LAMA: A linguistic aggregation of majority additive operator

Abstract

A problem that we had encountered in the aggregation process, is how to aggregate the elements that have cardinality Ͼ1. The purpose of this article is to present a new aggregation operator of linguistic labels that uses the cardinality of these elements, the linguistic aggregation of majority additive (LAMA) operator. We also present an extension of the LAMA operator under the two-tuple fuzzy linguistic representation model.

The maximizing deviation method for group multiple attribute decision making under linguistic environment

“…In group decision making, the collective overall preference values Z i (i ∈ N) are computed by Eq. (15).…”

“…Xu [25] briefly review the existing methods for determining the weights associated OWA operator, such as the linguistic quantifier's approach [30], the analytic approach [3]. A number of studies recently focused on group decision making under linguistic environment [1,2,[6][7][8][9][10][11][12][13][14][15]17,18,[21][22][23][24]26,27,29,31] and thus a lot of linguistic aggregation operators were proposed. They are linguistic weighted geometric averaging (LWGA) operator and linguistic ordered weighted geometric averaging (LOWGA) operator [22], uncertain linguistic OWA (ULOWA) operator and uncertain linguistic hybrid aggregation (ULHA) operator [23], linguistic aggregation of majority additive (LAWA) operator [15], uncertain linguistic geometric mean (ULGM) operator, uncertain linguistic weighted geometric mean (ULWGM) operator, uncertain linguistic OWG (ULOWG) operator, induced ULOWG (IULOWG) operator [26], etc.…”

Computing with words in decision making: foundations, trends and prospects

“…As the result of the aggregation is not usually an integer, that Fig. 8 Example of the linguistic model proposed by Xu (2004b) is, does not correspond to one of the labels in S, it is also necessary to introduce an approximation function app 2 (·) to obtain a solution on the S terms set: Aggregation operators that operate in this linguistic model are the Linguistic Ordered Weighted Averaging (LOWA) operator (Herrera et al 1996a) (based on the OWA operator and the convex combination of linguistic labels), the Linguistic Weighted Disjunction (LWD), Linguistic Weighted Conjunction (LWC), the Linguistic Weighted Averaging (LWA) (Herrera and Herrera-Viedma 1997), the Linguistic Aggregation of Majority Additive (LAMA) operator (Peláez and Doña 2003) and the Majority Guided Induced Linguistic Aggregation Operators . Linguistic symbolic computational model based on virtual linguistic terms (Xu 2004b): In this model, the discrete term set S = {s − g 2 , .…”

“…The aggregation of 2-tuple linguistic information can be achieved by applying some extensions of classical aggregation operators to the 2-tuple linguistic model that can be found in the literature as the Arithmetic Mean, the Weighted Average Operator, the Ordered Weighted Aggregation (OWA) operator, the LOWA operator , the Lattice-based Linguistic-Valued Weighted Aggregation (LVWA) ) and the LAMA operator (Peláez and Doña 2003).…”

Belief Merging and Judgment Aggregation in Fuzzy Setting

“…It is worthy to compare our aggregation operator to operators in the fuzzy aggregation. For example, fuzzy LAMA operator (see Peláez and Doña [17]) has unrestricted domain, anonymity, monotonicity, unanimity, and citizen sovereignty. Ironically, it does not ensure collective rationality.…”