Decision Making by Hybrid Probabilistic - Possibilistic Utility Theory

It is presented an approach to decision theory based upon nonprobabilistic uncertainty. There is an axiomatization of the hybrid probabilisticpossibilistic mixtures based on a pair of triangular conorm and triangular norm satisfying restricted distributivity law, and the corresponding non-additive Smeasure. This is characterized by the families of operations involved in generalized mixtures, based upon a previous result on the characterization of the pair of continuous t-norm and t-conorm such that the former is restrictedly distributive over the latter. The obtained family of mixtures combines probabilistic and idempotent (possibilistic) mixtures via a threshold.Decision making, Utility theory, Possibilistic mixture, Hybrid probabilistic- possibilistic mixture, Triangular norm, Triangular conorm, Pseudoadditive measure.

Fuzzy Mathematics

This book provides a timely overview of topics in fuzzy mathematics. It lays the foundation for further research and applications in a broad range of areas. It contains break-through analysis on how results from the many variations and extensions of fuzzy set theory can be obtained from known results of traditional fuzzy set theory. The book contains not only theoretical results, but a wide range of applications in areas such as decision analysis, optimal allocation in possibilistics and mixed models, pattern classification, credibility measures, algorithms for modeling uncertain data, and numerical methods for solving fuzzy linear systems. The book offers an excellent reference for advanced undergraduate and graduate students in applied and theoretical fuzzy mathematics. Researchers and referees in fuzzy set theory will find the book to be of extreme value

Tropical Attitudes in Strategic Interactions under Ignorance

Assuming only ordinal preferences as transparent, we study players interacting under the veil of ignorance, that cannot produce beliefs as probability measures but rather have coarse beliefs represented as subsets of opponents' actions. These players follow either $\max \max$ or $\max \min$ decision criteria. The criteria can be identified as optimistic and pessimistic attitudes, respectively, which we refer to as ``tropical''. Explicitly formalizing these attitudes and how players reason under ignorance, we characterize the behavioral implications related to common belief in these events: while optimism is related to Point Rationalizability, a new algorithm -- Wald Rationalizability -- captures pessimism. Our characterizations allow us to uncover novel connections and results: ($i$) regarding optimism, we prove that dropping the (implicit) assumption that whatever a player believes is also true allows to capture wishful thinking \`a la Yildiz (2007), thus reversing an existence failure described therein; ($ii$) by studying how pessimism and optimism relate to B\"orgers dominance, we shed light on the appropriate notion of rationality in ordinal games; ($iii$) finally, with respect to pessimism, our analysis identifies Wald Rationalizability as the limit point of players becoming infinitely risk averse, hence, clarifying the conceptual underpinnings behind a discontinuity in the analysis of Rationalizability in presence of varying risk attitudes hinted in Weinstein (2016).Comment: Previous title: "Strategic Interactions under Ignorance: A Theory of Tropical Players'

A critical review of the approaches to optimization problems under uncertainty

Ankara : The Department of Industrial Engineering and the Institute of Engineering and Science of Bilkent University, 2001.Thesis (Master's) -- Bilkent University, 2001.Includes bibliographical references leaves 58-72.In this study, the issue of uncertainty in optimization problems is studied. First of all, the meaning and sources of uncertainty are explained and then possible ways of its representation are analyzed. About the modelling process, different approaches as sensitivity analysis, parametric programming, robust optimization, stochastic programming, fuzzy programming, multiobjective programming and imprecise optimization are presented with advantages and disadvantages from different perspectives. Some extensions of the concepts of imprecise optimization are also presented.Gürtuna, FilizM.S

Optimism and pessimism in strategic interactions under ignorance

We study players interacting under the veil of ignorance, who have—coarse—beliefs represented as subsets of opponents' actions. We analyze when these players follow max⁡min or max⁡max decision criteria, which we identify with pessimistic or optimistic attitudes, respectively. Explicitly formalizing these attitudes and how players reason interactively under ignorance, we characterize the behavioral implications related to common belief in these events: while optimism is related to Point Rationalizability, a new algorithm—Wald Rationalizability—captures pessimism. Our characterizations allow us to uncover novel results: (i) regarding optimism, we relate it to wishful thinking á la Yildiz (2007) and we prove that dropping the (implicit) “belief-implies-truth” assumption reverses an existence failure described therein; (ii) we shed light on the notion of rationality in ordinal games; (iii) we clarify the conceptual underpinnings behind a discontinuity in Rationalizability hinted in the analysis of Weinstein (2016)