On account of the existence of uncertainty, DEA occasionally faces the situation of imprecise data, especially when a set of DMUs include missing data, ordinal data, interval data, stochastic data, or fuzzy data. Therefore, how to evaluate the efficiency of a set of DMUs in interval environments is a problem worth studying. In this paper, we discussed the new method for evaluation and ranking i...

Uncertainty propagation in complex engineering systems with fuzzy variables constitutes a significant challenge. This paper proposes a Polynomial Chaos type spectral approach based on orthogonal function expansion. A fuzzy variable is represented as a set of interval variables via the membership function. The interval variables are further transformed into the standard interval [−1,1]. Smooth n...

The centroid of an interval type-2 fuzzy set (IT2 FS) provides a measure of the uncertainty of such a FS. Its calculation is very widely used in interval type-2 fuzzy logic systems. In this paper, we present properties about the centroid of an IT2 FS. We also illustrate many of the general results for a T2 fuzzy granule (FG) in order to develop some understanding about the uncertainty of the FG...

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...

It is well known fact that binary relations are generalized mathematical functions. Contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. Some basic operations on functions such as the inverse and composition are applicable to binary relations as well. Depending on the domain or range or both are fuzzy value fuzzy set, i...

The concept of the rough set was originally proposed by Pawlak as a formal tool for modelling and processing incomplete information in information systems, then in 1990, Dubois and Prade first introduced the rough fuzzy sets and fuzzy rough sets as a fuzzy extension of the rough sets. The aim of this paper is to present a new extension of the rough set theory by means of integrating the classic...

This paper presents the application of interval type-2 fuzzy inference systems (IT2FIS) in short term load forecasting (STLF) on special days. This is a continuation work of application interval type-2 fuzzy systems (IT2FSs) using Karnik Mendel algorithm. Special days here mean local Balinese holidays such as national and local culture-based public holidays, consecutive holidays, and days prece...

This paper introduces a new concept in fuzzy set theory, that of a fuzzy element. It embodies the idea of fuzziness only, thus contributing to the distinction between fuzziness and ideas of imprecision. A fuzzy element is to a fuzzy set what an element is to a set. A fuzzy element is as precise as an element, just more gradual that the latter. Applications of this notion to fuzzy cardinality, f...