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In this paper, we show how the Kantorovich problem appears in many constructions in the theory of belief functions. We demonstrate this on several relations on belief functions such as inclusion, equality and intersection of belief functions. Using the Kantorovich problem we try to measure these relations and as the result we obtain various functionals like the Wasserstein distance on belief functions.

It is an important feature of a monotone measure that it is not additive in general. In the paper we propose the mathematical tool, based on canonical sequences of monotone measures, for analyzing additivity of monotone measures on subalgebras and give a way of generating such monotone measures. It turns out that the generating rule can be considered as an effect of a linear operator defined on the set of monotone measures. We also investigate in what cases the sequence of such operators behaves commutatively and preserve continuity properties from the generating monotone measure.

The traditionally used way of arguing the solution of the problem, formed by an intelligent system, is to explain the course of logical inference. The sequence of rules applied, using facts and hypotheses, is considered to be information that can convince the user of the validity or reliability of the conclusion obtained. The disadvantage of such a mechanism is that it reflects the formally correct, but senseless course of assessing the truth of facts and rules. The argumentation of the obtained solution is based on the tracing protocol, which, in fact, does not differ in any way from the debug tracing of programs. The reasoning is far from the meaning of the problem. For the analysis of spatial situations using diagrams, maps and plans provided by geographic information systems, the basis of argumentation can be the relationship between cartographic objects, which do not depend on knowledge about these objects. The idea of organizing the search for arguments by studying spatial relations arises. Relationships of inheritance, aggregation, composition, generalization and association of object classes can be used here. The paper examines the dependences of the indicator of the reliability of the expert conclusion in the intellectual system for individual relations and their combinations.

This article discusses the problem of material flow management in production. Materials management includes the task of operational and scheduling. The main difficulty in planning is the correct accounting of the predicted parameters. It should be noted that complex production processes are characterized by a large number of parameters and interdependence of input data. It is the correct accounting of the parameters of the problem that will allow obtaining an optimal or close to optimal solution for the problem of allocating production resources. The article proposes an approach to the construction and analysis of a model of a production complex in conditions of uncertainty. The article discusses the subsystems of the model, taking into account the restrictions on the determined parameters. An approach to solving the problem of redistributing material flows and choosing a sequence for performing individual technological operations with fuzzy parameters is proposed.

In the paper, we formalize the notion of contradiction between belief functions: we argue that belief functions are not contradictory if they provide non-contradictory models for decision-making. To elaborate on this idea, we take the decision rule from imprecise probabilities and show that sources of information described by belief functions are not contradictory iff the intersection of corresponding credal sets is not empty. We demonstrate that evidential conjunctive and disjunctive rules fit with this idea and they are justified in a probabilistic setting. In the case of contradictory sources of information, we analyze possible conjunctions and show how the result can be described by generalized credal sets. Based on generalized credal sets, we propose a measure of contradiction between information sources and find its axiomatics. We show how the contradiction correction can be produced based on generalized credal sets and how it can be done on sets of surely desirable gambles.

In this paper, the concept of minimal intuitionistic dominating vertex subset of an intuitionistic fuzzy graph was considered, and on its basis, the notion of a domination set as an invariant of the intuitionistic fuzzy graph was introduced. A method and an algorithm for finding all minimal intuitionistic dominating vertex subset and domination set was proposed. This method is the generalization of Maghout's method for fuzzy graphs. The example of finding the domination set of the intuitionistic fuzzy graph were considered as well.

Spatial situations are the subject of analysis in many life support systems, manufacturing and business. Finding a solution of applied problem in conditions of lack of information gives rise to an interactive process of studying the situation, the participants of which are the user-analyst and geoinformation service. In the process of interaction, the analyst seeks to achieve situation awareness sufficient to generate, evaluate and make rational decisions. This paper explores the functioning of an intelligent recommender system designed to reduce the cognitive load on the user. At the heart of its work is planning a sequence of analysis contexts. The context refers to the information structure necessary for the presentation of cartographic information to the analyst. It is assumed that the geoservice has a set of contexts, and each analysis session is a time series of contexts. The problem of minimizing the number of contexts providing the necessary situational awareness of the analyst is considered. The presentation of the experience of analysis by the components of level, trend and rhythm is proposed. The results of an experimental study of the proposed method are presented too.

This paper considers the task of organizing a rational interaction between a geographic information service (GIS) and a user who analyzes spatial data. The purpose of the analysis is to develop a solution to an applied problem in conditions of incompleteness and uncertainty of information about both the final goal and the solution procedure. The work considers an interactive visual analysis of a space region, where the GIS delivers data from cartographic sources and the user compiles and analyzes the cartographic representation of the workspace in real-time. The task of guiding the analysis process to maintain its intelligent orientation is formulated. The meaning of the analysis process is associated with achieving situation awareness of the user, which will ensure the adoption of higher quality decisions. A control method based on the selection of an adequate context from the set of contexts described in the GIS has proposed. A two-component context model has proposed in the form of a kernel and a set of valid kernel transformations preserving the meaning of the context. The intelligent orientation of the analysis has stabilized using the proposed presentation. The problem of determining the optimal number of GIS contexts has considered which minimizes the complexity of the analysis and relation has obtained for its calculation. The problem of maximizing the utility of cartographic images generated by GIS at the user’s request has formulated. A representation of the analysis workspace by skeleton and environment has proposed, which has used to ensure maximum utility. The results of an experimental study of the layout of an intelligent system for managing the analysis are presented too.

The work is devoted to solving the problem of tracking objects with modern robotic systems. An algorithm for tracking objects based on the representation of images in the form of clouds of singular points using intuitionistic fuzzy sets is considered. The developed method takes into account the geometric structure of the tracked object. The truth of the found comparisons of the singular points of the images is evaluated by categories such as “not quite accurate”, “almost exactly”, “absolutely accurate”. The results of the experiments, as well as estimates of the stability and speed of the algorithm, demonstrate the high quality of the task of tracking objects in a video sequence.

To model conflict, non-specificity and contradiction in information, upper and lower generalized credal sets are introduced. Any upper generalized credal set is a convex subset of plausibility meas...

The problem of controlling the reconfiguration of the mechanical transport system is considered with the aim of minimizing the total transportation costs. The features of decision making about the choice of the reconfiguration option in the conditions of the lack of information on the dynamics of the state of the external environment are analyzed. The approach to decision-making based on the use of experience is described. The distinctive feature of the approach is the presentation of knowledge about the precedents of reconfiguration in the form of images. The model of the image is given. The principle of obtaining logical conclusions on the basis of image analysis is described. The operations of comparing and transforming images are discussed. The features of the implementation of the transformation operator in the mechanical transport system are considered.

Solving complex informal problems using spatial data is often used in industry and business. In the absence of a solution algorithm, analyst resorts to a heuristic search for a solution, which is based on an interactive dialogue with a geographic information system (GIS). The analyst builds a cartographic workspace by sending GIS queries. The workspace is explored visually using software tools for spatial, statistical, and other special types of analysis. During the analysis, the user raises his situational awareness. It is important to organize the dialogue wisely as there is a danger of cognitive overload. In the latter case, there is a possibility of making the wrong decision. This paper proposes a method for representing knowledge about the process of analyzing spatial situations. The essence of the method is that knowledge is represented by chains of contexts and patterns of appropriate user behavior in visual analysis. A model of an image of a chain of contexts is proposed, which consists of the center of the image and its admissible transformations. A method of organizing a dialogue is described, which allows a GIS to develop recommendations for choosing a context in a chain of contexts. Patterns of level, tendency, and rhythm are proposed to represent knowledge about appropriate behavior. Application of the proposed method of knowledge representation in recommender GIS improves the quality of spatial data analysis.

The aim of this paper is to show that the Kantorovich problem, well known in models of economics and very intensively studied in probability theory in recent years, can be viewed as the basis of some constructions in the theory of belief functions. We demonstrate this by analyzing specialization relation for finitely defined belief functions and belief functions defined on reals. In addition, for such belief functions we consider the Wasserstein metric and study its connections to disjunctions of belief functions.

In this paper we consider the problem of finding the invariant of a fuzzy temporal graph, namely, a fuzzy internally stable set. Fuzzy temporal graph is a generalization of a fuzzy graph on the one hand, and a temporal graph on the other hand. In this paper, a temporal fuzzy graph is considered, in which the connectivity degree of vertices varies in discrete time. The notion of maximum internally stable subset of fuzzy temporal graph is considered. A method and an algorithm for finding all maximal internally stable sets are proposed which makes it possible to find a fuzzy internally stable set. The example of definition of internal stable fuzzy set is considered as well.

Non-additive measures, capacities or generally set functions are widely used in decision models, data processing and game theory. In these applications we can find many structures identified as linear transformations or linear operators. The most remarkable of them are Choquet integral, Mobius transform, interaction transform, Shapley value. The main goal of the presented paper is to study some of them recently called event-based linear transformations. We describe them considering the set of all possible linear operators as a linear space w.r.t. their linear combinations and compute the dimensions of its some subspaces. We also study the consensus requirement, i.e. we analyze the condition when the linear operator maps one family of non-additive measures to other family.

In the paper we investigate the criteria of choosing generalized Dempster-Shafer rules for aggregating sources whose information is represented by belief functions. The approach is based on measuring various types of uncertainty in information and we use for this purpose in particular linear imprecision indices. Some results concerning properties of such rules are also presented.

This work presents a fuzzy resource-constrained project scheduling problem that is one of the operational research problems that can be defined as a combinatorial NP-hard problem of constructing a special plan for performing a number of precedence related tasks subject to limited uncertain resources. It is relevant to use fuzzy numbers when activity durations rely on human estimations and due to lack of historical data there is no opportunity to predict them accurately. The goal is to construct a fuzzy heuristic-based approach to obtain a near optimal solution in a reasonable computational time.

This paper investigates the problem of geoinformation modeling of situations and solutions adopted in the implementation of logistics projects. The task is solved within the framework of the geoinformation model, which displays the experience of implementation of similar projects. The performance criterion of the model is the reliability of the generated decisions. The decision is reliable if it corresponds to the reality displayed by the electronic map. The displaying method previously completed projects into a given space-time area is analyzed. The method is based on the image representation of geoinformation models. The geoinformation model of the logistics project includes a scheme consisting of logistics centers and transportation routes. The procedure of displaying of project image is described that is implemented by an intelligent component with knowledge about displaying. Principles of the reliability evaluation of the results of the transformation are discussed.

The problem of optimal allocation of service centers is considered in this paper. It is supposed that the information received from GIS is presented like second kind fuzzy graphs. Method of optimal location as method of finding fuzzy base set of second kind fuzzy graph is suggested. Basis of this method is building procedure of reachability matrix of second kind fuzzy graph in terms of reachability matrix of first kind fuzzy graph. This method allows solving not only problem of finding of optimal service centers location but also finding of optimal location k-centers with the greatest degree and selecting of service center numbers. The algorithm of the definition of fuzzy base set for second kind fuzzy graphs is considered. The example of finding optimum allocation centers in second kind fuzzy graph is considered too.

In this paper the problem of defining service centres optimum allocation in transportation network is observed. It is supposed that transportation network is described by a fuzzy interval graph. The notion of fuzzy set of strong connectivity is introduced. It is shown that the problem of service centers location can be reduced to a problem of finding fuzzy set of strong connectivity. The method and algorithm of finding fuzzy set of strong connectivity is considered in this paper. The example of finding optimum allocation of centers in fuzzy interval graph is considered.

This paper is devoted to the task of the two-commodity maximum flow finding in a fuzzy temporal graph. Arcs of the network are assigned by the fuzzy arc capacities and crisp transit times. All network’s parameters can vary over time, therefore, it allows to consider network as dynamic one. The task is to maximize total flow passing through the network, considering temporal nature of the network. Such methods can be applied in the real railways, roads, when it is necessary to take into account the commodities of two types solving the task of the optimal cargo transportation, for example, passenger and cargo trains or motor cars and lorries Method of operating fuzzy numbers for flow tasks is proposed that doesn’t lead to the blurring of the resulting number.