Aggregation functions: Means

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).

An axiomatic approach to finite means

In this paper we analyze the notion of a finite mean from an axiomatic point of view. We discuss several axiomatic alternatives, with the aim of establishing a universal definition reconciling all of them and exploring theoretical links to some branches of Mathematics as well as to multidisciplinary applications

Mathematical Approaches to Sustainability Assessment and Protocol Development for the Bioenergy Sustainability Target Assessment Resource (Bio-STAR)

Bioenergy is renewable energy made of materials derived from biological, non-fossil sources. In addition to the benefits of utilizing an energy source that is renewable, bioenergy is being researched for its potential positive impact on climate change mitigation, job creation, and regional energy security. It has also been studied to investigate possible challenges related to indirect and direct land-use change and food security. Bioenergy sustainability assessment provides a method to identify, quantify, and interpret indicators, or metrics, of bioenergy sustainability in order to study trade-offs between environmental, social, and economic aspects of bioenergy production and use. Assessment is crucial to inform policymakers, researchers, and stakeholders as they make decisions to support the development of a sustainable bioeconomy in the United States and globally. It is the purpose of this dissertation to identify and derive mathematical techniques that aid in the development of the Bioenergy Sustainability Target Assessment Resource (Bio-STAR). Guiding principles for Bio-STAR include (i) adaptability for assessing diverse bioenergy production pathways, (ii) exibility to support a range of analyses that researchers and policymakers may seek to undertake, and (iii) mathematical robustness with respect to the operations utilized. Key components of sustainability assessment are defined and presented in the first chapter. Of the key components, Normalization and Aggregation represent areas in which the mathematical processes utilized are critical to assessment outcomes. As such, mathematical theory is developed for Normalization and Aggregation in sustainability assessment and presented in the second and third chapters, respectively. This theory is applied in the fourth chapter to inform the development of protocols for the Bioenergy Sustainability Target Assessment Resource. Bioenergy is seen as component of a sustainable energy future in the United States. Bioenergy is unique among renewable energy sources in that it can be produced in a variety of ways. Bio-STAR is a tool that will enable policymakers, researchers, and stakeholders to explore these many bioenergy options from a sustainability viewpoint and make decisions that will guide the U.S. and the world towards a sustainable energy future

Multiple-Criteria Decision Making

Decision-making on real-world problems, including individual process decisions, requires an appropriate and reliable decision support system. Fuzzy set theory, rough set theory, and neutrosophic set theory, which are MCDM techniques, are useful for modeling complex decision-making problems with imprecise, ambiguous, or vague data.This Special Issue, “Multiple Criteria Decision Making”, aims to incorporate recent developments in the area of the multi-criteria decision-making field. Topics include, but are not limited to:- MCDM optimization in engineering;- Environmental sustainability in engineering processes;- Multi-criteria production and logistics process planning;- New trends in multi-criteria evaluation of sustainable processes;- Multi-criteria decision making in strategic management based on sustainable criteria

Changing Choices

Changing choices psychological relativity theory unifying theory transformation parameters psychology psygologie koornstra choice dynamics The book contains a unifying theory on how the common object space is metrically transformed by individuals with different transformation parameters, due to their other previous experiences, to individually different psychological spaces for judgment on the one hand and preference on the other hand. Individual experiences also change generally, whereby the psychological spaces also change generally for each individual. The theory, therefore, is a psychological relativity theory of perception, judgment, preference, and choice dynamics. This book is a must read for all behavioural, economic, and social scientists with theoretical interest and some understanding of multidimensional data analyses. It integrates more than twenty theories on perception, judgment, preference, and risk decisions into one mathematical theory. Knowledge of advanced mathematics and modern geometry is not needed, because the mathematical subsections can be skipped without loss of understanding, due to their explanation and illustration by figures in the text

A characterization of the ordered weighted averaging functions based on the ordered bisymmetry property

This paper deals with a characterization of a class of aggregation operators. This class concerns operators which are symmetric, increasing, stable for the same positive linear transformations and present a property close to the bisymmetry property: the ordered bisymmetry property. It is proved that the class investigated contains exactly the ordered weighted averaging operators (OWA) introduced by Yager in 1988

Conflicting Objectives in Decisions

This book deals with quantitative approaches in making decisions when conflicting objectives are present. This problem is central to many applications of decision analysis, policy analysis, operational research, etc. in a wide range of fields, for example, business, economics, engineering, psychology, and planning. The book surveys different approaches to the same problem area and each approach is discussed in considerable detail so that the coverage of the book is both broad and deep. The problem of conflicting objectives is of paramount importance, both in planned and market economies, and this book represents a cross-cultural mixture of approaches from many countries to the same class of problem