Measure and integral with purely ordinal scales

We develop a purely ordinal model for aggregation functionals for lattice valued functions, comprising as special cases quantiles, the Ky Fan metric and the Sugeno integral. For modeling findings of psychological experiments like the reflection effect in decision behaviour under risk or uncertainty, we introduce reflection lattices. These are complete linear lattices endowed with an order reversing bijection like the reflection at $0$ on the real interval $[-1,1]$. Mathematically we investigate the lattice of non-void intervals in a complete linear lattice, then the class of monotone interval-valued functions and

Agency Decision-Making for Climate Change: Cost-Benefit Analysis, the Precautionary Principle, and the Bounds of Rationality

Climate change tests the limits of human understanding of complexity and uncertainty. It challenges assumptions about our presumed power of control over this planet. This paper examines the theory of how governmental executive branch agencies make regulation decisions about climate change using the decision-making methodologies of cost-benefit analysis and the precautionary principle, and as influenced by perceptions of the bounds of human rationality and ability to deal with risk and uncertainty

Fuzzy measures and integrals in MCDA

This chapter aims at a unified presentation of various methods of MCDA based onfuzzy measures (capacity) and fuzzy integrals, essentially the Choquet andSugeno integral. A first section sets the position of the problem ofmulticriteria decision making, and describes the various possible scales ofmeasurement (difference, ratio, and ordinal). Then a whole section is devotedto each case in detail: after introducing necessary concepts, the methodologyis described, and the problem of the practical identification of fuzzy measuresis given. The important concept of interaction between criteria, central inthis chapter, is explained in details. It is shown how it leads to k-additivefuzzy measures. The case of bipolar scales leads to thegeneral model based on bi-capacities, encompassing usual models based oncapacities. A general definition of interaction for bipolar scales isintroduced. The case of ordinal scales leads to the use of Sugeno integral, andits symmetrized version when one considers symmetric ordinal scales. Apractical methodology for the identification of fuzzy measures in this contextis given. Lastly, we give a short description of some practical applications.Choquet integral; fuzzy measure; interaction; bi-capacities

Toward a Theory of Multi-Method Modeling and Simulation Approach

The representation via simulation models can easily lead to simulation models too simple for their intended purpose, or with too much detail, making them hard to understand. This problem is related to limitations of the modeling and simulation methods. A multi-method Modeling and Simulation (M&S) approach has the potential for improved representation by taking advantage of methods\u27 strengths and mitigating their weaknesses. Despite a high appeal for using multiple M&S methods, several related problems should be addressed first. The current level of theoretical, methodological, and pragmatic knowledge related to a multi-method M&S approach is limited. It is problematic that there is no clearly identified purpose and definition of the multi-method M&S approach. Theoretical and methodological advances are vital to enhancing the application of a multi-method M&S approach to address a broader range of scientific inquiries, improve quality of research, and enable finding common ground between scientific domains. This dissertation explored theoretical principles and research guidelines of a multi-method M&S approach. The analyzed literature offered perspectives related to the purpose, terms, and research guidelines of a multi-method M&S approach. A pragmatic philosophical stance was used to provide the basis for the choice of terms and definitions relevant to a multi-method M&S approach were proposed. The degrees of falsifiability are adapted to the M&S domain, which allowed for developing complementarity principles as the theoretical basis of a multi-method M&S approach. Next, a blueprint of a multi-method M&S approach called method formats was derived, because transitions toward formats must seek justifications in order to increase research objectivity and transparency. A sample set of methods was explored in the context of a proposed sample set of criteria. None of the methods were evaluated with the maximum score for every criterion, which implied that if all those characteristics were required within a research context, then, none of the methods could provide the highest possible score without combining methods. Finally, a case study that included a multi-method simulation model was developed, providing a data layer for evaluation of complementarity principles. The case study contributed to the credibility of complementarity principles as a reason to use a multi-method M&S approach and value of pseudo-triangulation as a mean of verification of a selected approach