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In almost every work on fuzzy sets, the existence of membership functions taking part in the considered model is assumed and it is not studied in depth whether or not such functions exist. On the other hand, generally the relationship between a certain studied characteristic and its referential set is not problematic since it is usually a matter of direct measurement. However, in a great variety of situations it is necessary to work with properties whose measurement is not obvious, but is an object of study in itself. In this work, we start by approaching the description of the cases in which the existence of a membership function can be guaranteed. Next, we consider the situations where one faces linguistic terms associated with attributes that cannot be directly measured; in such cases, the existence of a membership function cannot be assured. However, the conditions of existence and methods for the construction of those membership functions may be based on the psychological measurement theory.

Comparison tools for fuzzy sets are an indispensable topic. Mostly of this tools deal with fuzzy sets from the view of similarity, order and so forth. A comparison tool based on coherence intuitive concept is presented. For constructing this concept, one start from three basics properties. A development of this tool is presented, equally coherence measures are connected with Fishburn-Yager's ambiguity measures. Two methods for constructing coherence measures are shown: one from ambiguity measures and other from metrics on [0,1 ] m . Concretely, has been constructed various coherence measures from different ambiguity measures and different metrics. Equivalency between some coherence measures has been shown. This paper finish with numeric examples presented in order to check coherence measures displayed.

Biological entities (ranging from bacteria to humans) can engage in many and varied types of social interaction, from altruistic cooperation to open conflict. A paradigmatic case of social interaction is cooperative problem solving (CPS), where a group of autonomous entities work together to achieve a common goal. For example, we might find a group of people working together to move a heavy object, play a symphony, choose a business strategy, or write a joint paper. CPS has been studied by researchers from a variety of areas such as distributed A. I., soft computing, economics, philosophy, organization science, and the social and natural sciences among others.