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Prioritized induced probabilistic distances in transparency and access to information laws

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Abstract

In this paper, a new extension of the ordered weighted average (OWA) operator is developed using four different methods: prioritized operators, induced operators, probabilistic operators and distance techniques. This new operator is called the prioritized induced probabilistic ordered weighted average distance (PIPOWAD) operator. The primary advantage is that we include in one formulation different characteristics and information provided by a group of decision makers to compare actual and ideal situations. Finally, an example of transparency and access to information law in Mexico is presented to forecast the score based on the expectations of decision makers. © 2016 Int. Association for Fuzzy-Set Management and Economy. All rights reserved.

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... This operator is important in group decision making when not all the decision makers have the same importance in the decision. Usually, this operator is important when different experts are questioned about the situations and each of them give different values and to everyone to be included in the results each one of them are given a weight based on their experience and importance in the decision [44,45]. The formulation is as follows. ...
... The main idea of this operator is that the reordering step will be performed based on induced variables determined by the decision maker, and allows for considering different values and to everyone to be included in the results. Each one of them are given a weight based on their experience and importance in the decision [44,45]. Thus, by having induced variables and decision-prioritizing aspects in a group of experts, it is possible to consider both the information derived from the data and the opinions of the decision makers in group decisions. ...
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The main aim is to propose a new method for estimating the Human Development Index using ordered weighted average. To develop this method, ordered weighted geometric average (OWGA), induced OWGA prioritized OWA (POWA) operator are studied. Using Human Development Index formulation in combination to aggregations operators presented above is proposed the prioritized induced ordered weighted geometric average (PIOWGA) operator. A mathematical application is carried out to estimate the Human Development Index and compare it with the traditional method and other existing methods. Finally, it is noted that decision makers have an influence on the order given in the ranking by its attitude and criterion, and method can capture the subjective information prioritized by them.
... For future research, a new extension of the MLR with different OWA operators will be done. Such is the case of moving averages [53,54] in the case of using specific ranges in the series, Bonferroni means [55,56] extending the cases of analysis to other parameters, prioritized operators [57,58] to give importance to certain arguments and opinions related to the variables and logarithmic operators [59,60] to work with different scales of data. ...
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This paper introduces the multiple linear regression heavy ordered weighted average (MLR-HOWA) operator. On the MLR-HOWA operator, the beta values are obtained with the use of the HOWA means. In that sense, it provides a new range of possibilities by under or overestimating the result based on the decision maker’s expectations and knowledge. Therefore, the MLR-HOWA provides a forecasting tool that can analyze multiple scenarios from minimum to maximum. The main properties and two extensions using induced and generalized variables are also presented. An application in exchange rate forecasting based on inflation and interest rate as independent variables for five Latin American countries is submitted. Among the main results, it is possible to identify that the forecasting error is reduced when different combinations of MLR with OWA operators are done.
... Within the aggregation operators, one that has been studied and widely applied in different contexts is the ordered weighted average (OWA) operator [15,16]. The main characteristic of the OWA operator is that based on the reordering step, it is possible to obtain the maximum or minimum result, and with the use of a weighting vector, the aptitude, knowledge and expectation of the decision maker can be included in the result [17][18][19][20][54][55][56][57]. An extension that will be used in this paper is the probabilistic OWA (POWA) operator [21]. ...
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The objective of the paper is to present an extension of the ordered weighted average (OWA) operator, probability OWA (POWA) operator, distance measures and Pythagorean membership grades. These new operators are called the Pythagorean membership grade OWA distance (PMGOD) operator and the probabilistic Pythagorean membership grade OWA distance (PPMGOD) operator. This extension includes in one formulation the ability to measure the ideal vs. real situation of the distance operators, the weighting vector and reordering step of the OWA operator and the way in which it includes uncertainty based on the satisfaction of the criteria of the Pythagorean membership degree. These propositions are applied to new business ventures in the city of Colombia, where the decision maker can express his/her concerns about the uncertainty and probabilities of the current business environment and, thus, generate a better decision-making process.
... For future work, it is possible to add other mathematical methods to the volatility formulation such as Bonferroni means [7,5] and prioritized operators in group decision making (Perez-Arellano et al. [40], Aviles-Ochoa et al. [3]). Additionally, we will also apply these formulations in group decision making [6,51], Merigó et al. [34], and largescale group decision making [12], theory of expertons [22,28], forgotten effects [2] and in combination with different approaches for aggregation operators [41,27,4]. ...
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Agricultural products have experienced sudden changes in prices in recent years as a result of volumes of production and demand at the international level. Volatility is a key element in understanding the difficulties that the market may have. However, the traditional formula for volatility only considers historical information and does not consider decision makers' knowledge and skills. To improve this approach and obtain more accurate results consistent with the reality of the market, the ordered weighted averaging (OWA) operator is used. These new approaches are the OWA-Volatility, Induced OWA-Volatility, Heavy OWA-Volatility, Probabilistic OWA-Volatility, Induced Probabilistic OWA-Volatility and Induced Heavy OWA-Volatility. In addition, some particular cases are presented in which the aggregation process is only applied to one part of the formula or quasi-arithmetic means are used. An example of volatility calculations for corn prices in 2017 is presented.
... Since the appearance of the OWA operator, many extensions have been proposed, including logarithmic averaging operators [19][20][21], moving averages [22][23][24] and Bonferroni means [25,26]. These developments have been applied to diverse fields, such as decision sciences [27,28], finance [29,30], and policy decision-making [31,32]. Moreover, multiple extensions have been developed using the Bonferroni OWA operator, which have been diversified with distance measures applied to problems in personnel selection [33,34], induced variables applied to forecast and business risk management [35,36] and extensions with central tendency measures such as variance and covariance [37,38]. ...
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Financial markets have been characterized in recent years by their uncertainty and volatility. The price of assets is always changing so that the decisions made by consumers, producers, and governments about different products is not still accurate. In this situation, it is necessary to generate models that allow the incorporation of the knowledge and expectations of the markets and thus include in the results obtained not only the historical information, but also the present and future information. The present article introduces a new extension of the ordered weighted averaging (OWA) operator called the Bonferroni probabilistic ordered weighted average (B-POWA) operator. This operator is designed to unify in a single formulation the interrelation of the values given in a data set by the Bonferroni means and a weighted and probabilistic vector that models the attitudinal character, expectations, and knowledge of the decision-maker of a problem. The paper also studies the main characteristics and some families of the B-POWA operator. An illustrative example is also proposed to analyze the mathematical process of the operator. Finally, an application to corn price estimation designed to calculate the error between the price of an agricultural commodity using the B-POWA operator and a leading global market company is presented. The results show that the proposed operator exhibits a better general performance than the traditional methods.
... In future research, we plan to make more extensions of aggregation operators using prioritized operators (Pérez-Arellano, León-Castro, Avilés-Ochoa, & Merigó 2017;Avilés-Ochoa, Perez-Arellano, León-Castro, & Merigó, 2017), Bonferroni means (Blanco-Mesa, Merigó, & Kacprzyk, 2016;Blanco-Mesa, León-Castro, & Merigó, 2018;Y. He, Z. He, & Chen, 2015), Choquet integrals (Belles-Sampera, Merigó, Guillén, & Santolino, 2014), distance operators (Merigó & Casanovas, 2011;Liu & Chen, 2017), Hesitant fuzzy sets (Ren, Xu, & Hao, 2017;Zeng & Yao, 2018), intuitionistic fuzzy sets (Liu, J. X. ...
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Book
Dynamic MCDM, Habitual Domains and Competence Set Analysis for Effective Decision Making in Changeable Spaces.- The Need for and Possible Methods of Objective Ranking.- Preference Function Modelling: The Mathematical Foundations of Decision Theory.- Robustness in Multi-criteria Decision Aiding.- Preference Modelling, a Matter of Degree.- Fuzzy Sets and Fuzzy Logic-Based Methods in Multicriteria Decision Analysis.- Argumentation Theory and Decision Aiding.- Problem Structuring and Multiple Criteria Decision Analysis.- Robust Ordinal Regression.- Stochastic Multicriteria Acceptability Analysis (SMAA).- Multiple Criteria Approaches to Group Decision and Negotiation.- Recent Developments in Evolutionary Multi-Objective Optimization.- Multiple Criteria Decision Analysis and Geographic Information Systems.
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Although the electronic revolution in publishing fostered a new Information Age, the need for government documents in tangible format continues. This paper examines the historical roots of congressional printing compared to 21st century challenges to information policy. The author argues that the founding fathers intentionally did not include language mandating the printing of government information, aside from the Journal as described in the Constitution, for the simple reason that they viewed it as an inherent obligation on the part of all elected officials. As such, restrictive information policies, such as the U.S.A. Patriot Act, impinge upon the original intent of the founding fathers and indeed, threaten the ideal of a democratic society.
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The aim of this paper is to develop an ordered weighted distance (OWD) measure, which is the generalization of some widely used distance measures, including the normalized Hamming distance, the normalized Euclidean distance, the normalized geometric distance, the max distance, the median distance and the min distance, etc. Moreover, the ordered weighted averaging operator, the generalized ordered weighted aggregation operator, the ordered weighted geometric operator, the averaging operator, the geometric mean operator, the ordered weighted square root operator, the square root operator, the max operator, the median operator and the min operator are also the special cases of the OWD measure. Some methods depending on the input arguments are given to determine the weights associated with the OWD measure. The prominent characteristic of the OWD measure is that it can relieve (or intensify) the influence of unduly large or unduly small deviations on the aggregation results by assigning them low (or high) weights. This desirable characteristic makes the OWD measure very suitable to be used in many actual fields, including group decision making, medical diagnosis, data mining, and pattern recognition, etc. Finally, based on the OWD measure, we develop a group decision making approach, and illustrate it with a numerical example.
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For more than 150 years, the United States Government Printing Office (GPO), along with its Federal Depository Library Program (FDLP), has supported an informed citizenry and democracy by ensuring access and preservation to a broad swath of federal government information. This collaborative national public information program between local libraries and the national government, if it is to survive beyond its second century of service, must overcome profound challenges within a rapidly evolving complex of e-government policies and principles. The FDLP can (and must) find a way to serve its traditional values – permanent and public access to government information – that allows for growth and change within the demands of a dynamic electronic environment between the governors and the governed.
Article
The ordered weighted averaging (OWA) operator was developed by Yager [IEEE Trans. Syst., Man, Cybernet. 18 (1998) 183]. Later, Yager and Filev [IEEE Trans. Syst., Man, Cybernet.––Part B 29 (1999) 141] introduced a more general class of OWA operators called the induced ordered weighted averaging (IOWA) operators, which take as their argument pairs, called OWA pairs, in which one component is used to induce an ordering over the second components which are exact numerical values and then aggregated. The aim of this paper is to develop some induced uncertain linguistic OWA (IULOWA) operators, in which the second components are uncertain linguistic variables. Some desirable properties of the IULOWA operators are studied, and then, the IULOWA operators are applied to group decision making with uncertain linguistic information.
Article
We develop a new approach that uses the ordered weighted averaging (OWA) operator in the selection of financial products. In doing so, we introduce the ordered weighted averaging distance (OWAD) operator and the ordered weighted averaging adequacy coefficient (OWAAC) operator. These aggregation operators are very useful for decision-making problems because they establish a comparison between an ideal alternative and available options in order to find the optimal choice. The objective of this new model is to manipulate the attitudinal character of previous methods based on distance measures, so that the decision maker can select financial products according to his or her degree of optimism, which is also known as the orness measure. The main advantage of using the OWA operator is that we can generate a parameterized family of aggregation operators between the maximum and the minimum. Thus, the analysis developed in the decision process by the decision maker is much more complete, because he or she is able to select the particular case in accordance with his or her interests in the aggregation process. The paper ends with an illustrative example that shows results obtained by using different types of aggregation operators in the selection of financial products.
Book
Aggregation of information is of primary importance in the construction of knowledge based systems in various domains, ranging from medicine, economics, and engineering to decision-making processes, artificial intelligence, robotics, and machine learning. This book gives a broad introduction into the topic of aggregation functions, and provides a concise account of the properties and the main classes of such functions, including classical means, medians, ordered weighted averaging functions, Choquet and Sugeno integrals, triangular norms, conorms and copulas, uninorms, nullnorms, and symmetric sums. It also presents some state-of-the-art techniques, many graphical illustrations and new interpolatory aggregation functions. A particular attention is paid to identification and construction of aggregation functions from application specific requirements and empirical data. This book provides scientists, IT specialists and system architects with a self-contained easy-to-use guide, as well as examples of computer code and a software package. It will facilitate construction of decision support, expert, recommender, control and many other intelligent systems.
Article
We consider criteria aggregation problems where there exists a prioritization relationship over the criteria. We suggest that prioritization between criteria can be modeled by making the weights associated with a criteria dependent upon the satisfaction of the higher priority criteria. We consider a number of aggregation operators in which there exists a prioritization relationship between the arguments. We first introduce a prioritized scoring operator and a closely related prioritized averaging operator. We next introduce a prioritized “anding” and then a prioritized “oring” operator.
Article
With respect to risk decision making problems with interval probability in which the attribute values take the form of the uncertain linguistic variables, a multi-attribute decision making method based on prospect theory is proposed. To begin with, the uncertain linguistic variables can be transformed into the trapezoidal fuzzy number, and the prospect value function of the trapezoidal fuzzy number based on the decision-making reference point of each attribute and the weight function of interval probability can be constructed; then the prospect value of attribute for every alternative is calculated through prospect value function of the trapezoidal fuzzy number and the weight function of interval probability, and the weighted prospect value of alternative is acquired by using weighted average method according to attribute weights, and all the alternatives are sorted according to the expected values of the weighted prospect values; Finally, an illustrate example is given to show the decision-making steps, the influence on decision making for different parameters of value function and different decision-making reference point, and the feasibility of the method.
Article
In this paper, we present a new decision-making approach that uses distance measures and induced aggregation operators. We introduce the induced ordered weighted averaging distance (IOWAD) operator. IOWAD is a new aggregation operator that extends the OWA operator by using distance measures and a reordering of arguments that depends on order-inducing variables. The main advantage of IOWAD is that it provides a parameterized family of distance aggregation operators between the maximum and the minimum distance based on a complex reordering process that reflects the complex attitudinal character of the decision-maker. We studied some of IOWAD’s main properties and different particular cases and further generalized IOWAD by using Choquet integrals. We developed an application in a multi-person decision-making problem regarding the selection of investments. We found that the main advantage of this approach is that it is able to provide a more complete picture of the decision-making process, enabling the decision-maker to select the alternative that it is more in accordance with his interests.
Article
We indicate that the problem of prioritized criteria arises in situations in which there exists a relationship between the criteria so that lack of satisfaction by the higher priority criteria cannot be readily compensated for by satisfaction by lower priority criteria. Typical of this situation is the relationship between safety and cost. We consider the problem of criteria aggregation in this environment. Central to our approach is the use of importance weights to enforce this prioritization imperative. We apply our use of priority based importance weights to the case where the scope of the criteria aggregation is an OWA type aggregation.
Article
This article presents findings from the 2006 Public Libraries and the Internet study and other research that demonstrate the impact of public Internet access in public libraries on the communities and individuals that the libraries serve. This article focuses on the importance of public library Internet access in times of emergencies and for a range of electronic government (e-government) services at the individual and community-wide levels. Public access computing and Internet access in public libraries function as a first choice, first refuge, and last resort in a range of emergency and e-government circumstances, allowing individuals to engage successfully in essential e-government services such as registering for Medicare or other benefits and filing tax information. With this key centrality as agents of government services, public libraries increasingly play significant roles in times of emergencies, like the aftermath of a hurricane, in which communities rely on the public library Internet access to request aid, try to find missing family and friends, file Federal Emergency Management Agency (FEMA) and insurance claims, and begin rebuilding their lives. This article also discusses the need to revise government policy related to the role of public libraries in their support of e-government as public libraries increasingly serve as agents of e-government.
Article
We consider the problem of multicriteria decision making (MCDM) in the situation in which there exists a prioritization of criteria. A good example of prioritization among criteria occurs in the case of air travel, where concerns about passenger safety have a higher priority then economic concerns. Tradeoffs between saving on gasoline usage and jeopardizing passenger safety are unacceptable. We show how this prioritization of criteria can be modeled by using importance weights in which the weights associated with the lower priority criteria are related to the satisfaction of the higher priority criteria. We provide some models that allow for the formalization of these prioritized MCDM problems using both the Bellman-Zadeh paradigm for MCDM and the ordered weighted averaging (OWA) operator method.
Models for the research of forgotten effects
  • A Kaufmann
  • J Gil Aluja
Kaufmann, A.; Gil Aluja, J. (1988). Models for the research of forgotten effects. (In Spanish), Spain, Milladoiro.