International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

The paper focuses on the study of the contradiction between two Atanassov's intuitionistic fuzzy sets. First, taking into account some characterizations obtained in previous papers, some functions are defined in order to measure the degrees of contradiction. Besides the principal properties of these measures are pointed out. Finally, some results relating self-contradiction and contradiction between two Atanassov's intuitionistic fuzzy sets are achieved.

Since many complex decision making problems can be solved solely by means of an appropriate algorithm, checking the quality of such algorithm is a key issue, even more relevant in the presence of fuzzy uncertainty. In this paper we postulate that the design and formal specification of algorithms can be translated into a fuzzy framework introducing fuzzy first order logic and assert transformations. Following the classical crisp scheme we first formalize the concepts of a fuzzy algorithm specification and a fuzzy computing state, and then a new fuzzy computational logic is presented, so we can derive a computational reasoning for correctness of algorithms. A proposal for the evaluation and setting of suitable degrees of truth to computing states is also introduced.

Evidence theory has been acknowledged as an important approach to dealing with uncertain, incomplete and imperfect information. In this framework, different formal techniques have been developed in order to address information aggregation and conflict handling. The variety of proposed models clearly demonstrates the range of possible underlying assumptions in combination rules. In this paper we present a review of some of the most important methods of combination and conflict handling in order to introduce a more generic rule for aggregation of uncertain evidence. We claim that the models based on mass multiplication can address the problem domains where randomness and stochastic independence is the dominant characteristic of information sources, although these assumptions are not always adhered to many practical cases. The proposed combination rule here is not only capable of retrieving other classical models, but also enables us to define new families of aggregation rules with more flexibility on dependency and normalization assumptions.

The purpose of the paper is to study how to solve a type of matrix games with payoffs of triangular fuzzy numbers. In this paper, the value of a matrix game with payoffs of triangular fuzzy numbers has been considered as a variable of the triangular fuzzy number. First, based on two auxiliary linear programming models of a classical matrix game and the operations of triangular fuzzy numbers, fuzzy optimization problems are established for two players. Then, based on the order relation of triangular fuzzy numbers the fuzzy optimization problems for players are decomposed into three-objective linear programming models. Finally, using the lexicographic method maximin and minimax strategies for players and the fuzzy value of the matrix game with payoffs of triangular fuzzy numbers can be obtained through solving two corresponding auxiliary linear programming problems, which are easily computed using the existing Simplex method for the linear programming problem. It has been shown that the models proposed in this paper extend the classical matrix game models. A numerical example is provided to illustrate the methodology.

In this paper, we introduce a new method for packet transmission delay analysis and prediction in mobile ad hoc networks. We apply a fuzzy logic system (FLS) to coordinate physical layer and data link layer. We demonstrate that type-2 fuzzy membership function (MF), i.e., the Gaussian MFs with uncertain variance is most appropriate to model BER and MAC layer service time. Two FLSs and one neural network: a singleton type-1 FLS, an interval type-2 FLS and back-prop neural network (NN) are designed to predict the packet transmission delay based on the BER and MAC layer service time. Simulation results show that the interval type-2 FLS performs much better than the type-1 FLS in transmission delay prediction. And FLSs performs better than back-prop NN. We use the forecasted transmission delay to adjust the transmission power, and it shows that the interval type-2 FLS performs much better than a type-1 FLS, and FLSs are performs better than back-prop NN in terms of energy consumption, average delay and throughput. Besides, we obtain the performance bound based on the actual transmission delay.

The scheduling problems with fuzzy processing times and fuzzy due dates are investigated in this paper. The concepts of earliness and tardiness are interpreted by using the concepts of possibility and necessity measures that were developed in fuzzy sets theory. Many types of objective function will be taken into account through the different combinations of possibility and necessity measures. The purpose of this paper is to obtain the optimal schedules based on these objective functions. The genetic algorithm will be invoked to tackle these objective functions. Four numerical examples are also provided and solved by using the commercial software MATLAB.

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.