of  -open sets when these are planted into the framework of Ying’s fuzzifying topological spaces (by Łukasiewicz logic in [0, 1]). In this paper we introduce some sorts of operations, called general fuzzifying opera...

This paper presents two variants of pentavalued representation for neutrosophic entropy. The first is an extension of Kaufman's formula and the second is an extension of Kosko's formula. Based on the primary three-valued information represented by the degree of truth, degree of falsity and degree of neutrality there are built some penta-valued representations that better highlights some specifi...

Shannon entropy was defined for probability distributions and then its using was expanded to measure the uncertainty of knowledge for systems with complete information. In this article, it is proposed to extend the using of Shannon entropy to under-defined or over-defined information systems. To be able to use Shannon entropy, the information is normalized by an affine transformation. The const...

Geographical data is inherently uncertain. There are a variety of sources that contribute to this uncertainty. Operations performed on data during an analysis will most likely only increase this uncertainty. To understand the uncertainty in the results of an analysis, requires information about the uncertainty in the input data, and some idea about how various analysis operations propagate and ...