Multiple Criteria Ranking and Choice with All Compatible Minimal Cover Sets of Decision Rules

We introduce a new multiple criteria ranking/choice method that applies Dominance-based Rough Set Approach (DRSA) and represents the Decision Maker's (DM's) preferences with decision rules. The DM provides a set of pairwise comparisons indicating whether an outranking (weak preference) relation should hold for some pairs of reference alternatives. This preference information is structured using the lower and upper approximations of outranking (S) and non-outranking (S c ) relations. Then, all minimal-cover (MC) sets of decision rules being compatible with this preference information are induced. Each of these sets is supported by some positive examples (pairs of reference alternatives from the lower approximation of a preference relation) and it does not cover any negative example (pair of alternatives from the upper approximation of an opposite preference relation). The recommendations obtained by all MC sets of rules are analyzed to describe pairwise outranking and non-outranking relations, using probabilistic indices (estimates of probabilities that one alternative outranks or does not outrank the other). Furthermore, given the preference relations obtained in result of application of each MC set of rules on a considered set of alternatives, we exploit them using some scoring procedures. From this, we derive the distribution of ranks attained by the alternatives. We also extend the basic approach in several ways. The practical usefulness of the method is demonstrated on a problem of ranking Polish cities according to their innovativeness

Vive la Différence? Structural Diversity as a Challenge for Metanormative Theories

Decision-making under normative uncertainty requires an agent to aggregate the assessments of options given by rival normative theories into a single assessment that tells her what to do in light of her uncertainty. But what if the assessments of rival theories differ not just in their content but in their structure -- e.g., some are merely ordinal while others are cardinal? This paper describes and evaluates three general approaches to this "problem of structural diversity": structural enrichment, structural depletion, and multi-stage aggregation. All three approaches have notable drawbacks, but I tentatively defend multi-stage aggregation as least bad of the three

Редукция многопозиционных задач и гибридизация критериев принятия решений

Проблематика. Оскільки прийняття рішень завжди зачіпає багато підходів й евристик, а також недостатня статистика і хід часу можуть породжувати цілі послідовності задач прийняття рішень, то розглядається задача врахування множинних станів і критеріїв. Мета дослідження. Розробка методу редукції загальної задачі прийняття рішень з множинними станами поряд з урахуванням множинних критеріїв через їх гібридизацію для однозначного розв’язання єдиної задачі прийняття рішень. Методика реалізації. Пропонується алгоритм зведення скінченної множини задач прийняття рішень до єдиної задачі прийняття рішень. Також формалізується гібридизація критеріїв прийняття рішень, яка дає змогу отримати єдину множину оптимальних альтернатив. Результати дослідження. На практиці ця множина містить лише одну альтернативу. Тут, завдяки дії закону великих чисел (множинних критеріїв), чим більше число критеріїв, що залучаються до гібридизації, тим більш надійним, згідно зі сформульованим виразом, виходить рішення. Висновки. Представлені редукція багатопозиційних задач і гібридизація критеріїв прийняття рішень забезпечують для дослідника одну задачу прийняття рішень, число оптимальних розв’язків якої має бути меншим, ніж за будь-якими іншими підходами. Також це дає змогу ранжувати альтернативи з більшими надійністю та достовірністю. Крім того, утворюються надійні ваги (пріоритети) для скаляризації багатокритеріальних задач.Background. Due to that decision making is always involving a great deal of approaches and heuristics, and poor statistics and time course can generate series of decision making problems, the problem of regarding multiple states and criteria is considered. Objective. The goal is to develop an approach for reducing the multiple state decision making problem along with regarding multiple criteria by their hybridization to solve disambiguously a single decision making problem. Methods. An algorithm of reducing a finite series of decision making problems to a single problem is suggested. Also a statement is formulated to hybridize decision making criteria allowing to get a single optimal alternatives’ set. Results. Practically, this set contains just a single alternative. And, owing to the law of large numbers (of multiple criteria), the greater number of criteria is involved into the hybridization, the more reliable decision by the formulated statement is. Conclusions. The represented multiple state problem reduction and decision making criteria hybridization both provide a researcher with the one decision making problem whose number of optimal solutions must be less than that by any other approaches. Besides, it allows to rank alternatives at higher reliability and validity. Furthermore, reliable weights (priorities) for scalarizing multicriteria problems are produced.Проблематика. Поскольку принятие решений всегда затрагивает много подходов и эвристик, а также недостаточная статистика и течение времени могут порождать целые последовательности задач принятия решений, то рассматривается задача учета множественных состояний и критериев. Цель исследования. Разработка метода редукции общей задачи принятия решений с множественными состояниями наряду с учетом множественных критериев путем их гибридизации для однозначного решения единственной задачи принятия решений. Методика реализации. Предлагается алгоритм приведения конечного множества задач принятия решений к единственной задаче принятия решений. Также формализуется гибридизация критериев принятия решений, позволяющая получить единственное множество оптимальных альтернатив. Результаты исследования. На практике это множество содержит всего лишь единственную альтернативу. Здесь, благодаря действию закона больших чисел (множественных критериев), чем больше число критериев, вовлекаемых в гибридизацию, тем более надежным, согласно сформулированному выражению, выходит решение. Выводы. Представленные редукция многопозиционных задач и гибридизация критериев принятия решений обеспечивают для исследователя одну задачу принятия решений, число оптимальных решений которой должно быть меньше, чем согласно любым другим подходам. Также это позволяет ранжировать альтернативы с большими надежностью и достоверностью. Кроме того, создаются надежные веса (приоритеты) для скаляризации многокритериальных задач

Reason-based choice: a bargaining rationale for the attraction and compromise effects

Among the most important and robust violations of rationality are the attraction and the compromise effects. The compromise effect refers to the tendency of individuals to choose an intermediate option in a choice set, while the attraction effect refers to the tendency to choose an option that dominates some other options in the choice set. This paper argues that both effects may result from an individual's attempt to overcome the difficulty of making a choice in the absence of a single criterion for ranking the options. Moreover, we propose to view the resolution of this choice problem as a cooperative solution to an intra-personal bargaining problem among different selves of an individual, where each self represents a different criterion for choosing. We first identify a set of properties that characterize those choice correspondences that coincide with our bargaining solution, for some pair of preference relations. Second, we provide a revealed-preference foundation to our bargaining solution and characterize the extent to which these two preference relations can be uniquely identified. Alternatively, our analysis may be reinterpreted as a study of (inter-personal) bilateral bargaining over a finite set of options. In that case, our results provide a new characterization, as well as testable implications, of an ordinal bargaining solution that has been previously discussed in the literature under the various names of fallback bargaining, unanimity compromise, Rawlsian arbitration rule and Kant-Rawls social compromise.Behavioral economics, attraction and compromise effects, bargaining

Policy-making and policy assessments with partially ordered alternatives

The present work collects three essays on social choice and decision-making in the presence of multiple objectives and severe informational limitations. When feasible alternatives must be ordered according to their performance under various criteria, it is typically necessary to make use of a specific functional relation and assume the implied rates of substitution between scores in different criteria. In the special case of collective choice and voting, rather than having proper rates of substitution, each individually preferred ordering of the alternatives is usually weighted according to its frequency in the population. Both decision frameworks imply the availability of extensive information about such functional relation and the proper weights of each criterion or must acknowledge a vast and arbitrary discretion to those in charge of resolving the decision process. The alternative approach herein discussed consists in applying the Pareto criterion to identify Pareto-superior alternatives in each pairwise comparison, a procedure that easily produces an incomplete ordering. Then, applying a tool of Order Theory, a complete ordering is identified from the linear extensions of the partially ordered set derived from the Pareto criterion. The claim is that this method highlights conflicts in value judgements and in incomparable criteria, allowing to search for a conflict-mitigating solution that doesn\u2019t make assumptions on the reciprocal importance of criteria or judgements. The method is actually a combination of existing but unrelated approaches in Social Choice Theory and in Order Theory and provides outcomes with interesting properties. The essays present, respectively, an axiomatic discussion of the properties of this approach and two applications to policy issues

Co-constructive development of a green chemistry-based model for the assessment of nanoparticles synthesis

Nanomaterials (materials at the nanoscale, 10−9m) are extensively used in several industry sectors due to the improved properties they empower commercial products with. There is a pressing need to produce these materials more sustainably. This paper proposes a Multiple Criteria Decision Aiding (MCDA) approach to assess the implementation of green chemistry principles as applied to the protocols for nanoparticles synthesis. In the presence of multiple green and environmentally oriented criteria, decision aiding is performed with a synergy of ordinal regression methods; preference information in the form of desired assignment for a subset of reference protocols is accepted. The classification models, indirectly derived from such information, are composed of an additive value function and a vector of thresholds separating the pre-defined and ordered classes. The method delivers a single representative model that is used to assess the relative importance of the criteria, identify the possible gains with improvement of the protocol’s evaluations and classify the non-reference protocols. Such precise recommendation is validated against the outcomes of robustness analysis exploiting the sets of all classification models compatible with all maximal subsets of consistent assignment examples. The introduced approach is used with real-world data concerning silver nanoparticles. It is proven to effectively resolve inconsistency in the assignment examples, tolerate ordinal and cardinal measurement scales, differentiate between inter- and intra-criteria attractiveness and deliver easily interpretable scores and class assignments. This work thoroughly discusses the learning insights that MCDA provided during the co-constructive development of the classification model, distinguishing between problem structuring, preference elicitation, learning, modeling and problem-solving stages

Impact Assessment of Qualitative Policy Scenarios; A Comparative Case Study on Land Use in Sicily

The purpose of this paper is to offer a contribution to the study of integrated assessment procedures for evaluating the effectiveness of agri-environmental policy strategies. While in the past the studies in this context have typically concentrated on the contents of methods in isolation, there is a growing trend towards methodological perspectives that support the linking of such methods. The focus here is on the combination of discrete multicriteria approaches used for handling qualitative information in a sequence of steps: the regime method, the evamix method and rough-set analysis. The first two methods will be used to obtain a ranking of four alternative scenarios of agri-environmental policies in a selected area of study, in this case, Sicily. The results obtained are discussed and re-analysed by using the rough-set approach as a recent meta-analytical tool. Finally, the analysis findings are applied to an investigation into the potential effectiveness of agricultural policies in promoting sustainable rural development in Sicily. © 2003, MCB UP Limite