International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

A major purpose of this paper is to show the broad import and applicability of the theory of probability as proposed by de Finetti, which differs radically from the usual one (based on a measure-theoretic framework). In particular, with reference to a coherent conditional probability, we prove a characterization theorem, which provides also a useful algorithm for checking coherence of a given assessment. Moreover it allows to deepen and generalise in useful directions de Finetti’s extension theorem (dubbed as “the fundamental theorem of probability”), emphasising its operational aspects in many significant applications.

When using a t-norm for combining fuzzy sets, no compensation between small and large degrees of membership takes place. On the other hand, a t-conorm provides full compensation. Since many real situations do not fall into either one category, so-called compensatory operators have been proposed in the literature [H.-J. Zimmermann and P. Zysno, Fuzzy Sets and Systems4 (1980) 37–51] which are non-associative in nature. In this paper, associative compensatory operators (whose domain is the unit square with the exception of the two points (0, 1) and (1, 0) and whose only associative extensions to the whole unit square are the aggregative operators suggested in [J. Dombi, Europ. J. Oper. Res.10 (1982) 282–293]) are studied and their representation in terms of multiplicative generators is given. It is shown that these operators are constructed with the help of strict t-norms and t-conorms, in a way which is similar to ordinal sums. Finally, the duals of such operators are shown to be again associative compensatory operators, and a characterization of self-dual operators is given.

Some procedures for synthesizing values of judgements in multicriteria decision making have been provided by several authors. The functionals of synthesis they consider are frequently means. The most general form of these operators involves both a weighting function w and a continuous and strictly monotonic function φ. Our aim is to analyze the behaviour of the aggregation operator F_ωφ depending on w and φ. To this purpose we introduce a pre-ordering relation on the set W of weighting functions and on the set Φ of continuous and strictly monotonic functions, which allows us to compare the synthesizing functionals.

The well-founded model is one of the most popular models of general logic programs, i.e. logic programs with negation in the bodies of clauses. We present a method for constructing this model for general deductive databases, which are logic programs without any function symbols. The method adopts paraconsistent relations as the semantic objects associated with the predicate symbols of the database. Paraconsistent relations are a generalization of ordinary relations in that they allow manipulation of incomplete as well as inconsistent information. The first step in the model construction method is to transform the database clauses into paraconsistent relation definitions involving these operators. The second step is to build the well-founded model iteratively. Algorithms for both steps are presented and their termination and correctness is also established.

This work is concerned with the problem of representing and handling disjunctive and missing information in the framework of logic fuzzy databases. We use the general term of incomplete information to refer both disjunctive or missing information. To pose the problem, we firstly give a brief summary about the underlying Logic Fuzzy Database Model. Starting from the concept of logic fuzzy database, which is a general fuzzy database that can be represented in a logic framework, we see how disjunctive and missing information can be represented and handled.