International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

Let and be, respectively, the classes of all copulas and quasi-copulas whose diagonal section is δ. We determine under which conditions on δ we have: (a) both and consist of a singleton; (b) . Moreover, a simple construction of copulas with a given convex diagonal section is introduced.

We introduce the syntax, semantics, and an axiom system for a PDL-based extension of the logic for order of magnitude qualitative reasoning, developed in order to deal with the concept of qualitative velocity, which together with qualitative distance and orientation, are important notions in order to represent spatial reasoning for moving objects, such as robots. The main advantages of using a PDL-based approach are, on the one hand, all the well-known advantages of using logic in AI, and, on the other hand, the possibility of constructing complex relations from simpler ones, the flexibility for using different levels of granularity, its possible extension by adding other spatial components, and the use of a language close to programming languages.

In data mining problems, data is usually provided in the form of data tables. To represent knowledge discovered from data tables, a decision logic (DL) is proposed in rough set theory. DL is an instance of propositional logic, but we can use other logical formalisms to describe data tables. In this paper, we propose two descriptions of data tables based on first-order data logic (FODL) and attribute value-sorted logic (AVSL) respectively. In the context of FODL, we show that explicit definability and implicit definability in classical logic implies the notion of definability in rough set theory. We also show that AVSL is particularly useful for the representation of properties of many-valued data tables.

In this paper, we study a concept of solution for a bargaining problem involving two players and unknown parameters in the case of complete ignorance. The solution we propose is based on the Nash solution for a bargaining problem and the maxmin principle of Wald. We also give some properties of this solution and sufficient conditions for its existence. Finally, we propose an adequate procedure for its determination and an illustrative example.

In this paper we introduce the concept of Generalized Atanassov's Intuitionistic Fuzzy Index. We characterize it in terms of fuzzy implication operators and propose a construction method with order automorphisms. Finally, we obtain, by means of special aggregation functions applied to the generalized Atanassov's intuitionistic fuzzy index, the Atanassov's intuitionistic fuzzy entropy given by Burillo and Bustince.

In particular, imprecise observations or possible perturbations mean that data in a network flows may well be better represented by intervals or fuzzy numbers than crisp quantities. In this paper we first consider the minimum cost flow problem with compact interval-valued lower and upper bounds, flows, and costs. We present a new method that shows this problem is solved using two minimum cost flow problems with crisp data. Then this result is extended to networks with fuzzy lower and upper bounds, flows, and costs. One of the best algorithms to solve the minimum cost flow problem with crisp data is the cost scaling algorithm of Goldberg and Tarjan.¹⁷ In this paper, the cost scaling algorithm is modified for fuzzy lower and upper bounds, flows and costs. The running time of the modified algorithm is equal to the running time of the cost scaling algorithm with crisp data.

We analyze various models introduced in social choice to aggregate individual preferences. We show that on the basis of most of these models there is a system of functional equations such that, in many cases, the origin of impossibility results in a social choice model is the non-existence of a solution for the corresponding system. Among the functional equations considered, we pay a particular attention to general means and associativity, proving that the existence of an associative bivariate mean is equivalent to the existence of a semilatticial partial order. This key result allows us to explain how the knowledge of associative bivariate means can be used to solve social choice paradoxes. In our analysis we deal both with crisp and fuzzy settings.

This paper presents a method for ranking a set of decision making units according to their level of efficiency and which takes into account uncertainty in the data. Efficiency is analysed using fuzzy DEA techniques and the ranking is based on the statistical analysis of cases that include representative situations. The method enables the removal of the sometimes unrealistic hypothesis of a perfect trade-off between increased inputs and outputs. This model is compared with other DEA models that work with imprecise or fuzzy data. As an illustration, we apply our ranking method to the evaluation of a group of Spanish seaports, as well as teams playing in the Spanish football league. We compare the results with other methods and we show that our method enables a total ranking of the seaports, and that the ranking of football teams is found to be more consistent with final league positions.

This paper introduces and studies a class of cooperative interval games suitable to model market situations with two corners where players face interval uncertainty regarding the outcome of cooperation. In one corner there is a powerful player called the big boss; the other corner contains players that need the big boss to benefit from cooperation. Various characterizations of big boss interval games are given. The interval core of a big boss interval game is explicitly described, bi-monotonic allocation schemes using interval core elements are introduced, and it is shown that each element of the interval core of a big boss interval game is extendable to such a scheme. Two value-type interval solution concepts are defined on the class of big boss interval games which generate for each such game the same interval core allocation which is extendable to a bi-monotonic interval allocation scheme.

Please send your abstracts (or copies of papers that you want to see reviewed here) to vladik@utep.edu, or by regular mail to Vladik Kreinovich, Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA.