A new method is proposed to solve the multiple attribute decision making (MADM) problems with the trapezoid fuzzy linguistic variables ( Vs TFL ) based on the trapezoid fuzzy linguistic hybrid harmonic averaging (TFLHHA ) operator. To begin with, this paper reviews the concept and operational rules of the Vs TFL , the calculation method of the possibility degree with Vs TFL , and the comparison...

Abstract. The 2-tuple linguistic computational model is an important tool to deal with linguistic information. To extend the application of hesitant fuzzy linguistic term sets and avoid information loss, this paper introduces hesitant fuzzy 2-tuple linguistic term sets that are expressed by using several symbolic numbers in [0,1]. Considering the order relationship between hesitant fuzzy 2tuple...

The cloud model, which can implement uncertain transformation between a qualitative concept and its quantitative instantiations, has attracted great attentions in multi-criteria decision-making problems with linguistic information. This paper proposes some operations and a possibility degree of trapezium clouds as well as several new aggregation operators: the trapezium cloud weighted arithmeti...

Many multiple attribute group decision making (MAGDM) problems with linguistic information involve uncertainties, which significantly increase the complexity and difficulty in decision analysis. In order to solve such problems, we require appropriate aggregation operators that are capable of dealing with uncertain linguistic information. In this paper, firstly, the uncertain two-tuple linguisti...

In this paper, a logarithmic operational law for intuitionistic fuzzy numbers is defined, in which the based $$\ell$$ real number such that $$\ell \in \left( {0,1} \right)$$ with condition \ne 1$$ . Some properties of laws have been studied and on these, several Einstein averaging geometric operators, namely weighted (LIFEWA) operator, ordered (LIFEOWA) hybrid (LIFEHA) (LIFEWG) (LIFEOWG) (LIFEH...

Yager’s ordered weighted averaging (OWA) operator has been widely used in soft decision making to aggregate experts’ individual opinions or preferences for achieving an overall decision. The traditional Yager’s OWA operator focuses exclusively on the aggregation of crisp numbers. However, human experts usually tend to express their opinions or preferences in a very natural way via linguistic te...

In the study, we propose the Associated Probability Intuitionistic Fuzzy Weighted Averaging (As-P-IFWA) and the Associated Probability Intuitionistic Fuzzy Weighted Geometric (As-P-IFWG) aggregation operators with associated probabilities of a fuzzy measure presenting an uncertainty. Decision makers' evaluations are given as intuitionistic fuzzy values and are used as the arguments of the aggre...

Fermatean fuzzy linguistic (FFL) set theory provides an efficient tool for modeling a higher level of uncertain and imprecise information, which cannot be represented using intuitionistic (IFL)/Pythagorean (PFL) sets. On the other hand, scale function (LSF) is better way to consider semantics terms during evaluation process. It worth noting that existing operational laws aggregation operators (...

In this paper we consider linguistic information aggregation problems where a prioritization relationship exists over attributes. The authors define a prioritized 2-tuple ordered weighted averaging (PTOWA) operator to aggregate satisfactions of alternatives under attributes with a linear prioritized ordering. The authors then use the PTOWA and a TOWA operator to aggregate linguistic information...

To solve multiple attribute decision making problems with intuitionistic trapezoidal fuzzy information, two optimization models based on the maximizing deviation method, by which the attribute weights can be determined, is established. We utilize the intuitionistic trapezoidal fuzzy weighted geometric mean (ITFWGM) operator to aggregate the intuitionistic trapezoidal fuzzy information correspon...