We give a geometrical interpretation of the interval-valued fuzzy set (IVFS). Based on the geometrical background, we propose new distance measures between IVFSs and compare these measures with distance measures proposed by Burillo and Bustince (1996) and Grzegorzewski (2004), respectively. Furthermore, we extend three methods for measuring distances between IVFSs to interval-valued intuitionis...

it is firstly proved that the multi-input-single-output (miso) fuzzy systems based on interval-valued $r$- and $s$-implications can approximate any continuous function defined on a compact set to arbitrary accuracy.  a formula to compute the lower upper bounds on the number  of interval-valued fuzzy sets needed to achieve a pre-specified approximation  accuracy for an arbitrary multivariate con...

The main attribution of this paper is to propose two methods to construct entropy of interval valued fuzzy sets (IVFSs). First, we use an IVFS to construct two FSs and define entropy by similarity measure of the two FSs; then we use an IVFS to construct two IVFSs and also define entropy by similarity measure of the two IVFSs. At the same time, we give two examples to show that our methods are e...

In this paper, Ginsberg’s/Fitting’s theory of bilattices is invoked as a natural accommodation and powerful generalization to both intuitionistic fuzzy sets (IFSs) and interval-valued fuzzy sets (IVFSs), serving on one hand to clarify the exact nature of the relationship between these two common extensions of fuzzy sets, and on the other hand providing a general and intuitively attractive frame...

Fault diagnosis is an important task for the normal operation and maintenance of equipment. In many real situations, the diagnosis data cannot provide deterministic values and are usually imprecise or uncertain. Thus, interval-valued fuzzy sets (IVFSs) are very suitable for expressing imprecise or uncertain fault information in real problems. However, existing literature scarcely deals with fau...

In 1965, Zadeh introduced the concept of fuzzy subsets. Latter many authors defined different directions of fuzzy subsets. Turksen (1986) generalized the concept of fuzzy set in terms of interval-valued fuzzy set (IVFS). Several researchers present a number of results using IVFSs. Using these concept of (IVFS) Pal and Shyamal (2006) introduced interval-valued fuzzy matrices and shown several pr...

Several algorithms exist to address the issues concerning parameter reduction of soft sets. The most recent concept of Normal Parameter Reduction (NPR) is introduced, which overcomes the problem of suboptimal choice and added parameter set of soft sets. However, the algorithm involves a great amount of computation. In this thesis, a New Efficient Normal Parameter Reduction algorithm (NENPR) of ...

In this paper we deal with the problem of extending Zadeh's operators on fuzzy sets (FSs) to interval-valued (IVFSs), set-valued (SVFSs) and type-2 (T2FSs) fuzzy sets. Namely, it is known that seeing FSs as SVFSs, or T2FSs, whose membership degrees are singletons is not order-preserving. We then describe a family of lattice embeddings from FSs to SVFSs. Alternatively, if the former singleton vi...

We present a family of algebraic structures, called rectangular bilattices, which serve as a natural accommodation and powerful generalization to both intuitionistic fuzzy sets (IFSs) and interval-valued fuzzy sets (IVFSs). These structures are useful on one hand to clarify the exact nature of the relationship between the above two common extensions of fuzzy sets, and on the other hand provide ...

The assessment and selection of green supplier development programs are an intriguing and functional research subject. This paper proposes a group decision-making approach considering possibilistic statistical concepts under uncertainty to assess green supplier development programs (GSDPs) via interval-valued fuzzy sets (IVFSs). Possibility theory is employed to regard uncertainty by IVFSs. A n...