International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

Relationships between risk measures and imprecise probability theory have received relatively limited attention in the literature. This paper contributes to filling this gap as far as Dutch risk measures are concerned. Using imprecise previsions as a starting point, a novel generalized family of Dutch risk measures is introduced, its properties with respect to several alternative consistency notions are analyzed and its advantageous features discussed. Any such measure corresponds to an imprecise prevision correcting a first-approach uncertainty measure, while preserving its consistency properties in several cases, ranging from coherence to a weak generalization of the concept of capacity. Further, it is shown that the proposed family of measures has a practical significance in the application context of insurance pricing, since, unlike the original formulation, it may ensure a risk loading to each risk taker and is even compatible with the practice of double loading in premium policies.

The intuitionistic fuzzy set (IFS) characterized by a membership function and a non-membership function, was introduced by [K. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems20 (1986) 87–96] as a generalization of Zadeh' fuzzy set [L. A. Zadeh, "Fuzzy sets", Information and Control8 (1965) 338–356] to deal with fuzziness and uncertainty. In this paper, the dynamic multiple attribute decision making (DMADM) problems with intuitionistic fuzzy information are investigated. The notions of intuitionistic fuzzy variable and uncertain intuitionistic fuzzy variable are defined, and two new aggregation operators called dynamic intuitionistic fuzzy weighted geometric (DIFWG) operator and uncertain dynamic intuitionistic fuzzy weighted geometric (UDIFWG) operator are proposed. Moreover, a procedure based on the DIFWG and IFWG operators is developed to solve the dynamic intuitionistic fuzzy multiple attribute decision making problems where all the decision information about attribute values takes the form of intuitionistic fuzzy numbers collected at different periods, and a procedure based on the UDIFWG and IIWG operators is developed for uncertain dynamic intuitionistic fuzzy multiple attribute decision making problems under interval uncertainty in which all the decision information about attribute values takes the form of interval-valued intuitionistic fuzzy numbers collected at different periods. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Given a binary relation defined on a set, we study its representability by means of a monotonic function that takes values on a suitable universal codomain (that depends on the kind of relation considered). We pay an special attention to the representability of interval orders, studying their alternative universal codomains, some of them equivalent to the set of symmetric triangular fuzzy numbers.

The Cauchy equation for automorphisms of the unit interval is fulfilled only by the identity mapping. We consider two weakened forms of this Cauchy equation: the reciprocity equation and the n-divisibility equation. Although the solution sets of both functional equations are quite large, requiring that an automorphism is both reciprocal and n-divisible, drastically increases the set of obligatory fixed points. However, increasing n also enlarges the domain on which the automorphism can be chosen freely. We also describe the solution sets of two functional equations that arise by composing the reciprocity and n-divisibility property.

How to make a prompt decision for uncertainty investment is always a key problem in financial market. In this paper, we present a new dynamic portfolio selection strategy in stock market. The investor is assumed to seek an investment strategy that will maximize his/her final wealth and minimize the total risk. An analytically optimal strategy in closed form is obtained by solving a dynamic programming problem. Some applications are also presented to illustrate this model.

In this paper, we propose an uncertain linguistic hybrid geometric mean (ULHGM) operator, which is based on the uncertain linguistic weighted geometric mean (ULWGM) operator and the uncertain linguistic ordered weighted geometric (ULOWG) operator proposed by Xu [Z. S. Xu, "An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations", Decision Support Systems41 (2006) 488–499] and study some desirable properties of the ULHGM operator. We have proved both ULWGM and ULOWG operators are the special case of the ULHGM operator. The ULHGM operator generalizes both the ULWGM and ULOWG operators, and reflects the importance degrees of both the given arguments and their ordered positions. Based on the ULWGM and ULHGM operators, we propose a practical method for multiple attribute group decision making with uncertain linguistic preference relations. Finally, an illustrative example demonstrates the practicality and effectiveness of the proposed method.

In this paper we show an approximation for , where u is a fuzzy interval and is obtained from a continuous function f applying the Zadeh's extension principle. In this process, we used a decomposition for u and the linear spline function for the approximation of f. A bound for the error in the approximation is given. Also, some examples are presented.

Bayesian networks have been known as a powerful knowledge representation model and a computational architecture for reasoning under uncertainty. However, there are still some obstacles in applying them for practical applications. Among them are learning parameters, or the conditional probability tables from data. Much work in the field focuses on handling incomplete data, i.e. data with missing values. In this paper, we propose an approach for learning parameters of Bayesian networks from soft data, the values of which may be imprecise or uncertain, given by beliefs or confidence scales. Theoretical justification of the approach is given, and experimental results demonstrated the effectiveness of our approach.

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