Interval-valued fuzzy sets are based on the algebra of subintervals of the unit interval [0, 1]. We study valuations as a special type of measures on this algebra. We present a description of all valuations which preserve the standard fuzzy negation and extend the identity on the elements of the form (x, x). Consequences for sublattices are formulated. Keywords— Girard algebra, interval-valued ...

In this paper we introduce the notion of interval valued hesitant fuzzy soft topological space. Also the concepts of interval valued hesitant fuzzy soft closure; interior and neighbourhood are introduced here and established some important results.

In this work we use interval-valued fuzzy sets in the Fuzzy C-Means algorithm for image segmentation. We introduce interval-valued restricted equivalence functions as a way of measuring the equivalence between the intervals associated to different pixels. We propose two construction methods for those new functions. We also prove experimentally that with these new concepts, the algorithm provide...

In this paper, for a complete lattice L, we introduce interval-valued L-fuzzy ideal (prime ideal) of a near-ring which is an extended notion of fuzzy ideal (prime ideal) of a near-ring. Some characterization and properties are discussed.

It is known that interval-valued fuzzy sets provide a more adequate description of expert uncertainty than the more traditional “type-1” (number-valued) fuzzy techniques. In the current approaches for using interval-valued fuzzy techniques, it is usually assumed that all fuzzy sets m(x) ∈ [m(x), m(x)] are possible. In this paper, we show that it is reasonable to restrict ourselves only to fuzzy...

‎Selecting the most suitable robot among their wide range of specifications and capabilities is an important issue to perform the hazardous and repetitive jobs‎. ‎Companies should take into consideration powerful group decision-making (GDM) methods to evaluate the candidates or potential robots versus the selected attributes (criteria)‎. ‎In this study‎, ‎a new GDM method is proposed by utilizi...

Objective To develop a classifier that tackles the problem of determining the risk of a patient of suffering from a cardiovascular disease within the next ten years. The system has to provide both a diagnosis and an interpretable model explaining the decision. In this way, doctors are able to analyse the usefulness of the information given by the system. Methods Linguistic fuzzy rule-based clas...

Here we study the notions of lattice-valued finite state machine and lattice-valued fuzzy transformation semigroup when the lattice consists of all the closed subintervals contained in [0, 1]. So, we can apply techniques of interval-valued fuzzy sets to fuzzy automata. In particular, we prove that Atanassov’s Kα operators allow us to retrieve the information given by the transition functions of...

uzzy graph theory is finding an increasing number of applications in modeling real time systems where the level of information inherent in the system varies with different levels of precision. In the applied field, the success of the use of fuzzy set theory depends on the choice of the membership function that we make. However, there are applications in which experts do not have precise knowled...