International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

Comonotone maxitivity and minitivity of Sugeno integral can be seen as commuting of the Sugeno integral and max, resp. min operator for comonotone functions. In the paper, we look for the other operators commuting with the Sugeno integral when comonotone functions are considered. We give full description of all such commuting operators, which can be classified into 18 classes.

In this paper, we study opposite diagonal sections of quasi-copulas and copulas. The best-possible upper bound for the set of copulas with a given opposite diagonal section being known, we focus on the best-possible lower bound, which in general is a quasi-copula. Moreover, it exhibits an interesting type of bivariate symmetry called opposite symmetry.

The subject of the paper is related with the decision making problems with several objectives and a committee of experts. Models for aggregating opinions of experts and consensus reaching on the alternatives with respect to different objectives are presented. A modeling in a metric space is studied and a game theoretic interpretation is introduced. In this framework a procedure for monitoring and enhancing consensus is considered.

Classical ontologies are not suitable to represent imprecise nor uncertain pieces of information. Fuzzy Description Logics were born to represent the former type of knowledge, but they require an appropriate fuzzy language to be agreed on and an important number of available resources to be adapted. This paper faces these problems by presenting a reasoning preserving procedure to obtain a crisp representation for a fuzzy extension of the logic which includes fuzzy nominals and trapezoidal membership functions, and uses Gödel implication in the semantics of fuzzy concept and role subsumption. This reduction makes it possible to reuse a crisp representation language as well as currently available reasoners. Our procedure is optimized with respect to related work, reducing the size of the resulting knowledge base. Finally, we also suggest some further optimizations before applying crisp reasoning.

Ease of Doing Business (EDB) indicators are essential to overall understanding and evaluation of national business environment, and strategy formulation for business policy and regulations. The World Bank does an annual study of these indicators for over 170 nations, but there are many complications and uncertainties involved in the work. This paper proposes a new systematic approach that employs fuzzy set theory to generate composite EDB indicators for ranking and classification problems. We implemented this approach and illustrate its steps and procedures. A case study example for Canada is also presented in which EDB indicators are evaluated, linguistically identified, and ranked. This approach demonstrates the ease of using this fuzzy application, and its potential benefits for future research. We also compare ranking results, obtained from our proposed approach, with the World Bank's results.

The flow shop scheduling problems with fuzzy processing times are investigated in this paper. For some special kinds of fuzzy numbers, the analytic formulas of the fuzzy compltion time can be obtained. For the general bell-shaped fuzzy numbers, we present a computational procedure to obtain the approximated membership function of the fuzzy completion time. We define a defuzzification function to rank the fuzzy numbers. Under this ranking concept among fuzzy numbers, we plan to minimize the fuzzy makespan and total weighted fuzzy completion time. Because the ant colony algorithm has been successfully used to solve the scheduling problems with real-valued processing times, we shall also apply the ant colony algorithm to search for the best schedules when the processing times are assumed as fuzzy numbers. Numerical examples are also provided and solved by using the commercial software MATLAB.

The intuitionistic fuzzy set (IFS) introduced by Atanassov in 1986 is characterized by two functions and has rarely been applied to the game theory yet. The aim of this paper is to develop the concept and methodology of matrix games with payoffs of Atanassov's IFSs. In this methodology, the concepts of the solutions for matrix games with payoffs of Atanassov's IFSs are defined based on the degree of membership and the degree of non-membership. It is proven that matrix games with payoffs of Atanassov's IFSs have solutions, which can be obtained through solving a pair of nonlinear programming models derived from two auxiliary nonlinear bi-objective programming models. The proposed method is illustrated with a numerical example.

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