A fuzzy controller can be seen as an algorithm that, given a fuzzy set (input) and a set of linguistic rules, computes the degree of possibility of every control value. Using a valid and complete proof system for possibilistic logic, we will prove that fuzzy controllers enjoy the following property: every possibility measure that satisfies the degrees of possibility of the input and of the ling...

We reformulate Mesiar’s hypothesis [Possibility measures, integration and fuzzy possibility measures, Fuzzy Sets and Systems 92 (1997) 191196], which as such was shown to be untrue by Murofushi [Two-valued possibility measures induced by σ-finite σ-additive measures, Fuzzy Sets and Systems 126 (2002) 265268]. We prove that a two-valued σ-maxitive measure can be induced by a σ-additive measure u...

A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The proposed semantics is based on fuzzy sets of interpretations. It is tolerant to partial inconsistency. Satisfiability is extended from interpretations to fuzz...

Justification logic originated from the study of the logic of proofs. However, in a more general setting, it may be regarded as a kind of explicit epistemic logic. In such logic, the reasons why a fact is believed are explicitly represented as justification terms. Traditionally, the modeling of uncertain beliefs is crucially important for epistemic reasoning. While graded modal logics interpret...

Subjective uncertainty is one of the most essential subjects for evaluation that was the reason Fuzzy theory was proposed. Related research areas are widely spread such as decision making, data analysis, information retrieval, psychology, and human computer interaction and so on. As a basis for various researches mathematical interpretation of evaluation methods occupies an important position. ...

Latest scientific and engineering advances have started to recognize the need of defining multiple types of uncertainty. Probabilistic modeling cannot handle situations with incomplete or little information on which to evaluate a probability, or when that information is nonspecific, ambiguous, or conflicting [1]. Many generalized models of uncertainty have been developed to treat such situation...

Clouds are a concept for uncertainty mediating between the concept of a fuzzy set and that of a probability distribution. A cloud is to a random variable more or less what an interval is to a number. We discuss the basic theoretical and numerical properties of clouds, and relate them to histograms, cumulative distribution functions, and likelihood ratios. We show how to compute nonlinear transf...

In this paper, we study the notion of an ample or complete field, a special case of the well-known fields and σ-fields of sets. These collections of sets serve as candidates for the domains of possibility and necessity measures, and are therefore important for the further development of a general fuzzy set and possibility theory. The existence of a one-one relationship between ample fields and ...

This article deals with a method to describe and manage spatial knowledge. Each georeferenced data is considered as an information source, whose location and value are independently described. The method proposed in this paper uses the information sources to infer the value of any request zone . This method is able to treat imprecise or uncertain, qualitative and quantitative data. It can be ap...

The setting of formal concept analysis presupposes the existence of a relation between objects and properties. Knowing that an unspecified object has a given property induces a formal possibility distribution that models the set of objects known to possess this property. This view expressed in a recent work by the authors of the present paper, has led to introduce the set-valued counterpart to ...