Ordering based decision making: a survey

Decision making is the crucial step in many real applications such as organization management, financial planning, products evaluation and recommendation. Rational decision making is to select an alternative from a set of different ones which has the best utility (i.e., maximally satisfies given criteria, objectives, or preferences). In many cases, decision making is to order alternatives and select one or a few among the top of the ranking. Orderings provide a natural and effective way for representing indeterminate situations which are pervasive in commonsense reasoning. Ordering based decision making is then to find the suitable method for evaluating candidates or ranking alternatives based on provided ordinal information and criteria, and this in many cases is to rank alternatives based on qualitative ordering information. In this paper, we discuss the importance and research aspects of ordering based decision making, and review the existing ordering based decision making theories and methods along with some future research directions

Decomposition of fuzzy relations: An application to fuzzy preferences

In this article, working in the spirit of the classical Arrovian models in the fuzzy setting and their possible extensions, we go deeper into the study of some type of decompositions defined by t-norms and t-conorms. This allows us to achieve characterizations of existence and uniqueness for such decompositions and we provide rules to obtain them under some specific conditions. We conclude by applying such results to the study of fuzzy preferences, a key concept in Fuzzy Social Choice

Ambiguity Measures for preference-based decision viwewpoints

This paper examines the ambiguity of subjective judgments, which are represented by a system of pairwise preferences over a given set of alternatives. Such preferences are valued with respect to a set of reasons, in favor and against the alternatives, establishing a complete judgment, or viewpoint, on how to solve the decision problem. Hence, viewpoints entail particular decisions coming from the system of preferences, where the preference-based reasoning of a given viewpoint holds according to its soundness or coherence. Here we explore such a coherence under the frame of ambiguity measures, aiming at learning viewpoints with highest preference-score and minimum ambiguity. We extend existing measures of ambiguity into a multi-dimensional fuzzy setting, and suggest some future lines of research towards measuring the coherence or (ir)rationality of viewpoints, exploring the use of information measures in the context of preference learning

Paradigm Shift in Game Theory : Sociological Re-Conceptualization of Human Agency, Social Structure, and Agents’ Cognitive-Normative Frameworks and Action Determination Modalities

This article aims to present some of the initial work of developing a social science grounded game theory—as a clear alternative to classical game theory. Two distinct independent initiatives in Sociology are presented: One, a systems approach, social systems game theory (SGT), and the other, Erving Goffman’s interactionist approach (IGT). These approaches are presented and contrasted with classical theory. They focus on the social rules, norms, roles, role relationships, and institutional arrangements, which structure and regulate human behavior. While strategic judgment and instrumental rationality play an important part in the sociological approaches, they are not a universal or dominant modality of social action determination. Rule following is considered, generally speaking, more characteristic and more general. Sociological approaches, such as those outlined in this article provide a language and conceptual tools to more adequately and effectively than the classical theory describe, model, and analyze the diversity and complexity of human interaction conditions and processes: (1) complex cognitive rule based models of the interaction situation with which actors understand and analyze their situations; (2) value complex(es) with which actors operate, often with multiple values and norms applying in interaction situations; (3) action repertoires (rule complexes) with simple and complex action alternatives—plans, programs, established (sometimes highly elaborated) algorithms, and rituals; (4) a rule complex of action determination modalities for actors to generate and/or select actions in game situations; three action modalities are considered here; each modality consists of one or more procedures or algorithms for action determination: (I) following or implementing a rule or rule complex, norm, role, ritual, or social relation; (II) selecting or choosing among given or institutionalized alternatives according to a rule or principle; and (III) constructing or adopting one or more alternatives according to a value, guideline, or set of criteria. Such determinations are often carried out collectively. The paper identifies and illustrates in a concluding table several of the key differences between classical theory and the sociological approaches on a number of dimensions relating to human agency; social structure, norms, institutions, and cultural forms; patterns of game interaction and outcomes, the conditions of cooperation and conflict, game restructuring and transformation, and empirical relevance. Sociologically based game theory, such as the contributions outlined in this article suggest a language and conceptual tools to more adequately and effectively than the classical theory describe, model, and analyze the diversity, complexity, and dynamics of human interaction conditions and processes and, therefore, promises greater empirical relevance and scientific power. An Appendix provides an elaboration of SGT, concluding that one of SGT’s major contributions is the rule based conceptualization of games as socially embedded with agents in social roles and role relationships and subject to cognitive-normative and agential regulation. SGT rules and rule complexes are based on contemporary developments relating to granular computing and Artificial Intelligence in general.Peer reviewe

Knowledge-based processing for aircraft flight control

This Contractor Report documents research in Intelligent Control using knowledge-based processing in a manner dual to methods found in the classic stochastic decision, estimation, and control discipline. Such knowledge-based control has also been called Declarative, and Hybid. Software architectures were sought, employing the parallelism inherent in modern object-oriented modeling and programming. The viewpoint adopted was that Intelligent Control employs a class of domain-specific software architectures having features common over a broad variety of implementations, such as management of aircraft flight, power distribution, etc. As much attention was paid to software engineering issues as to artificial intelligence and control issues. This research considered that particular processing methods from the stochastic and knowledge-based worlds are duals, that is, similar in a broad context. They provide architectural design concepts which serve as bridges between the disparate disciplines of decision, estimation, control, and artificial intelligence. This research was applied to the control of a subsonic transport aircraft in the airport terminal area

Comparison of random variables from a game-theoretic perspective

This work consists of four related parts, divided into eight chapters. A ¯rst part introduces the framework of cycle-transitivity, developed by De Baets et al. It is shown that this framework is ideally suited for describing and compar- ing forms of transitivity of probabilistic relations. Not only does it encompass most already known concepts of transitivity, it is also ideally suited to describe new types of transitivity that are encountered in this work (such as isostochas- tic transitivity and dice-transitivity). The author made many non-trivial and sometimes vital contributions to the development of this framework. A second part consists of the development and study of a new method to compare random variables. This method, which bears the name generalized dice model, was developed by De Meyer et al. and De Schuymer et al., and can be seen as a graded alternative to the well-known concept of ¯rst degree stochastic dominance. A third part involves the determination of the optimal strategies of three game variants that are closely related to the developed comparison scheme. The de¯nitions of these variants di®er from each other solely by the copula that is used to de¯ne the payo® matrix. It turns out however that the characterization of the optimal strategies, done by De Schuymer et al., is completely di®erent for each variant. A last part includes the study of some combinatorial problems that orig- inated from the investigation of the transitivity of probabilistic relations ob- tained by utilizing the developed method to compare random variables. The study, done by De Schuymer et al., includes the introduction of some new and interesting concepts in partition theory and combinatorics. A more thorough discussion, in which each section of this work is taken into account, can be found in the overview at the beginning of this manuscript. Although this work is oriented towards a mathematical audience, the intro- duced concepts are immediately applicable in practical situations. Firstly, the framework of cycle-transitivity provides an easy means to represent and compare obtained probabilistic relations. Secondly, the generalized dice model delivers a useful alternative to the concept of stochastic dominance for comparing random variables. Thirdly, the considered dice games can be viewed in an economical context in which competitors have the same resources and alternatives, and must choose how to distribute these resources over their alternatives. Finally, it must be noted that this work still leaves opportunities for future research. As immediate candidates we see, ¯rstly the investigation of the tran- sitivity of generalized dice models in which the random variables are pairwisely coupled by a di®erent copula. Secondly, the characterization of the transitivity of higher-dimensional dice models, starting with dimension 4. Thirdly, the study of the applicability of the introduced comparison schemes in areas such as mar- ket e±ciency, portfolio selection, risk estimation, capital budgeting, discounted cash °ow analysis, etc