Variances with Bonferroni means and ordered weighted averages

Bonferroni Weighted Logarithmic Averaging Distance Operator Applied to Investment Selection Decision Making

Distance measures in ordered weighted averaging (OWA) operators allow the modelling of complex decision making problems where a set of ideal values or characteristics are required to be met. The objective of this paper is to introduce extended distance measures and logarithmic OWA-based decision making operators especially designed for the analysis of financial investment options. Based on the immediate weights, Bonferroni means and logarithmic averaging operators, in this paper we introduce the immediate weights logarithmic distance (IWLD), the immediate weights ordered weighted logarithmic averaging distance (IWOWLAD), the hybrid weighted logarithmic distance (HWLD), the Bonferroni ordered weighted logarithmic averaging distance (B-OWLAD) operator, the Bonferroni immediate weights ordered weighted logarithmic averaging distance (B-IWOWLAD) operator and the Bonferroni hybrid weighted logarithmic distance (HWLD). A financial decision making illustrative example is proposed, and the main benefits of the characteristic design of the introduced operators is shown, which include the analysis of the interrelation between the modelled arguments required from the decision makers and the stakeholders, and the comparison to an ideal set of characteristics that the possible companies in the example must portray. Moreover, some families, particular cases and brief examples of the proposed operators, are studied and presented. Finally, among the main advantages are the modeling of diverse perspectives, attitudinal characteristics and complex scenarios, through the interrelation and comparison between the elements with an ideal set of characteristics given by the decision makers and a set of options.

Variances and Logarithmic Aggregation Operators: Extended Tools for Decision-Making Processes

Variance, as a measurement of dispersion, is a basic component of decision-making processes. Recent advances in intelligent systems have included the concept of variance in information fusion techniques for decision-making under uncertainty. These dispersion measures broaden the spectrum of decision makers by extending the toolset for the analysis and modeling of problems. This paper introduces some variance logarithmic averaging operators, including the variance generalized ordered weighted averaging (Var-GOWLA) operator and the induced variance generalized ordered weighted averaging (Var-IGOWLA) operator. Moreover, this paper analyzes some properties, families and particular cases of the proposed operators. Finally, an illustrative example of the characteristic design of the operators is proposed using real-world information retrieved from financial markets. The objective of this paper is to analyze the performance of some equities based on the expected payoff and the dispersion of its elements. Results show that the equity payoff results present diverse rankings combined with the proposed operators, and the introduced variance measures aid decision-making by offering new tools for information analysis. These results are particularly interesting when selecting logarithmic averaging operators for decision-making processes. The approach presented in this paper extends the available tools for decision-making under ignorance, uncertainty, and subjective environments.

A multicriteria hierarchical approach for portfolio selection in a stock exchange

The objective of the paper is to present a multiple criteria hierarchical process (MCHP) approach for portfolio selection in a stock exchange. One of the problems that investors usually face is which stock should be included in the portfolio. This paper helps investors answer that question, and the paper presents an MCHP approach using different criteria based on financial ratios that the decision maker (in this case, the investor) will give different weights to make a portfolio based on her preferences; different importance is given to each criterion. An example using the Mexican Stock Exchange is presented.

Pythagorean membership grade distance aggregation: An application to new business ventures

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.

Bonferroni Prioritized Aggregation Operators Applied to Government Transparency

This article applies the Bonferroni prioritized induced heavy ordered weighted average (OWA) to analyze a series of data and focuses on the Bonferroni average and heavy induced prioritized aggregation operators. The objective of the present work is to present a new aggregation operator that combines the heavy induced prioritized Bonferroni and its formulations and represents the Bonferroni mean with variables that induce an order with vectors that are greater than one. This work develops some extensions using prioritization. The main advantage is that different types of information provided by a group of decision makers to compare real situations are included in this formulation. Finally, an example using the operators to calculate the transparency of the websites of the 32 states of Mexico was performed. The main idea was to visualize how the ranking can change depending on the importance of the five components of the methodology. The main results show that it is possible to detect some important changes depending on the operator and the experts considered.

Bonferroni Probabilistic Ordered Weighted Averaging Operators Applied to Agricultural Commodities’ Price Analysis

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.