Quasi-arithmetic means and OWA functions in interval-valued and Atanassov's intuitionistic fuzzy set theory

In this paper we propose an extension of the well-known OWA functions introduced by Yager to interval-valued (IVFS) and Atanassov’s intuitionistic (AIFS) fuzzy set theory. We first extend the arithmetic and the quasi-arithmetic mean using the arithmetic operators in IVFS and AIFS theory and investigate under which conditions these means are idempotent. Since on the unit interval the construction of the OWA function involves reordering the input values, we propose a way of transforming the input values in IVFS and AIFS theory to a new list of input values which are now ordered

Estimations of expectedness and potential surprise in possibility theory

This note investigates how various ideas of 'expectedness' can be captured in the framework of possibility theory. Particularly, we are interested in trying to introduce estimates of the kind of lack of surprise expressed by people when saying 'I would not be surprised that...' before an event takes place, or by saying 'I knew it' after its realization. In possibility theory, a possibility distribution is supposed to model the relative levels of mutually exclusive alternatives in a set, or equivalently, the alternatives are assumed to be rank-ordered according to their level of possibility to take place. Four basic set-functions associated with a possibility distribution, including standard possibility and necessity measures, are discussed from the point of view of what they estimate when applied to potential events. Extensions of these estimates based on the notions of Q-projection or OWA operators are proposed when only significant parts of the possibility distribution are retained in the evaluation. The case of partially-known possibility distributions is also considered. Some potential applications are outlined

Generalizations of weighted means and OWA operators by using unimodal weighting vectors

Producción CientíficaWeighted means and OWA operators are two families of functions well known in the literature. Given that both are specific cases of the Choquet integral, several procedures for constructing capacities that generalize simultaneously those of the weighted means and the OWA operators have been suggested in recent years. In this paper we propose two methods that allow us to address the previous issue and that provide us with a wide variety of capacities when the weighting vector associated with the OWA operator is unimodal.Este trabajo forma parte del proyecto de investigación: MEC-FEDER Grant ECO2016-77900-P

The induced 2-tuple linguistic generalized OWA operator and its application in linguistic decision making

We present the induced 2-tuple linguistic generalized ordered weighted averaging (2-TILGOWA) operator. This new aggregation operator extends previous approaches by using generalized means, order-inducing variables in the reordering of the arguments and linguistic information represented with the 2-tuple linguistic approach. Its main advantage is that it includes a wide range of linguistic aggregation operators. Thus, its analyses can be seen from different perspectives and we obtain a much more complete picture of the situation considered and are able to select the alternative that best fits with with our interests or beliefs. We further generalize the operator by using quasi-arithmetic means, and obtain the Quasi-2-TILOWA operator. We conclude this paper by analysing the applicability of this new approach in a decision-making problem concerning product management.linguistic decision making, linguistic generalized mean, 2-tuple linguistic owa operator, 2-tuple linguistic aggregation operator

"The connection between distortion risk measures and ordered weighted averaging operators"

Distortion risk measures summarize the risk of a loss distribution by means of a single value. In fuzzy systems, the Ordered Weighted Averaging (OWA) and Weighted Ordered Weighted Averaging (WOWA) operators are used to aggregate a large number of fuzzy rules into a single value. We show that these concepts can be derived from the Choquet integral, and then the mathematical relationship between distortion risk measures and the OWA and WOWA operators for discrete and nite random variables is presented. This connection oers a new interpretation of distortion risk measures and, in particular, Value-at-Risk and Tail Value-at-Risk can be understood from an aggregation operator perspective. The theoretical results are illustrated in an example and the degree of orness concept is discussed.Fuzzy systems; Degree of orness; Risk quantification; Discrete random variable JEL classification:C02,C60

OWA operators in the calculation of the average green-house gases emissions

This study proposes, through weighted averages and ordered weighted averaging operators, a new aggregation system for the investigation of average gases emissions. We present the ordered weighted averaging operators gases emissions, the induced ordered weighted averaging operators gases emissions, the weighted ordered weighted averaging operators gases emissions and the induced probabilistic weighted ordered weighted averaging operators gases emissions. These operators represent a new way of analyzing the average gases emissions of different variables like countries or regions. The work presents further generalizations by using generalized and quasi-arithmetic means. The article also presents an illustrative example with respect to the calculations of the average gases emissions in the European region