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The definitions and basic properties of so called uncertain variables are presented. The uncertain variables are described by certainty distributions given by an expert and characterizing approximate values of the variables. Control problems for uncertain systems with static and dynamic plants are considered. A method of the stability analysis for a system with uncertain parameters is described. Simple examples illustrate the presented approaches.

The paper is concerned with static plants described by a knowledge representation in the form of relations or logical formulas with unknown parameters. The learning algorithms consisting of step‐by‐step knowledge validation and updating have been presented for different versions. The theorems concerning the convergence of the learning processes have been given for the open‐loop and closed‐loop learning decision‐making system. The extension for the case with uncertain observations has been suggested. Simple examples illustrate the presented approach.

To present new results concerning the applications of the uncertain variables to analysis and decision problems in a class of uncertain knowledge‐based systems described by a relational knowledge representation.

The analysis and decision‐making problems are formulated, the general forms of the solutions are described, the theorem concerning the optimal solution is presented, numerical examples illustrating the general theoretical approaches are included.

The uncertain variables have been proved as convenient tool for solving specific optimization problems based on relational knowledge representations with unknown parameters.

Formulation and solving optimization problem for the given certainty threshold, application to the problem of resource and task distributions in a complex of parallel operations, indications of possible practical applications.

In many decision‐making problems under parameter uncertainty, the most popular stochastic approach is not used because of its serious drawbacks. The purpose of this paper is to present another approach, which copes with the uncertainty of parameters. It uses a precise criterion evaluating a decision with respect to uncertain parameters. This precision by the maximum operator is performed on a term based on the criterion and called the relative regret. The approach is applied to the allocation problems in a complex of operations.

The resource allocation problems in a complex of operations of independent and dependent structures to minimize a total execution time of all operations are investigated. Then, the results are extended for the problem of a task allocation in the complex of independent operations. The case is considered when the parameters in the functional models of the operations are uncertain, and their values belong to the intervals of known bounds. The solution algorithms for the uncertain problems are based on known solution algorithms for the corresponding deterministic problems. The solution algorithms for the latter problems are outlined in the paper.

The main contribution of the paper consists in presenting the property that it is possible for the uncertain problems considered to replace the solution of the uncertain allocation problems by solving a number of corresponding deterministic problems.

The useful and interesting property of the solution algorithm for the allocation problems, in general, cannot be applied to the other decision‐making problems under uncertainty. As an example of such a problem, a simple routing‐scheduling problem is presented for which, however, a number of possible parameter scenarios can be substantially limited.

The allocation problems addressed in the paper have a variety of applications in computer systems and in manufacturing systems. Moreover, a lack of crisp values for the parameters in models of individual operations is rather common.

The paper extends previous results for the allocation problems in a complex of operations.

The purpose of this paper is to present results concerning resource distribution problems for a class of production systems composed of production operations described by relations with uncertain parameters – for newly considered serial‐parallel and parallel‐serial structures.

The resource distribution problems are formulated. For the typical mathematical model of a single production operation, the resource distribution algorithms are derived analytically or, when that is impossible, numerical procedures for finding solutions to distribution problems are suggested.

The uncertain variables have been proved as a convenient tool for solving specific optimization problems in production management based on relational knowledge representation with unknown parameters.

The paper presents analytical resource distribution and numerical algorithms for determining the optimal resource distribution, which may be applied in knowledge‐based management‐level decision systems for serial‐parallel and parallel‐serial structures of production systems.

The purpose of this paper is to determine and evaluate resource allocation algorithms for mixed‐structure operation systems with unknown parameters characterized by experts using the formalism of C‐uncertain variables.

Aggregation and decomposition of mathematical models of operations, performed using analytical‐numerical optimization methods, lead to serial and parallel structures for which allocation algorithms are known. Evaluation of allocations carried out by means of a computer simulation.

Resource allocation problems for mixed‐structure operation systems may be solved by applying aggregation, decomposition and allocation algorithms determined for simple structures. Allocation algorithms based on C‐uncertain variables outperform these based on basic uncertain variables.

Application of the presented algorithms is limited to some mixed structures, however, the methodology used appears general enough to allow developing algorithms for other mixed structures.

The algorithms developed may be embedded into a knowledge‐based system supporting management‐level decisions concerning optimal distribution of limited financial resources.

Originally determined rules for aggregation and decomposition, as well as resulting allocation algorithms. The presented methodology seems promising for developing a general resource allocation algorithm – valid for any mixed structure of an operation system.