International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

In this paper we study some properties of the polytope of belief functions on a finite referential. These properties can be used in the problem of identification of a belief function from sample data. More concretely, we study the set of isometries, the set of invariant measures and the adjacency structure. From these results, we prove that the polytope of belief functions is not an order polytope if the referential has more than two elements. Similar results are obtained for plausibility functions.

Both the weighted entropy, which generalizes the Shannon entropy, and the weighted quadratic index, which generalizes the Gini-Simpson index, are used for getting a unified treatment of some diversity measures proposed recently in ecology. The weights may reflect the ecological importance, rarity, or economic value of the species from a given habitat. The weighted measures, being concave functions, may be used in the additive partition of diversity. The weighted quadratic index has a special advantage over the weighted entropy because its maximum value has a simple analytical formula which allows us to introduce a normed measure of dissimilarity between habitats. A special case of weighted quadratic index is the Rich-Gini-Simpson index which, unlike the Shannon entropy and the classic Gini-Simpson index, behaves well when the number of species is very large. The weighted entropy and the weighted quadratic index may also be used to measure the global diversity among the subsets of species. In this context, Rao's quadratic index of diversity between the pairs of species, based on the phylogenetic distance between species, is obtained as a particular case and is generalized to measure the diversity among the triads of species as well.

A weakly connected dominating set (WCDS) of graph G is a subset of G so that the vertex set of the given subset and all vertices with at least one endpoint in the subset induce a connected sub-graph of G. The minimum WCDS (MWCDS) problem is known to be NP-hard, and several approximation algorithms have been proposed for solving MWCDS in deterministic graphs. However, to the best of our knowledge no work has been done on finding the WCDS in stochastic graphs. In this paper, a definition of the MWCDS problem in a stochastic graph is first presented and then several learning automata-based algorithms are proposed for solving the stochastic MWCDS problem where the probability distribution function of the weight associated with the graph vertices is unknown. The proposed algorithms significantly reduce the number of samples needs to be taken from the vertices of the stochastic graph. It is shown that by a proper choice of the parameters of the proposed algorithms, the probability of finding the MWCDS is as close to unity as possible. Experimental results show the major superiority of the proposed algorithms over the standard sampling method in terms of the sampling rate.

Owing to the fluctuations in the financial markets, many financial variables such as expected return, volatility, or exchange rate may occur imprecisely. But many portfolio selection models consider precise input of these values. Therefore, this paper studies a multiobjective international asset allocation problem under fuzzy environment. In our portfolio selection model, both of the return risk and the exchange risk are considered. The coefficient matrices in the objectives and constraints and the decision value are considered as fuzzy variables. The calculation of the portfolio and efficient frontier is derived by considering the exchange risk in the fuzzy environment. An empirical study is performed based on a portfolio of six securities denominated in six different currencies, i.e., USD, EUR, JPY, CNY, HKD, and GBP. The α-level closed interval portfolio and the fuzzy efficient frontier are obtained with different values of α ∈ (0, 1]. The empirical results indicate that the fuzzy asset selection method is a useful tool for dealing with the imprecise problem in the real world.

In this paper, we propose a new mathematical model to analyze bimatrix goal game under entropy environment. This new approach incorporates the entropy function of the players as an objective to the bimatrix game. The solution concepts behind this game are based on getting the probability to achieve some specified goals. We consider the solution, not only by the payoff values, but also by the probability to get them. Numerical examples are presented to illustrate the methodology in the paper.

The aim of this paper is to develop a new methodology for solving group decision making problems in which preference comparisons between alternatives are expressed with Atanassov's intuitionistic fuzzy (IF) preference relations. In this methodology, the generalized ordered weighted averaging (GOWA) operator is extended to develop the Atanassov's IF set (IFS) generalized ordered weighted averaging (IFSGOWA) operator, which can aggregate vague or imprecise information expressed with the Atanassov's IFSs. The Atanassov's IFSGOWA operator based methodology is further developed to solve group decision making problems with Atanassov's IF preference relations. A real example of the agroecological region assessment problem is used to illustrate the implementation and applicability of the proposed methodology. It is also shown that the obtained decision results could be affected by the choice of the parameter lambda and the nature of the weights.

In this paper a two level supply chain system is studied, in which the final demand is assumed to be fuzzy with triangular membership function. The inventory control policy of (r, Q) is followed for this system and unsatisfied demand is assumed to be back ordered. The objective is to minimize the total cost of the system, including ordering, holding and shortage costs. The model happens to be a nonlinear programming. Considering the complexity arising from the model, we also develop a genetic algorithm to obtain a near-optimal solution. The method is illustrated through some numerical examples.

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: Vladik Kreinovich Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA.