Engineering and scienti c measurement results of continuous quantities are not precise numbers but more or less non-precise. Therefore so-called non-precise numbers are necessary to describe measurement results. Non-precise numbers are special fuzzy subsets of the set of real numbers. For vector quantities so-called fuzzy vectors are the best up to date model for related measurements.

We introduce and study fuzzy hypervector spaces based on fuzzy singletons. In this regard by considering the notion of fuzzy singletons, we characterize a fuzzy hypervector space fuzzily spanned by a fuzzy subset. Then we use these results to introduce the concept of fuzzy freeness of a fuzzy subset μ of a hypervector space V and finally we characterize it in terms of linear independence in the...

The fundamental concept of a fuzzy set, introduced by Zadeh in his classic paper [5] of 1965, has been applied by many authors to generalize some of the basic notions of algebra. In this note we characterize the semigroups for which each fuzzy ideal is prime, also the semigroups for which each fuzzy right ideal is prime. In Section 2, we prove that a semigroup is fully fuzzy prime if and only i...

The aim of this paper is to present a general framework for comparing fuzzy sets with respect to a general class of fuzzy orderings. This approach includes known techniques based on generalizing the crisp linear ordering of real numbers by means of the extension principle, however, in its general form, it is applicable to any fuzzy subsets of any kind of universe for which a fuzzy ordering is k...

Necessary and sufficient conditions under which two fuzzy sets (in the most general, poset valued setting) with the same domain have equal families of cut sets are given. The corresponding equivalence relation on the related fuzzy power set is investigated. Rela­ tionship of poset valued fuzzy sets and fuzzy sets for which the co-domain is Dedekind-MacNeille completion of that posets is deduced.

In the present paper, using novel generalizations of the Hukuhara di¤erence for fuzzy sets, we introduce and study new generalized di¤erentiability concepts for fuzzy valued functions. Several properties of the new concepts are investigated and they are compared to similar fuzzy di¤erentiabilities …nding connections between them. Characterization and relatively simple expressions are provided f...

In many applications, spatial data often are prone to uncertainty and imprecision. To model this, fuzzy regions have been developed. Our initial model was a fuzzy set over a two dimensional domain, allowing for fuzzy regions and fuzzy points to be modelled. The model had some limitations: all points where treated independently, and it was not possible to group points together. Furthermore, it d...

in this paper, we deal with molaei’s generalized groups. we definethe notion of a fuzzy generalized subgroup with respect to a t-norm (ort-fuzzy generalized subgroup) and give some related properties. especially,we state and prove the representation theorem for these fuzzy generalizedsubgroups. next, using the concept of continuity of t-norms we obtain a correspondencebetween tf(g), the set of ...

During the last years, the fuzzy set theory was one of the most innovative,active and fruitful areas of research for applications, especially in the field of industrial processes. The aim of this brief introduction is to give some ideas about the foundations of the fuzzy system: defintions, semantics and applications. We will deal also with the relation with Artificial Neural Network (ANN) and ...

This work presents an approach to the automatic interpretation of the visual field to enable ophthalmology patients to be classified as glaucomatous and normal. The approach is based on a neuro-fuzzy system (NEFCLASS) that enables a set of rules to be learnt, with no a priori knowledge, and the fuzzy sets that form the rule antecedents to be tuned, on the basis of a set of training data. Anothe...