Two definitions of fuzzy sets with Boolean-valued membership functions, introduced by Drossos and Markakis and called by them external and internal Boolean fuzzy sets, are compared with a third, classical definition descending more directly from the original Zadeh's and Goguen's ideas. Under some rather general conditions, internal and classical Boolean fuzzy sets are proved to be equivalent in...

the main purpose of this paper is to find t-best approximations in fuzzy normed spaces. we introduce the notions of t-proximinal sets and f-approximations and prove some interesting theorems. in particular, we investigate the set of all t-best approximations to an element from a set.

background: advances in information technology and data collection methods have enabled high-speed collection and storage of huge amounts of data. data mining can be used to derive laws from large data volumes and their characteristics. similarly, fuzzy logic by facilitating the understanding of events is considered a suitable complement to scientific data mining. materials and methods: the pre...

the present research aims to apply several approaches for suitability evaluation of lands under cultivation ofalfalfa and barley in chaharmil mechanized farming center, ardestan town, isfahan province, iran. climatic andsoil maps of the climate and soil data were provided in raster format. land evaluation carried out using maximumlimitation, parametric and multi-criteria (analytical hierarchy p...

Fuzzy implicators are the basic ingredients of many applications. So it becomes essential to study the various features of an implicator before implementing it in any practical application. This paper discusses the properties of transitivity of a fuzzy relation on a given universe and measure of fuzzy transitivity defined in terms of the Reichenbach fuzzy implicator which is an s-implicator.

In this work, we propose a pseudometric based on a fuzzy relation, which is itself derived from a fuzzy partition. This pseudometric is a metric in the particular case in which the fuzzy partition is composed solely by triangular fuzzy sets. We prove that these functions are indeed a pseudometric and a metric and illustrate their use in an experiment for the classification of land use in an are...

The fuzzy extension principle has been widely used to extend the domain of mathematical functions and relations from elements of a referential set to fuzzy subsets of that referential set. However, there are restrictions associated with the fuzzy extension principle. This paper addresses the question how restricted is the family of “fuzzy set to fuzzy set mappings” obtained by the fuzzy extensi...

Lattice-valued up-sets and down-sets of a poset are investigated under the cutworthy approach. It is proved that the collections of all lattice valued up-sets and down-sets of a given poset are complete lattices under fuzzy inclusion. Properties of these are investigated. For a given collection of crisp up-sets of a poset, necessary and sufficient conditions are given under which the family rep...

In crisp production inventory problem, let q, a, b, d, R and r be the quantity produced per cycle, the holding cost, production cost, production quantity per day, the total demand quantity and the demand quantity per day, respectively. We consider three fuzzification methods. Firstly, we fuzzify q, a, b, d, R and r to triangular fuzzy numbers. Secondly, we fuzzify d and r to triangular fuzzy nu...