International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

Possibility measures and credibility measures are widely used in fuzzy set theory. Compared with possibility measures, the advantage of credibility measures is the self-duality property. This paper gives a relation between possibility measures and credibility measures, and proves a sufficient and necessary condition for credibility measures. Finally, the credibility extension theorem is shown.

Starting from the definitions of the weak fuzzy subsethood measure (V.R. Young, Fuzzy subsethood. Fuzzy Sets and Systems, 77 (1996) 371–384) and of strong fuzzy inclusion, (D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications, New York, Academic Press, 1980) we define weak fuzzy S-subsethood measures. We analyze their axiomatization and present various constructions obtained by aggregating implication operators with special properties. We conclude by presenting the conditions under which we can construct fuzzy entropies and overlap indices from these measures.

Fuzzy arithmetic provides a powerful tool to introduce uncertainty into mathematical models. With Zadeh's extension principle, one can obtain a fuzzy-valued extension of any real-valued objective function. An efficient and accurate approach to computing expensive multivariate functions of fuzzy numbers is given by fuzzy arithmetic based on sparse grids. In many cases, not all uncertain input parameters carry equal weight, or the objective model exhibits separable structure. These characteristics can be exploited by dimension-adaptive algorithms. As a result, the treatment of even higher-dimensional problems becomes possible. This is demonstrated in this paper by a case study involving two large-scale finite element models in vibration engineering that are subjected to fuzzy-valued input data.

Some theorems concerning representation of fuzzy measure and the Choquet integral are shown independently by Murofushi and Sugeno (J. Math. Anal. Appl. 159, No 2, (1991), 532-549) and by Denneberg (Fuzzy sets and Systems, 92, (1997), 139-156). Using the mediator for representations, it is shown that the theorems are partially equivalent. The difference between them are also stated with some examples.

In this paper, we first introduce a network of learning automata, which we call it as distributed learning automata and then propose some iterative algorithms for solving stochastic shortest path problem. These algorithms use distributed learning automata to find a policy that determines a path from a source node to a destination node with minimal expected cost (length). In these algorithms, at each stage distributed learning automata determines which edges to be sampled. This sampling method may result in decreasing unnecessary samples and hence decreasing the running time of algorithms. It is shown that the shortest path is found with a probability as close as to unity by proper choice of the parameters of the proposed algorithms.

In this paper, two new fuzzy clustering algorithms are proposed based on the global optimization metaheuristic, Threshold Accepting. Their effectiveness is demonstrated in the case of five well-known medium sized data sets viz. Iris, Wine, Glass, E.Coli and Olive oil and a large data set Thyroid. In terms of the least objective functions value, these algorithms named TAFC-1 (Threshold Accepting based Fuzzy Clustering) and TAFC-2 outperformed the well-known Fuzzy C-Means (FCM) algorithm in the case of 4 data sets and in the remaining two data sets, FCM marginally outperformed the TAFC. Xie-Beni cluster validity index is used in arriving at the 'optimal' number of clusters for all the algorithms. Here a novel strategy is proposed whereby the FCM is invoked to find alternative decision vectors whenever the neighbourhood search fails in its pursuit. This hybrid scheme has worked well. In conclusion, these new algorithms can be used as viable and efficient alternatives to the FCM algorithm.

In this note we provide a proof for the existence theorem of possibility space for uncountable case and verify Cai's conjecture in 1996 [1]. The proof paves the way to link possibility space or possibilistic variable to the fuzzy set theory.

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.