Machine-Learning-Based Model for Indicators of the Resource-Based Security of Interests in High-Level Organizational Systems⋆

Abstract

Reliable situational awareness of resource sufficiency is vital for macro-level organizational systems that face deep uncertainty, multi-level decision chains and tight resource constraints. We present an end-to-end framework for a Composite Multi-functional System of Resource-based Security Indicators (RSI) that supports strategic and operational decisions in Multidimensional Management (MDM); the defense domain was considered as its notable representative. At the conceptual layer we formalize the management domain by a twolevel network of decision centers governed by Reference Concepts of Management (RCM). Each RCM represents either a strategic goal, a strategic capability, a crisis management task, or an activity ledger. For each RCM we derive individual indicators of performance well-being and resource well-being. Predicate relations between RCM types enable both direct and indirect (integrated or statistically inferred) estimates. Four functional indicators: express resource-risk diagnosis, vulnerability ranking, external-impact criticality and strategic-adaptation diagnosis - are produced by tailored aggregations of individual indicators and context data. We detail the machine-learning pipeline for the first, time-critical function. A heterogeneous ensemble of five classifiers (Bayes, SVM, Random Forest, kNN, Logistic Regression) is trained on historic ledgers and expert audits. To account for the NFL theorem, each classifier is weighted by a model-conformity coefficient (reflects data assumption violations) and by a quality index robust to class imbalance. Forecasting supports a single priority model or a weighted-voting ensemble. Future work will deliver prototypes, quantitative validation, N-ary classification and hybrid time-series forecasting, extending RSI support for high-stakes organizational decisions.

Keywords

• Machine-learning classification
• Resource-based security metrics
• weighted voting ensemble
• trategic decision support
• KPI monitoring 1

1. Problem Statement

An integrated presentation of information on the current state of objects and processes — tailored to the needs of decision-makers — is a key element of digital governance. At higher managerial tiers within large-scale Organizational systems (OS) and, especially, national and international projects, this requirement is commonly satisfied by indicator frameworks.

Numerous, largely complementary definitions of an indicator [1–3] describe it as a quantitative measure derived from a series of observed facts that characterizes the position of an object within a given domain, including its state of sufficiency or deficiency. Indicators are employed across many domains and serve diverse analytical purposes. For example, the widely used set of international indices of countries’ economic and political development [4] aggregates a large number of regularly documented variables, enabling progress tracking, identification of leverage points, and early diagnostics or forecasting.

Indicators for complex systems are typically composite [1, 5, 6]. Their constituent indicators often form a hierarchy in which successive levels refine specific properties, while the composite value is obtained by aggregating constituent scores with weighting coefficients [6]. In high-risk Problem areas (PAs), indicator structures become even more intricate [5, 7]; within the PA of national security, for instance, a composite indicator has been proposed that measures the system’s response to deviations from a homeostatic state once critical thresholds of individual components are exceeded [8].

Experience in social-welfare analysis shows the advantages of a composite-indicator system that combines not only various sub-domains but also metrics that differ in their management roles: social context (conditions), social status (desired outcomes), and social responsibility (interventions). Indicators of social well-being likewise integrate characteristics reflecting distinct sufficiency perspectives embedded in alternative definitions of quality of life [9].

A prominent subclass of indicators in management is Key Performance Indicators (KPIs). KPIs are commonly categorized into: • high-level and low-level KPIs, linked hierarchically, and • lagging (performance-outcome) and leading (operational) KPIs, where the latter guide actions aimed at improving the former [10].

In decision support, an indicator serves a wide range of analytical needs. Typical examples include comparing different objects — or the same object at different points in time — identifying bottlenecks in development processes, and diagnosing whether the current state of the system is acceptable or satisfactory.

The current indicator value becomes a decision criterion when its deviation from threshold levels (ideal, required, critical, etc.) or from baseline values associated with benchmark objects or situations exceeds a specified limit. Such trigger values may be defined on the basis of (i) aggregated direct observations of the indicator’s components or (ii) forecast- and classification-based estimates.

A number of pressing challenges in indicator design and use arise when supporting decisions that concern the resource-based security of interests in the management of Organizational systems (OS) and in projects of national or international scale. Such decisions are tightly linked to limited — and often unstable — resource inflows, as well as to specialized resource categories whose availability depends on external interactions and innovation aimed at creating the necessary resource base [11].

The most demanding requirements for relevant and effective indicators of resource-based security of interests (RSIs) are set by OS whose Problem area (PA) exhibits the following properties: • coexistence of distributed interest-security mechanisms with hierarchical operational control; • planning under uncertainty (including deep uncertainty); • simultaneous evaluation of the resource state with respect to both planned and crisis management capabilities and to norms of routine activities.

These complexities stem, on the one hand, from the OS structure — whose organizational elements retain their own internal management mechanisms — and, on the other hand, from a highly dynamic environment that demands flexible interaction in the face of new threats and opportunities affecting the OS’s strategic interests.

A characteristic representative of this PA multidimensional management class, hereafter denoted MDM, is activity in the military domain of national security. Developing adequate RSIs for decision support in MDM faces further specifics: • two distinct tiers of interest security — a global decision center and an internal hierarchy of implementation centers; • multi-faceted (goal-oriented) and multi-criteria (performance-oriented) interest systems held by stakeholders in the decision centers, which engage in diverse management interactions; • high uncertainty of both current and future decision contexts, driven by interdependencies with other PAs, environmental volatility, and shifting internal priorities; • the PA still lacks any a priori PA-specific model that formally relates interest-attainment KPIs to resource-availability indicators, even though empirical evidence leaves no doubt that this relationship is substantial.

Building on the above requirements and current trends in indicator design, we posit that effective resource-based security indicators (RSIs) must satisfy three design principles: • Compositeness – each RSI should integrate components that are relevant to the different interest systems operating within the OS; • Informational sufficiency – the model must rely solely on data that can be extracted from the OS business-process information environment, ensuring practical deployability; • Adaptivity – the model should detect triggers in the current OS state that call for method selection and parameter adjustment, and respond accordingly.

A promising paradigm for constructing an RSI model is to treat resource situations as a classification problem and apply machine-learning methodology [12]. This choice offers the following advantages: • the model is learned from documented operational history rather than from a priori theoretical

PA knowledge; • classes are defined by the stakeholder-accepted gradations of interest well-being that are already employed in expert decision making; • the same information space — routine resource monitoring, post-operation assessments, and scheduled expert audits — supports parallel evaluation of resource favourability from multiple decision-center viewpoints; • the RSI remains adaptive through incremental retraining and robust through dynamic selection and tuning of methods according to the statistical properties of observed resource states.

The study therefore aims to create conceptual knowledge models for the MDM PA that enable RSI construction with the above properties and to embed them in a composite, multi-functional indicator system for PA state assessment. Within that system the machine-learning RSI is developed to provide express diagnosis of resource risk to strategic interests. ( 1 ) ( 2 ) ( 3 )

2. Conceptual Model of Domain Si within the MDM Problem Area

The conceptual model is organized in two levels

{Lk} k =1,2 where L1 – management of interest security; L2 – management of internal activities that support those interests.

Each level is specified by a structural-and-functional model:

SFMk = (DCk , ВСk , MBk , IBk , RCMk , ERCMk) where DC – decision centers (DCs); BC – advisory and situational communications that support distributed decision making; MB – hierarchical management links; IB – regulatory information links; RCM – types of reference concepts of management;

ERCM – reference concepts of management.

Decision-center model

Every DC denoted dckl ∈ DCk (see ( 2 )) is described by

Mdckl =(T, RT, A, SUB, {(MI, idc, ircm)}, hrcm) where T – functional type; RT – role type; A – set of activity types; SUB ∈ ERCM – closest higher-level DC; MI – management impact on another center idc by means of the impact concept ircm ∈ ERCM; hrcm ∈ ERCM – concept that represents OS interests in domain Si for this DC.

The scheme supports the coexistence of hierarchical cascading [13], distributed [14] and deliberative [15] decision processes, and allows combining agile strategic planning [16] with capability-based planning [17].

Within each structural-and-functional model SFMk in ( 2 ) the set ERCMk captures the reference concepts of management. An individual concept rcm ∈ ERCM: • formalizes a specific aspect of OS stakeholder interests, • serves as the basic object of activity for a decision center of the corresponding functional type

T in model ( 3 ), • provides the information schema used to monitor domain Si, and • acts, depending on the DC level, either as a planning target at L1 (strategic tier) or as the operationalized output of strategy at L2 (operational tier).

Thus, ERCMk links the decision-center model Mdckl in ( 3 ) to the higher -level structure of SFMk in ( 2 ), supplying the conceptual “glue” that harmonizes hierarchical, distributed and deliberative decision processes.

RCM element types 1. Strategic goal where GO – target object; К – number of objects; GC – condition for desired state; MG – progress metric. 2.

Strategic capability

CAPi=(MTi, MCi,OCi,{RESik ,NRik }k=1,K),MCAPi,SSGi) ( 5 ) where MT – task whose execution capability is evaluated; MC – execution conditions; OC – set of key DCs to which the capability is delegated (see model ( 3 ));

RESk, NRk – resource type and norm (number of resource types K in ( 5 ) depends on the chosen resource model [17]);

MCAP – metric that evaluates the current level at which the CAP is being realized by the task performers;

SSG ⊆ {SGi} – subset of strategic goals that can be achieved through this CAP.

SGi =({GOik}k=1,…,K , GC i, MGi) ( 4 )

Crisis management task where PS – problem situation; TCAP – capabilities to be employed; PT ∈ DC – performer DCs; TR – operational resource plan; TF – deadline; ET – performance evaluations.

TAi =(PSi, TCAPi, PTi, TRi, TFi, ETi)

Activity ledger for an L2 DC

DCATi =(DCTi{(CTAik ,Rik, RSik)}k=1,…,3) where DCT – set of delegated capabilities; CTA – activity category: 1 - routine, 2 - capability support, 3 - crisis; R – performance rating; RS – resource support of the activity.

RSikl={TRSikl , NRSikl, MRSikl}l=1,…,L where TRS – resource type; NRS – norm or plan; MRS – current supply level; L – number of resource types.

Below in Table 1 we specify, for every DC type and level, its functional role, activity portfolio, managerial impacts, and the reference concept of management (RCM) that represents the center’s interests (strategic goal, capability, crisis-management task, etc.). This structure captures both hierarchical and distributed management schemes, records resource- and information flows among centers, and links the realization of the strategic interests of Si to ongoing operational activity at level L2.

This table enables precise mapping of resources, activities, and interests across both levels of the OS while supporting agile integration of hierarchical and distributed decision-making processes. ( 6 ) ( 7 ) ( 8 )

3. Composite Multi-Functional Indicator System for the PA

To provide expert-analytic support for decision making in the Organizational system (OS) described in the previous section, we introduce an Indicator System for Interest Well-Being (SI) that follows three design principles drawn from modern composite-indicator research (see Sect. 1): 1. Each constituent indicator must quantify the well-being level of a specific reference concept of management (RCM), which serves as the constructive representation of an interest. 2. Multiple decision-support functions imply that constituent indicators must be compositely integrated into several resulting indicators, each oriented toward a distinct function. 3. Inter-interest dependencies — expressed through relevance relations REL(tk1, tk2) among RCM types tk1, tk2 — govern whether an RCM of one type can influence, or supply data to, an RCM of another type.

Using the RCM models defined in ( 4 ) –( 8 ) we formalize relation predicate REL(Or, Os). These relations determine whether an RCM of one type can influence an RCM of another type or serve as an information source for integration. An RCM of a given type is referred to by the identifier introduced in ( 4 )–( 8 ), and an element A of the model of the s-th concept is denoted As.

REL(SGr, CAPs) ⇔ SGr ∈ SSGs ( 9 ) REL(TAr, CAPs) ⇔ CAPs ∈ TCAPr ( 10 ) REL(DCATr, TAs) ⇔ DCATr ∈ PTs ( 11 )

REL(SGr, TAs) ⇔ SGr ∈ PSs ( 12 ) REL(SGr, DCATs) ⇔ (∃ TAk : REL(DCATs, TAk) ∧ REL(SGr,TAk) ( 13 )

REL(CAPr, DCATs) ⇔ CAPr ∈ DCs ( 14 )

Model ( 16 ) interprets the attained performance well-being as the degree to which stakeholder needs are satisfied, using expert ratings on a verbal–numeric scale [18] that matches their business practice. Thus

EWBR(oc,t) = FIA(ER1, ER2, ER3) ( 17 ) is the direct estimate of the performance-aspect well-being of the interest represented by RCM oc. Interest well-being in the performance aspect: indirect estimates

An alternative to the direct score ( 17 ) is a pair of indirect estimate sets

({EMRI}, {EMRS}) where EMRI – integration-based estimates; EMRS – statistically derived estimates. ( 18 ) ( 20 )

The integration estimate EMRIk(oc,t) is obtained by aggregating the direct scores EWBR of all RCMs of the k-th type that are relevant to oc but differ from its own type TK.

EMRIk(oc,t) = FIMRk({EWBR(rckj,t)}j=1...J) ( 19 ) where ∀ j ∈ (1,…,J) REL(oc, rckj); FIMR – denotes the score-integration function.

Statistically derived estimates are built on a mass-observation array that records (i) the states of every RCM in the OS and (ii) the behaviorof the external environment. The procedure constructs and applies machine-learning models that capture the relationship between performance well-being of a given target interest and the resource-support well-being that is observed or inferred for other RCMs — either formally relevant to the target or hypothetically exerting an influence on it.

We formalize this data as an observation array MAOBS(TT), which spans the entire observation period TT = (TT1, TT2).

First, we introduce several special time sub-intervals inside the overall window TT: • T1 – the constant span between the j-th and (j + 1)-st scheduled audits of strategic-level RCMs (SG and CAP). The concrete instance of this span is denoted (TT1j1, TT1j2) ⊂ TT; • {{T2ij}i=1,…N}j=1,…M – the set of durations of those crisis-management tasks taij, that are carried out within the interval (TT1j1, TT1j2); • T3 – the regulatory update period for each activity ledger DCAT its j-th occurrence is the interval (TT3j1, TT3j2).

With these notations the observation array is expressed as

MAOBS(TT) = ({EWBRjk(SOk,TT1kj1)}k=1,K}j=1...J1, {{EWBRjl(OTAl,TT2lj1)}l=1...L}j=1...J2, {EWBRjm(DCATm,TT3mj1)}m=1...M}j=1...J3, {EWBSjk(SOk,TT3kj1)}k=1...K}j=1...J3,

{{EWBSjl(OTAl,TT2lj1)}l=1...L}j=1...J2, {EWBSjm(DCATm,TT3mj1)}m=1...M}j=1...J3, {{Rjr}r=1...NF}j=1...J1) where EWBR – direct performance-aspect well-being score; EWBS – resource-support well-being score; SOk – strategic-level RCM; OTAl – crisis-management task; DCATm – activity ledger of the m-th L2 decision center; J1 – number of audits; J2 – number of crisis tasks executed; J3 – number of DCAT content updates.

As an observation element for external-environment factors in the MAOBS model, we include the risk produced by the r-th external factor {Fr}r=1…N during the interval (TT1j1, TT1j2). This risk is evaluated by

Rjr = (Lri/Tj)∙Prj ( 21 ) where Lrі – duration of the action caused by Fr within the i-th audit interval; Prj – estimate of the factor’s intensity in that interval.

The statistically derived estimate EMRS (see ( 18 )) uses the elements of ( 20 ) as input data and is specified as

MEMRS(oc,t) = (MF, MT, {MMLj}j=1…J, {CRr}r=1…N, FIE) where MF – feature model; MT – target-variable model; {MMLj} – set of machine-learning models employed; CR – statistical criterion used to assess the quality of the results produced by the chosen MML; FIE – function that integrates the individual model outputs. ( 22 ) MF = {Fi, {SOij}j=1…Ji, CO(t), {SCik}k=1...Ki}i=1…N ( 23 ) where Fi – feature;

SOij ∈ MAOBS (see ( 20 )) – an observation-array element that can serve as a source for the feature value;

CO(t) – a predicate that specifies how SOij values are selected in time, depending on the position of moment t relative to the baseline time-intervals defined in ( 20 );

SCik – admissible scales for feature; N – total number of features.

Target-variable model can be defined as

MT = (TV, {SOTi}i=1…M,{SYN(t, Fi)}i=1…N, {SCTj}j=1…J) ( 24 ) where TV – target variable;

SOTi – an element of the observation array that corresponds to the EWBR evaluations of the RCM representing the target interest;

SYN(t, Fi) – rule for time-synchronizing the target and feature observations; SCTj – the j-th candidate scale applicable to the values of the target variable.

Constructing an EMRS-class well-being estimate allows the system to handle the following sources of uncertainty: • the evaluation moment t lies inside an audit interval that has not yet been completed; • one or more scheduled audits were skipped in several preceding planning intervals; • the direct score EWBR(oc,t) conflicts with the integration-based score EMRIk(oc,t) determined for t=TT1j1 or t=TT1j2.

Interest well-being in the resource-support aspect: evaluation

The resource-support aspect in ( 15 ) treats well-being as the closeness of the actually available amount of a given resource at time t to its normative (planned) level.

Direct evaluation is made only for Activity-ledger RCMs, (TK=DCAT).

In this case (see ( 8 ))

EWBS(oc,t)=FIA(ES1,ES2,ES3) where FIA – is the integration function for the category-specific scores ES.

ESi=FIS({(NRSij-CRSij)/NRSij}j=1…J) ( 26 ) where NRSij, CRSij – are, respectively, the normative and current resource supply; FIS – integrates the adequacy levels across the J resource types.

For any TK≠DCAT the resource well-being of oc is obtained by integrating the direct scores of all relevant ledgers:

EMWBSi(oc,t)=FIMS({EWBS(ork)}k=1…K) where each ork – is a DCAT type RCM such that REL(oc,ork) holds (cf.( 9 )-( 14 )); FIMS – the integration function over the K corresponding activity-ledger scores. ( 25 ) ( 27 ) Structure and composition of the indicator system

Building a composite, multifunctional Indicator System for Interest Well-Being (SI) for an Organizational System (OS) operating in an MDM problem area rests on the constructive combination of: • individual indicators IC , each describing the state of a single interest (these are the constituent indicators of the composite model discussed in Sect. 1); • several composite functional indicators ICF that characterize the entire interest system and are defined as specific compositions of the individual indicators.

An individual indicator ICi(SOj,t)} represents the state of an RSM SOj according to evaluation type i — direct (eqs. 17, 25) or integration-based (eqs. 19, 27).

Hence the overall indicator system is

SI(t)=({ICi(SOj,t)}j=1,…,N}i=1,…,M, {ICFk}k=1,…4) where ICi – individual indicator for RCM SOj under evaluation type i; ICFk – one of the four basic composite functional indicators.

The core decision-support functions relevant to the PA activity model described in Sect. 2 comprise the following: 1. Rapid diagnosis of problematic situations; 2. Compilation of a vulnerability ranking; 3. Identification of threatening external factors and their potential targets within the PA; 4. Assessment of current strategy elements for consistency with up-to-date needs.

For direction k the functional indicator IFk may rely on individual indicators and additional data. Formally, its model can be represented as

MICFk(t)=(BICk(t), ADk, PROCk(BICk,ADk),Rk) where BICk(t) ⊆ {{ICi(SOj,t)}j=1,…,N}i=1,…,M — the subset of individual indicators used;

ADk – additional information, including formalized knowledge about relationships between PA elements or observations not captured by any IC but present in dataset ( 20 );

PROCk – the procedure that calculates the indicator values; Rk – the output vector (with defined scales) intended for use in decision making. ( 28 ) ( 29 ) In Table 2, four functional indicators are described in accordance with structure ( 29 ).

The functional indicator Express diagnosis of resource risk to strategic interests — detailed in the next section — returns as its output an indirect performance well-being estimate of the given RCM so at time t, computed in the EMRS class (see ( 22 )).

The elements of its model ( 22 ) are specified below.

Feature model MF (cf. ( 23 )) comprises: • features Fi, each is, as an element of MAOBS ( 20 ), the direct resource-support well-being score EWBS(rso,to) drawn from the DC’s Activity ledger of the operational-level rso and fixed for a particular activity category and resource type; • predicate CO(t) selecting EWBS(rso,to) values under the condition

REL(so,rso) ∧ (to ∈ (TT1,t)) ( 30 )

Within MF the candidate scales SC include both (i) the standard continuous scale for EWBS on ( 0,1 ) and (ii) a scale of absolute resource quantities, the latter being used when the adopted normative values are deemed unreliable.

The target-variable model MT ( 24 ) permits only a binary scale, enabling indicator construction even when expert assessments are produced under deep uncertainty [20].

The temporal synchronization condition SYN for aligning target values TV with feature observations Fi in ( 24 ) is

∀(tok ∈ (TT1j1, TT1j2)) TV(so,tok)=TV(so,TT1j2) ( 31 )

Thus, every target-variable observation whose feature values fall within the window ending at moment is assigned the direct performance well-being score produced by experts at the close of the corresponding well-being audit of so.

The procedure PROC specified in ( 29 ) for this indicator is presented in Section 4. 4. Construction of the Express Diagnosis of Resource Risk to Strategic

Interests Indicator

This section presents the algorithm used to build and to forecast the resource-based security state of strategic goals. The task is solved with binary-classification models. The workflow comprises two major phases: model building (training) and forecasting. 4.1 Model-building (training) phase Step 1. Preparation of the training set

A. Period selection and data synchronization The training set is formed according to the feature model ( 23 ). Each input feature Fi is a numerical score of resource support EWBS for the corresponding Decision Center (DC) over the interval between two scheduled audits of the strategic goal. The predicate CO(t) aligns the time-stamp of EWBS with the moment of the expert performance well-being score ESG(Ta), which serves as the binary target variable (1 = satisfactory, 0 = unsatisfactory).

Every feature Fi can be represented in several alternative scales SCi. For resource indicators we employ at least two: • normalized EWBS ∈ ( 0,1 ); • absolute resource quantity.

When required, the normalized EWBS may be discretized into categorical levels; this eases expert interpretation and broadens the family of machine-learning models that can be applied. The absolute scale is preferable when the planned norms are considered potentially outdated, so that comparing against the raw values is more reliable. Maintaining several scales SCi increases model flexibility and ensures proper comparison of resource metrics under heterogeneous conditions.

B. Exploratory data analysis a) Sample size and completeness The dataset is examined for sufficiency with respect to the requirements of the intended model families. Missing values are handled either by deletion or by an appropriate imputation strategy, chosen after assessing both feasibility and impact on data integrity.

b) Distributional form and feature independence For every variable we test compliance with theoretical distributions assumed later in the pipeline (e.g., normal, log-normal) and identify pairs of highly correlated features. Whenever the detected correlation exceeds an admissible threshold, the offending features are either decorrelated (by transformation) or removed.

c) Balance of the target variable The ratio of satisfactory to unsatisfactory cases for ESG(Ta) is computed. If a pronounced skew is observed, the training set is rebalanced through oversampling/undersampling or by using class-weighted loss functions to prevent majority-class bias. Because most machine-learning algorithms are sensitive to imbalance, subsequent classification-quality metrics are calculated in a way so that unequal class distributions are properly reflected.

Step 2. Training the full set of candidate classifiers and generating base classifications Because no single learning algorithm is universally optimal (the No-Free-Lunch theorem (NFL) [21]) the indicator is built on a heterogeneous ensemble of learners. Candidate models were selected from the families surveyed in [22] according to four criteria: • representation of the main classification paradigms (statistical, geometric and logical); • compatibility between the algorithm’s data-volume requirements and the size of the available resource dataset; • documented evidence of successful practical use; • availability of efficient software implementations.

The resulting set PC = { MCi } comprises five classifiers: Bayesian classifier, Support-Vector Machines (SVM), Random Forests, k-Nearest-Neighbours (kNN) and Logistic Regression.

For every classifier MCi ∈ PC an expert characterization of the criticality of four data requirements was compiled from an extensive literature review [12, 23–53]:

KDi = {kdij}j=1,…,4 ( 32 ) where j = 1 – feature-distribution; j = 2 – feature independence; j = 3 – observation data balance; j = 4 – measurement scale.

Each requirement is graded on a three-level expert scale ekdij ∈ {0, 0.5, 1}, where 0 – no requirement, 0.5 – violations admissible, 1 – requirement critical. Table 3 summarizes the resulting scores and provides the supporting rationale. For every criterion j, four argumentation aspects Aaj are documented (with a = 1,2,3,4): 1 – existence of a primary limitation; 2 – available robustness techniques; 3 – availability of software implementing these techniques; 4 – potential risks associated with their application.

Measurement scale Aa4

The argumentative ratings presented in Table 3 enable subsequent steps of the algorithm to deploy each classifier within an adaptive ensemble model that reflects the problem area’s specific characteristics across the four assessed dimensions. These ratings support (i) the use of the indicator ensemble when the statistical properties of incoming data are still uncertain, and (ii) timely detection of the need 0 None

None Not required Random feature sampling at splits mitigates correlation impact R packages randomForest, ranger, randomForestSRC, imbalanced None None Possible loss of discrimina

tive power k-Nearest Neighbours (kNN) 0 0.5 0.5 None Feature dependencies distort Bias toward the majority

distance-based results class Not required Dimensionality reduction Class weights, resampling

(PCA, t-SNE) techniques R packages caret, ROSE, DMwR, kknn Minimal Potential loss of discriminative power

Logistic Regression 0 0.5 0.5 None; non-normality can Multicollinearity among pre- Bias toward the majority weaken reliability dictors class Transformations (logs, roots) Remove correlated features, Class weights, resampling to handle outliers PCA, L1/L2 regularization Base R stats::glm(); package caret Minimal Possible loss of discriminative power

Possible loss of discriminative power 0

Random Forest

0.5 Bias toward the majority class Class weights, resampling

None Not required None 0 0.5 Distance metric is scale-sensitive Normalization, standardization 0.5 Requires correct encoding of categorical variables fect coding, ordinal encoding Incorrect encoding may reduce accuracy for retraining — triggered when the current weight coefficients assigned to the ensemble’s classifiers deviate significantly from those learned earlier.

Step 3. Computing the trust degree of classifier For every classifier i a model-data conformity coefficient KDRi is calculated

KDRi = 1 4 4 =1 ⋅ where IVij ∈{0,1} — Incidence Variable denoting whether requirement j is violated ( 1 ) or not (0) for the current data set. for the given data.

A larger KDRi signals more severe violations of the classifier’s underlying assumptions and therefore lower suitability. Conversely, the value (1− KDRi) is interpreted as the trust degree of classifier i Step 4. Integral classification-quality assessment For every classifier an aggregated quality score KQi is computed. It combines several metrics that are robust to class-imbalance — Cohen’s Kappa, F1-score and MCC. A higher KQi indicates that the model reproduces the true state labels more accurately and consistently, even when the class distribution is highly skewed.

Step 5. Weighted voting

For every classifier an aggregated quality score

CMR = ⟨ , ,

5 ⟩ =1 where i — indexes the five base classifiers in the pool PC;

∈{0,1} — is the class label returned by the i-th classifier at Step 2.

The CMR array is partitioned into two subsets according to the class predicted by each model A weighted evidence index is then calculated for each subset:

SP = {CMRi | RCi = 1}, SN = {CMRi | RCi = 0}, SP ∪ SN = CMR where IP corresponds to the positive class ( 1 ) and IN to the negative class (0); ∣CMR∣ — is the total number of classifiers that cast a vote.

IP = IN = | | 1 1 | | = |1(1 − ) ∙ , CMRi ∈ ∑ | ∑| = 1|(1 − ) ∙ , CMRi ∈ bility. ( 33 ) ( 34 ) ( 35 ) ( 36 ) ( 37 ) ( 38 ) ( 39 ) Step 6. Generating the final prediction

Single-model (priority) mode judgment. 4.2 Forecasting phase After model training (Section 4.1) the forecasting phase repeats the same synchronization, verification, and feature-transformation procedures, then produces the class labels and maintains system adaptaThe prediction phase supports two modes:

Single-model (priority) mode. A single classifier, selected by ( 38 ), is applied.

Weighted-voting ensemble mode. The outputs of the five classifiers are integrated according to ( 39 ).

The classifier with the highest combined weight is selected and its binary output is taken as the final decision. = МСі|

∈ 1,5((1 − ) ∙ )

Weighted-voting ensemble mode Using the evidence indices IP and IN defined in ( 36 )–( 37 ), the final class label is determined as ICL = 1, 0, > < , = If IP = IN, the system returns undecided or, according to the operating protocol, requests an expert This two-level design permits flexible integration of heterogeneous algorithms and delivers robustness to shifts in the distribution of input data. The resulting estimates can feed both automated monitoring services and strategic management decision support.

The forecasting pipeline is governed by the learning paradigm of each classifier. Parameter-based models — Bayesian classifier, SVM, logistic regression, and Random Forest — are applied directly with their stored parameters; retraining is required only if the exploratory data analysis (EDA) performed at inference time reveals substantial divergence from the data characteristics observed during initial training.

The non-parametric kNN classifier belongs to the lazy-learning family: for every incoming query it searches the full training set for the nearest neighbors and therefore needs no separate training stage [54, 55].

Algorithmic adaptability is maintained through continuous monitoring of the aggregate quality metric KQi. When the running average over the last N predictions drops by more than δ%, the system automatically triggers retraining of the parametric models and refreshes the instance base used by kNN. This mechanism preserves the stability and accuracy of the indicator system under shifting data distributions and emerging feature dependencies.

5. Conclusions

The composite, multi-purpose resource-based security indicator system (RSI) presented in this paper provides decision support for resource-driven choices in a macro-level organizational system that features multi-tier governance and a high uncertainty — both in the hostile external environment and in rapidly shifting internal priorities.

The RSI framework classifies resource situations with machine-learning methods trained on historical observations and expert judgements, while clearly representing stakeholder needs and environmental changes. For every strategic or operational interest, a set of alternative well-being estimates acts as an individual indicator; well-being is analyzed in two complementary aspects: • Performance aspect — the degree to which the interest is achieved from the stakeholder perspective. • Resource aspect — the degree to which available resources meet the normative and planned levels defined by the hybrid management schemes in use.

Four composite functional indicators are produced by integrating individual indicators and cross relating the well-being of different interests. They support resource-conditioned decision making in the following directions: 1. Express diagnosis of resource risk to strategic interests (rapid detection of problem situations); 2. Vulnerability ranking (prioritizing interests and resources at risk); 3. Criticality of external factors (assessing the impact of threats from the environment); 4. Diagnostic of strategic adaptation needs (identifying elements of the current strategy that may require realignment).

The algorithm for the first indicator — express diagnosis of problem situations — forecasts the performance well-being of strategic goals on the basis of routine resource monitoring, interim assessments of crisis-management tasks, and capability status. A heterogeneous ensemble of binary classifiers is employed; their outputs are merged through weighted voting, where the weight equals the argumentation index that combines (i) the data-conformity coefficient — how well the classifier’s statistical assumptions match the observed data — and (ii) an aggregate quality score compiled from imbalance-robust metrics. This mechanism yields a robust indicator under prior uncertainty about data distributions and automatically triggers model retraining when conformity degrades.

Machine learning therefore becomes not merely a technical means of constructing the RSI but a core component of an intelligent decision-support platform for problem areas (PA) of the MDM class. Future work will extend the approach to the other composite indicators, employing multi-class classification and hybrid time-series forecasting, and will equip the indicator algorithm with a dedicated multi-criteria evaluation module that combines several imbalance-robust metrics into the aggregated quality score KQi. A concrete application is foreseen in the analytic integration of defense-resource information for decision support within the national-security domain.

Declaration on Generative AI

During the preparation of this work, the authors used OpenAI ChatGPT to translate text from Ukrainian into English and to rephrase sentences for improved clarity, conciseness, and style. After using this tool, the authors reviewed and edited the content as needed and take full responsibility for the publication’s content. [48] R. Akbani, S. Kwek, N. Japkowicz, Applying support vector machines to imbalanced datasets. In:

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