The multiplicative hesitant fuzzy information proposed by Xia (2012) uses the non-uniform scale to express the preference of the decision makers which has a broad application background. The key difference between multiplicative hesitant fuzzy information and hesitant fuzzy information is the former uses unsymmetrical scale in expressing the preferences about two alternatives but the latter use...

Information technology (IT) outsourcing has been recognized as a new methodology in many organizations. Yet making an appropriate decision with regard to selection and use of these methodologies may impose uncertainties and risks. Estimating the occurrence probability of risks and their impacts organizations goals may reduce their threats. In this study, an extended analytical hierarchical proc...

The n-dimensional fuzzy sets have been introduced as a generalization of interval-valued fuzzy sets, Atanassov’s intuitionistic and interval-valued intuitionistic fuzzy sets. In this paper we investigate t-norms on 3-dimensional sets which are joinmorphisms. Under some additional conditions we show that they can be represented using a representation which generalizes a similar representation fo...

Convexity is one of the most important geometric properties sets and a useful concept in many fields mathematics, like optimization. As there are also applications making use fuzzy optimization, it obvious that studies convexity frequent. In this paper we have extended notion for hesitant order to fulfill some necessary properties. Namely, found an appropriate definition on any ordered universe...

The notion of interval-valued intuitionistic fuzzy sets was first introduced by Atanassov and Gargov in 1989 as a generalization of both interval-valued fuzzy sets and intuitionistic fuzzy sets. In this paper we first apply the concept of interval-valued intuitionistic fuzzy sets to K-algebras. Then we introduce the notion of interval-valued intuitionistic fuzzy ideals (IIFIs, in short) of K-al...

A new hesitant fuzzy set (HFS)-ELECTRE for multi-criteria group decision-making (MCGDM) problems is developed in this paper. In real-world applications, the decision makers (DMs)’ opinions are often hesitant for decision problems; thus, considering the exact data is difficult. To address the issue, the DMs’ judgments can be expressed as linguistic variables that are converted into the HFSs, con...