Essentials of fuzzy modeling and control
Essentials of fuzzy modeling and control
Scheduling as a fuzzy multiple criteria optimization problem
Fuzzy Sets and Systems - Special issue on fuzzy multiple criteria decision making
Representation and application of fuzzy numbers
Fuzzy Sets and Systems - Special issue: fuzzy arithmetic
Reasonable properties for the ordering of fuzzy quantities (II)
Fuzzy Sets and Systems
Ranking fuzzy numbers using ω-weighted valuations
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
A context-dependent method for ordering fuzzy numbers using probabilites
Information Sciences—Informatics and Computer Science: An International Journal
Fuzzy scheduling with application to real-time systems
Fuzzy Sets and Systems
A Constructive Numerical Method for the Comparison of Intervals
PPAM '01 Proceedings of the th International Conference on Parallel Processing and Applied Mathematics-Revised Papers
Jobshop scheduling with imprecise durations: a fuzzy approach
IEEE Transactions on Fuzzy Systems
Information Sciences: an International Journal
A fuzzy logic approach to forecast energy consumption change in a manufacturing system
Expert Systems with Applications: An International Journal
Mathematics and Computers in Simulation
A new approach to the rule-base evidential reasoning: Stock trading expert system application
Expert Systems with Applications: An International Journal
Proceedings of the Winter Simulation Conference
Selection of efficient portfolios-probabilistic and fuzzy approach, comparative study
Computers and Industrial Engineering
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The basic paradigm of simulation is the probabilistic approach to describing real world uncertainty. However, in many cases we do not have an information that would be precise enough to build the corresponding probabilistic model or there are some human factors that prevent doing so. In such situations the mathematical tools of fuzzy set theory may be successfully used. It seems that the simplest and natural way to do this is to replace in our model the probability densities by the similar fuzzy intervals, but some inherent problems of fuzzy arithmetic must be resolved first to build adequate fuzzy models. The main problem is the comparison of fuzzy intervals. The paper presents a new method of crisp and fuzzy interval comparison (ordering), based on the probabilistic approach. We assume that the fuzzy numbers are represented as ordered α-level set. This makes it possible to take into account all the cases of intervals location and intersection as well as the case of ordering of interval and real number. The probabilistic approach is used only to infer the set of formulae for deterministic quantitative estimation of degree in which an interval is less than or equal to another interval. The measure of such a degree may be formally treated as probability, but the term "possibility" can also be used, as it good reflects the sense of interval relation in practical cases. On the basis of the proposed crisp and fuzzy interval comparison method and the usual fuzzy extension procedure, the technique for fuzzy modeling was elaborated. To illustrate its efficiency, the simple examples of fuzzy modeling of manufacturing and logistic systems are considered in comparison with the usual simulation results.