Logic-based preference representation languages are promising for expressing preferences over combinatorial domains. Sets of weighted formulas, called goalbases, can be used to define several such languages. How goalbases are translated into utility functions—that is, by what aggregation function this is done—is a crucial component of this type of language. In this paper, we consider the proper...

This paper deals with the characterization of some classes of aggregation functions often used in multicriteria decision making problems. The common properties involved in these characterizations are “increasing monotonicity” and “stability for positive linear transformations”. Additional algebraic properties related to associativity allow to completely specify the functions.

We investigate the problem of combining or aggregating several color values given in coding scheme RGB. For this reason, we study the problem of averaging values on lattices, and in particular on discrete product lattices. We study the arithemtic mean and the median on product lattices. We apply these aggregation functions in image reduction and we present a new algorithm based on the minimizat...

In this work we construct linear orders between pairs of intervals by using aggregation functions. We apply these orders in a decision-making problem where the experts provide their opinions by means of interval-valued fuzzy sets.

We consider voting games as procedures to aggregate individual preferences. We survey positive results on the non-emptiness of the core of voting games and explore other solutions concepts that are basic supersets of the core such as Rubinstein’s stability set and two types of uncovered sets. We consider cases where the sets of alternatives are ‘ordinary’ sets, finite sets and infinite sets wit...

This paper investigates U.S. bank common stock returns and their sensitivity to market risk, interest rate risk, and illiquidity risk. Due to known problems with conducting inference using Generalized Method of Moments, I use the Empirical Likelihood Block Bootstrap established in Allen, Gregory, and Shimotsu (2004). Preliminary results suggest that once the test-statistics are bootstrapped, ag...

In this paper we provide a way to generate a class of weighted average operator from n-dimensional overlap functions and aggregation functions. These weighted average operators are used in an algorithm of a multiattribute group decision making problem based on decision matrix. An illustrative example is considered with the application of our method for two specific weighted average operators of...

Thus, for each student a composite unscaled mark is generated for each course taken. However, the cohort of students taking a particular course P may be academically more able than the cohort of students taking course Q. This means that a composite unscaled mark of, say, 60 in course P represents a higher level of attainment than the same mark in course Q. Since marks in different courses are a...

This article discusses Lipschitz properties of generated aggrega-tion functions. Such generated functions include triangular norms and conorms, quasi-arithmetic means, uninorms, nullnorms and continuous generated functions with a neutral element. The Lipschitz property guarantees stability of aggregation operations with respect to input inaccuracies, and is important for applications. We provid...

The two-parts state-of-art overview of aggregation theory summarizes the essential information concerning aggregation issues. Overview of aggregation properties is given, including the basic classification of aggregation functions. In this first part, the stress is put on means, i.e., averaging aggregation functions, both with fixed arity (n-ary means) and with open arity (extended means).