Intuitionistic fuzzy sets (IFSs) have attracted more and more scholars’ attention due to their powerfulness in expressing vagueness and uncertainty. In the course of decision making with IFSs, aggregation operators play a very important role since they can be used to synthesize multidimensional evaluation values represented as intuitionistic fuzzy values into collective values. This paper propo...

Interval-valued intuitionistic fuzzy sets (IVIFSs), a generalization of fuzzy sets, is characterized by an interval-valued membership function, an interval-valued non-membership function.The objective of this paper is to deal with criteria aggregation problems using IVIFSs where there exists a prioritization relationship over the criteria.Based on the ${L}$ukasiewicz triangular norm, we first p...

A crucial issue related to the Atanassov’s intuitionistic fuzzy operators is how to determine their weights. Various weighted methods have been proposed last decades, but it seems that there is no investigation on the monotonous and proportioninvariant properties, which is decisive for aggregation and comparison of Atanassov’s intuitionistic fuzzy values in group decision making. In this paper,...

This paper will introduce a new method to obtain the order weightsof the Ordered Weighted Averaging (OWA) operator. We will first show therelation between fuzzy quantifiers and neat OWA operators and then offer anew combination of them. Fuzzy quantifiers are applied for soft computingin modeling the optimism degree of the decision maker. In using neat operators,the ordering of the inputs is not...

We present a new probabilistic decision making model by using the 2-tuple linguistic representation approach. We introduce the 2tuple linguistic probabilistic ordered weighted averaging (2T-LPOWA) operator. We study some of its particular cases including the 2-tuple linguistic probabilistic aggregation and the 2tuple linguistic arithmetic OWA operator. We show an application of the new approach...

The assessment of goods quality using experts is costly task in addition to their often unavailability. In this paper, we present a new method for ranking physical features of consumer goods according to their relevancy to multiple evaluators’ perception at different levels and selecting the most important ones for quality characterization. The main contribution of the paper is combining of fuz...

Abstract An aggregation operator of linguistic interval-valued intuitionistic fuzzy numbers (LIVIFNs) is an important tool for solving cognitively inspired decision-making problems with LIVIFNs. So far, many operators LIVIFNs have been presented. Each these works well in its specific context. But they are not always monotone because their operational rules invariant and persistent. Dempster-Sha...

141 Abstract Neutrosophic sets, being generalization of classic sets, fuzzy sets and intuitionistic fuzzy sets, can simultaneously represent uncertain, imprecise, incomplete, and inconsistent information existing in the real world. Neutrosophic theory has been developed in twenty first century and not much of arithmetic has been developed for this set. To solve any problem using neutrosophic da...

In this study, we first define the uncertain linguistic Choquet averaging (ULCA) operator and the generalized Shapley uncertain linguistic Choquet averaging (GS-ULCA) operator. Especially, the GS-ULCA operator does not only globally consider the importance of the elements and their ordered positions, but also overall reflect the correlations among them and their ordered positions. Meantime, som...