Decision analysis, the mechanism by which a final decision is reached in terms of choice (choosing an alternative or a subset of alternatives from a large set of alternatives), ranking (ranking alternatives of a set from the worst to the best), classification (assigning alternatives to some known classes or categories), or sorting (clustering alternatives to form homogeneous classes or categories) is certainly the most pervasive human activity. Some decisions are made routinely and do not need sophisticated algorithms to support decision analysis process whereas other decisions need more or less complex processes to reach a final decision. Methods and models developed to solve decision analysis problems are in constant evolution going from mechanist models of operational research to more sophisticated and soft computing-oriented models that attempt to integrate human attitude (emotion, affect, fear, egoism, altruism, selfishness, etc.). This complex, soft computing and near human mechanism of problem solving is rendered possible thanks to the overwhelming computational power and data storage possibility of modern computers. The purpose of this chapter is to present new and recent developments in decision analysis that attempt to integrate human judgment through bipolarity notion.
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Decision making is certainly the most pervasive human activity; indeed we spend a great proportion of our working day, hour, minute and even second, making decisions. Some decisions are made routinely and do not need models to support them whereas other decisions are so complex or important that sound decision support models are needed in order to avoid failure that may lead to very damageable or catastrophic consequences. These complex decisions share some features such as: multiplicity of objectives, multiplicity of attributes or criteria that characterize alternatives, uncertainty, multiplicity of actors, and so on. For these decision situations there is a need to have procedures or models that permit to capture all interactions and relationships between different elements of decision making process in order to reach an effective and efficient decision. Thus, a decision analysis problem is structured around the following important elements: decision makers, players, actors or stakeholders that are entities (persons, group of persons, organizations, etc.) that do have some interest or are engaged in decision analysis process; objectives (an objective in a decision analysis problem is something a decision maker cares about, wants to achieve, wants to optimize, wants to reach, etc.); alternatives (an alternative is a possibility opened to a decision maker that may permit him or her to realize his objectives); attributes or criteria (an attribute is a feature of an alternative that is used by a decision maker to evaluate this alternative with regard to pursued objectives).
The existence of many decision makers necessitate to have a coordination mechanism; the coordination scheme depends on the nature of the problem to solve and mainly the structure of alternatives: does each decision maker have his/her own decision alternatives set or all decision makers have to express their preferences over a common alternatives set ? The case where all decision makers have to pronounce themselves on a same set of alternatives is known in the literature as social choice or collective decision problems, see for instance Arrow (1951), whereas the case where each decision maker dispose of his/her own decisions set is referred to as game theory problems (von Neumann and Morgenstern, 1964). These two problems are considered in this chapter. Formerly these problems are presented in the following definition.
Definition 1: A collective decision problem is a decision problem where a certain number (possibly reduced to one) of agents, stakeholders or decision makers must select, rank, classify, or sort alternatives from a large set or universe
of alternatives in order to satisfy some collective and/or individual objectives. The choice problem is the main concern of this chapter.
A game problem is a decision problem where a certain number of agents, stakeholders, decision makers or players, each one having his/her own decision set 
where ni is the number of alternative decisions for player i and where the outcome (impact on one’s objectives) of a given player decision is conditioned by other players decisions.