Narrow Results

First a balancing property on a fuzzy measure is introduced. After that, the conditions of when an additive fuzzy measure is balanced are given and similar results are presented for 0-1 and S–decomposable fuzzy measures where S is a continuous t–conorm. Moreover, the concept of distance between two additive fuzzy measures is presented and some results related to the distance and the balancing property are developed.

In this paper we propose a generalization of the concept of symmetric fuzzy measure based in a decomposition of the universal set in what we have called subsets of indifference. Some properties of these are studied, as well as their Choquet integral. Finally, a degree of interaction between the subsets of indifference is defined.

One important issue in the theory of ordered weighted averaging (OWA) operators is the determination of the associated weighting vector. Recently, Fullér and Majlender² derived the minimal variability weighting vector for any level of orness using the Kuhn-Tucker second-order sufficiency conditions for optimality. In this note, we give a new proof of the problem.

The paper considers the analytical solution methods of the maximizing entropy or minimizing variance with fixed orness level problems and the maximizing orness with fixed entropy or variance value problems together. It proves that both of these two kinds of problems have common necessary conditions for their optimal solutions. The optimal solutions have the same forms and can be seen as the same OWA (ordered weighted averaging) weighting vectors from different points of view. The problems of minimizing orness problems with fixed entropy or variance constraints and their analytical solutions are proposed. Then these conclusions are extended to the corresponding RIM (regular increasing monotone) quantifier problems, which can be seen as the continuous case of OWA problems with free dimension. The analytical optimal solutions are obtained with variational methods.

In all decision making processes, the use of aggregation operators is necessary. Democratic decision problems cannot be considered a usual decision task due to the subjectivity of human' opinions and the complexity of social environments. To model these processes, the concept of work committee is used, where every citizen's opinion is represented in heterogeneous groups and aggregated to obtain a representative final opinion for the problem. In these environments, traditional operators don't represent the concept of discussion groups used in social models producing inadequate aggregations for these types of problems. The purpose of this paper is to present a new OWA operator where the weights are a function of the aggregate values in order to model the work committee and aggregate the citizens' opinions in democratic decision problems.

In this paper, we present a new intuitionistic fuzzy decision-making technique based on similarity measures and the ordered weighted average (OWA) operator. We develop the intuitionistic fuzzy ordered weighted similarity (IFOWS) measure. The main advantage of the IFOWS measure is that it can alleviate the influence of unduly large (or small) deviations on the aggregation results by assigning them low (or high) weights. Moreover, it provides a very general formulation that includes a wide range of aggregation similarity measures and aggregates the input arguments taking the form of intuitionistic fuzzy values rather than exact numbers. We further develop the interval-valued intuitionistic fuzzy ordered weighted similarity (IVIFOWS) measure. Then we apply the developed similarity measures for consensus analysis in group decision-making with intuitionistic fuzzy information. Finally, a practical case is used to illustrate the developed procedures.

The concept of moving average is studied. We analyze several extensions by using generalized aggregation operators, obtaining the generalized moving average. The main advantage is that it provides a general framework that includes a wide range of specific cases including the geometric and the quadratic moving average. This analysis is extended by using the generalized ordered weighted averaging (GOWA) and the induced GOWA (IGOWA) operator. Thus, we get the generalized ordered weighted moving average (GOWMA) and the induced GOWMA (IGOWMA) operator. Some of their main properties are studied. We further extend this approach by using distance measures suggesting the concept of distance moving average and generalized distance moving average. We also consider the case with the OWA and the IOWA operator, obtaining the generalized ordered weighted moving averaging distance (GOWMAD) and the induced GOWMAD (IGOWMAD) operator. The paper ends with an application in multi-period decision making.

Ordered Weighted Averaging (OWA) operators are a family of aggregation functions for data fusion. If the data are real numbers, then OWA operators can be characterized either as a special kind of discrete Choquet integral or simply as an arithmetic mean of the given values previously ordered. This paper analyzes the possible generalizations of these characterizations when OWA operators are defined on a complete lattice. In addition, the set of all n-ary OWA operators is studied as a sublattice of the lattice of all the n-ary aggregation functions defined on a distributive lattice.

This study proposes a novel concept of Scatter for probability distribution (on [0,1]). The proposed measurement is different from famous Shannon Entropy since it considers [0,1] as a chain instead of a normal set. The measurement works easily and reasonably in practice and conforms to human intuition. Some interesting properties like symmetricity, translation invariance, weak convergence and concavity of this new measurement are also obtained. The measurement also has good potential in more theoretical studies and applications. The novel concept can also be suitably adapted for discrete OWA operators and RIM quantifiers. We then propose a new measurement, the Preference Scatter, with its normalized form, the Normalized Preference Scatter, for OWA weights collections. We analyze its reasonability as a new measurement for OWA weights collections with comparisons to some other measurements like Orness, Normalized Dispersion and Hurwicz Degree of OWA operators. In addition, the corresponding Preference Scatter for RIM quantifiers is defined.

This paper presents the prioritized induced heavy ordered weighted average (PIHOWA) operator. This operator combines an unbounded weighting vector, an induced vector and a prioritized vector and can be applied to the group decision-making process where the information provided by each decision maker does not have the same importance. An application of this operator is done in governmental transparency in Mexico based on the Open Government Metric (OGM). Among the main results it is possible to visualize how the relative importance of each component can generate important change in the top 10 ranking.

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 possibility 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.

In this paper, comparisons of OWA operators and ordinal OWA operators are carried out by using lattice theoretic methods. It is proved first that in both cases, the set of all aggregation operators forms a lattice, then the concept of positive valuation is used to measure the "orness" of aggregation operators and the structures of all such possible "orness" measures are determined.

Several real-world applications (e.g., scheduling, configuration, …) can be formulated as Constraint Satisfaction Problems (CSP). In these cases, a set of variables have to be settled to a value with the requirement that they satisfy a set of constraints. Classical CSPs are defined only by means of crisp (Boolean) constraints. However, as sometimes Boolean constraints are too strict in relation to human reasoning, fuzzy constraints were introduced.

When fuzzy constraints are considered, human reasoning usually performs some compensation between alternatives. Thus other operators than t-norms are advisable. Besides of that, not all constraints can be considered with equal importance. In this paper we show that the WOWA operator can consider both aspects: compensation between constraints and constraints of different importance.

It is well known that the Choquet and Sugeno integrals w.r.t. a discrete fuzzy measure can be considered as aggregation operators. In this paper, we study in detail two special cases of symmetric fuzzy measures, i.e. fuzzy measures of which the values only depend upon the cardinality of the arguments. The first case is that of a symmetric k-order additive fuzzy measure, i.e. a fuzzy measure of which the Möbius transform vanishes in sets with cardinality greater than k. A new increasing sequence of binomial OWA operators is introduced. It is recalled that weighted sums of aggregation operators, with possibly negative weights, may also lead to aggregation operators. The Choquet integral w.r.t. a symmetric k-order additive fuzzy measure is then characterized as such a weighted sum of the first k binomial OWA operators. The second case is that of a symmetric k-order maxitive fuzzy measure, i.e. a fuzzy measure of which the possibilistic Möbius transform vanishes in sets with cardinality greater than k. The Sugeno integral w.r.t. a symmetric k-order maxitive fuzzy measure is then characterized as a weighted maximum of the last k order statistics.

We introduce the uncertain generalized OWA (UGOWA) operator. This operator is an extension of the OWA operator that uses generalized means and uncertain information represented as interval numbers. By using UGOWA, it is possible to obtain a wide range of uncertain aggregation operators such as the uncertain average (UA), the uncertain weighted average (UWA), the uncertain OWA (UOWA) operator, the uncertain ordered weighted geometric (UOWG) operator, the uncertain ordered weighted quadratic averaging (UOWQA) operator, the uncertain generalized mean (UGM), and many specialized operators. We study some of its main properties, and we further generalize the UGOWA operator using quasi-arithmetic means. The result is the Quasi-UOWA operator. We end the paper by presenting an application to a decision-making problem regarding the selection of financial strategies.

This paper presents the ordered weighted average weighted average inflation (OWAWAI) and some extensions using induced and heavy aggregation operators and presents the generalized operators and some of their families. The main advantage of these new formulations is that they can use two different sets of weighting vectors and generate new scenarios based on the reordering of the arguments with the weights. With this idea, it is possible to generate new approaches that under- or overestimate the results according to the knowledge and expertise of the decision-maker. The work presents an application of these new approaches in the analysis of the inflation in Chile, Colombia, and Argentina during 2017.

Multi-criteria decision-making (MCDM) methods are used in the selection and evaluation of alternatives. However, too many decision criteria and numerical calculations will increase the computational complexity and make the calculation process difficult to understand. In this paper, a weighted 2-tuple fuzzy linguistic representation model is proposed. The contributions of this study are as follows: (1) Feature selection method was used to remove the redundant or irrelevant feature attributes, thereby simplifying calculations and reducing calculation complexities. (2) The integration of the 2-tuple linguistic representation model simplifies the complexity of numerical calculations. The calculation of qualitative scales can be closer to the human thinking model, and loss of information can be avoided during calculations through the appropriate model. (3) Information fusion technology, i.e., ordered weighted average operator (OWA), was used. The method simplifies the traditional OWA calculation and can be calculated according to the priority order of the indicators. (4) Four major shareholding companies in Taiwan 50 ETF stocks were selected as experimental cases. In total, 992 tuples were obtained and 29 technical indicators were analyzed. The results indicate that case A1 is the most stable among the four stocks considered under different decision-making situations, and it has the first priority ranking.

A fundamental issue about installation of photovoltaic solar power stations is the optimization of the energy generation and the fault detection, for which different techniques and methodologies have already been developed considering meteorological conditions. This fact implies the use of unstable and difficult predictable variables which may give rise to a possible problem for the plausibility of the proposed techniques and methodologies in particular conditions. In this line, our goal is to provide a decision support system for photovoltaic fault detection avoiding meteorological conditions. This paper has developed a mathematical mechanism based on fuzzy sets in order to optimize the energy production in the photovoltaic facilities, detecting anomalous behaviors in the energy generated by the facilities over time. Specifically, the incorrect and correct behaviors of the photovoltaic facilities have been modeled through the use of different membership mappings. From these mappings, a decision support system based on ordered weighted averaging operators informs of the performances of the facilities per day, by using natural language. Moreover, a state machine is also designed to determine the stage of each facility based on the stages and the performances from previous days. The main advantage of the designed system is that it solves the problem of “constant loss of energy production”, without the consideration of meteorological conditions and being able to be more profitable. Moreover, the system is also scalable and portable, and complements previous works in energy production optimization. Finally, the proposed mechanism has been tested with real data, provided by Grupo Energético de Puerto Real S.A. which is an enterprise in charge of the management of six photovoltaic facilities in Puerto Real, Cádiz, Spain, and good results have been obtained for faulting detection.

In this paper we introduce a generalization of Atanassov's operators relating to each interval-valued fuzzy set a family of fuzzy sets. We construct a class of operators and we show that, under suitable conditions, dimension two OWA operators can be obtained from Atanassov's operators.

Aggregation operator is a basic issue in decision making analysis. The weighted OWA operators (denoted by WOWA operators) is an important numerical aggregation operator. In this paper, properties and extensions of WOWA operators are discussed. "orness" measures of WOWA operators is given. By an illustrative example, we show that WOWA operator can be used in aggregating numbers, and help us to gather more information to decision making.