A Tool for Aggregation with Words

Studies in Computational Intelligence, 2013

In this chapter, we propose a multi-person decision making procedure where agents judge the alternatives through linguistic expressions generated by an ordered finite scale of linguistic terms (for instance, 'very good', 'good', 'acceptable', 'bad', 'very bad'). If the agents are not confident about their opinions, they might use linguistic expressions composed by several consecutive linguistic terms (for instance, 'between acceptable and good'). The procedure we propose is based on distances and it ranks order the alternatives taking into account the linguistic information provided by the agents. The main features and properties of the proposal are analyzed.

Information Sciences, 1990

This paper presents a new approach to the summarization of linguistic data. A fuzzy mean, or average, for linguistic data is defined. Linguistic approximation is used to label the average membership function computed using the definition A measure of variation of the data, a fuzzy variance, is defined. Using the fuzzy variance and the range of the fuzzy data, a normalized measure of dispersion is constructed. A method for labeling this normalized measure is provided using linguistic approximation. Thus the concepts of mean, variance, and range are extended to the theory of fuzzy sets, and the values obtained are interpreted in a linguistic fashion. Examples illustrate each of these concepts.

Fuzzy Sets and Systems, 2000

... this work we concentrate on the issue of weighted aggregations and provide a possibilistic approach to the process of importance weighted transformation when both the importances (interpreted as benchmarks) and the ratings are given by symmetric triangular fuzzy numbers. ...

International Journal of …, 1993

This article is devoted to defining some aggregation operations between linguistic labels. First, from some remarks about the meaning of label addition, a formal and general definition of a label space is introduced. After, addition, difference, and product by a positive real number are formally defined on that space. The more important properties of these operations are studied, paying special attention to the convex combination of labels. The article concludes with some numerical examples. 0

Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-2011), 2011

Aggregation operators for linguistic variables usually assume a uniform and symmetrical distribution of the linguistic terms that define the variable. This paper defines the Induced Unbalanced Linguistic Ordered Weighted Average (IULOWA). This aggregator takes into account the fuzzy membership functions of the terms during the aggregation operations of the pairs of terms. There is no restriction on the form of the membership functions of the terms, which can be triangular or trapezoidal, non-symmetrical and non-equally distributed. Moreover, the paper proposes to use the specificity and fuzziness measures of the terms to induce the order of the arguments, providing some examples of this criterion in decision making.

Group Decision and Negotiation, 2012

We introduce a wide range of induced and linguistic generalized aggregation operators. First, we present the induced linguistic generalized ordered weighted averaging (ILGOWA) operator. It is a generalization of the OWA operator that uses linguistic variables, order inducing variables and generalized means in order to provide a more general formulation. One of its main results is that it includes a wide range of linguistic aggregation operators such as the induced linguistic OWA (ILOWA), the induced linguistic OWG (ILOWG) and the linguistic generalized OWA (LGOWA) operator. We further generalize the ILGOWA operator by using quasi-arithmetic means obtaining the induced linguistic quasi-arithmetic OWA (Quasi-ILOWA) operator and by using hybrid averages forming the induced linguistic generalized hybrid average (ILGHA) operator. We also present a further extension with Choquet integrals. We call it the induced linguistic generalized Choquet integral aggregation (ILGCIA). We end the paper with an application of the new approach in a linguistic group decision making problem.

Axioms

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 fuzzy linguistic (IFL)/Pythagorean fuzzy linguistic (PFL) sets. On the other hand, the linguistic scale function (LSF) is the better way to consider the semantics of the linguistic terms during the evaluation process. It is worth noting that the existing operational laws and aggregation operators (AOs) for Fermatean fuzzy linguistic numbers (FFLNs) are not valid in many situations, which can generate errors in real-life applications. The present study aims to define new robust operational laws and AOs under Fermatean fuzzy linguistic environment. To do so, first, we define some new modified operational laws for FFLNs based on LSF and prove some important mathematical properties of them. Next, the work defines several new AOs, namely, the FFL-weighted averaging (FFLWA) operator, the FFL-weighted geo...

2006

The focus of this paper is the linguistic weighted average (LWA), which is a generalization of the fuzzy weighted average (FWA) that is obtained by replacing the type-1 fuzzy inputs in the FWA by interval type-2 fuzzy sets (IT2 FSs). Consequently, the output of the LWA is an IT2 FS. In this paper, the relations between the LWA and the FWA are studied. It is shown that finding the LWA can be decomposed into finding two FWAs, where α-cuts and KM algorithms are used. Hence, the computational cost of a LWA is about twice that of a FWA. A flowchart for computing the LWA is also provided.

2019

One of the major problems of varied knowledge-based systems has to do with aggregation and fusion. Pang’s probabilistic linguistic term sets denotes aggregation of fuzzy information and it has attracted tremendous interest from researchers recently. The purpose of this article is to deal investigating methods of information aggregation under the probabilistic linguistic environment. In this situation we defined certain Einstein operational laws on probabilistic linguistic term elements (PLTESs) based on Einstein product and Einstein sum. Consequently, we develop some probabilistic linguistic aggregation operators, notably the probabilistic linguistic Einstein average (PLEA) operators, probabilistic linguistic Einstein geometric (PLEG) operators, weighted probabilistic linguistic Einstein average (WPLEA) operators, weighted probabilistic linguistic Einstein geometric (WPLEG) operators. These operators extend the weighted averaging operator and the weighted geometric operator for the ...

1999

The fuzzy linguistic approach has been applied successfully to many problems. However, there is a limitation of this approach imposed by its information representation model and the computation methods used when fusion processes are performed on linguistic values. This limitation is the loss of information caused by the need to express the results in the initial expression domain that is discrete via an approximate process. This loss of information implies a lack of precision in the final results from the fusion of linguistic information. In this paper, we present tools for overcoming this limitation. The linguistic information will be expressed by means of 2-tuples, which are composed by a linguistic term and a numeric value assessed in [ 0.5, 0.5). This model allows a continuous representation of the linguistic information on its domain, therefore, it can represent any counting of information obtained in a aggregation process. Together with the 2-tuple representation model we shall develop a computational technique for computing with words (CW) without any loss of information. Finally, different classical aggregation operators will be extended to deal with the 2-tuple linguistic model.