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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Models, Methods and Technological Usage of Expert Knowledge Formalization for Strategic Decision Making under Deep Uncertainty</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Olena Ilina</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Igor Sinitsyn</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Olga Slabospitska</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Institute of Software Systems of the National Academy of Sciences of Ukraine</institution>
          ,
          <addr-line>Academician Glushkov Avenue, 40, Kyiv, 03187</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>The paper aims at Expert Knowledge formalizing and technologically using for Proactive Anti-crisis Strategic Decisions making under deep uncertainty within dedicated ExpertAnalytical Methodology named DMDU EAM. DMDU EAM benefit is no essential resource demands while keeping the basic principles to deal with deep uncertainty (uncertainties and inconsistencies eliciting; Decision vulnerabilities searching instead prediction; Decision resilience against threats prior its effectiveness). Knowledge operation is enabled with DMDU EAM procedures such as formal analysis, individual expert assessment, Decision elements deliberative forming. Domain Ontologybased common information space ensures equal participants' awareness, expert judgments and their arguments constructive representation and knowledge reuse. Expert-analytical Proposals Selecting uses their Perspectivity Model. It is a sub-goals hierarchy where the nodes are represented with ontologically formalized definition for State of the Art corresponding sub-goal achievement. Leaf node depicts State of the Art with explicit expert Estimates of Certainty factor (from the Stanford algebra) being provided concerning its implementation through Decision element Proposal being assessed. Perspectivity Model also contains conditions for goal achievement violation being caused with environmental threats. Procedures for Estimates formal integration up to the Model provide extreme estimates of Proposals Perspectivity and Robustness regarding current uncertainty. Under unsatisfactory properties of integrated Estimates their deliberative adjustment is carried out using Uncertainty Map and arguments provided. The final reference Decision contains selected Goal-Means option and Recommendations to adapt it when Decision frame changes. EAM DMDU enables Deliberative multi-staged Process for Adaptive Decision forming aimed at expected future Crisis situation resolving. Further research is carried out for EAM DMDU instrumental tools development and its usage for defense resource management.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Problem statement</title>
      <p>prospectively impacted Model; impact Outcomes; these Outcomes’ importance within various
stakeholders Views.</p>
      <p>Basic methodological decision-making trends within DMDU problem area are Robust Decision
Making [3], Dynamic Adaptive Planning [4] and Dynamic Adaptive Policy Pathways [5]. They can
be referred to as global methodologies because consider the possible states of the world broadest
range.</p>
      <p>In modern OMS rapid and non-anticipated changeability of Factors and Priorities as well as
multivector Interests to be considered contribute drastically in Strategic and Proactive Decision making
concerning anti-crisis measures and development opportunities capturing.</p>
      <p>But high requirements that basic DMDU Methods pose to the Repository being created with model
experiments results make these Methods troublesome under resource limitations in place most of the
time. That’s why borrowing underlying Principles of DMDU Methods above (being elaborated for the
State and International management levels – defense planning, climate change anticipation etc.) is of
vital importance for dedicated Methodology elaboration that is resource-friendly for smaller-scale
OMS with limited capabilities.</p>
      <p>The paper presents a variant of such Methodology entitled DMDU Expert-Analytical Methodology
(DMDU EAM) as a compromise approach capable foundational DMDU principles to borrow but with
the emphasis shifting from the above Decision Space global modeling to professional knowledge and
experience of high-skilled domain Experts effective involving.</p>
      <p>DMDU EAM does not aim at global approaches full-fledged replacement. It does not provide
proved properties of Decisions and sets essential requirements for Expert skills, especially at the stage
of basic models preparing for further reuse.</p>
      <p>It benefits with:
1. Handling various types of uncertainty;
2. Capturing all Proactive anti-crisis Decision life cycle stages – from Problem Situation analysis
to Reference Decision adjustment for operational situation;
3. Meeting DMDU foundational principles including:
• Uncertainties and inconsistencies eliciting and specifying;
• Shifting the emphasis from the future predicting to vulnerabilities searching for Decision being
made with respect to possible threats from the future;</p>
      <p>• Searching for Decision options that are the most robust with respect to threats regarding all
essential aspects of its effectiveness;
• Preventive impacts elaboration on external environment for risks mitigation of possible threats.</p>
      <p>A particular aspect of the Methodology proposed is a Deliberative expert process [6, 7]
implementation including Experts presenting various viewpoints on Decision problem area.</p>
      <p>The standardized DMDU process being proposed and structured in [1] to compare the various
methods being developed combines the stages as follows:
• Process architecture defining with respect to adaptation mode;
• Alternatives and future scenarios exploration;
• Robustness analysis;
• Vulnerability analysis.</p>
      <p>Table 1 compares DMDU EAM with global methodologies based on solutions for these steps.</p>
      <sec id="sec-1-1">
        <title>Global methodologies’ Support</title>
      </sec>
      <sec id="sec-1-2">
        <title>Contrasting Adaptivity</title>
      </sec>
      <sec id="sec-1-3">
        <title>Paradigms: Protective (protect</title>
        <p>basic plan against
contingencies) vs. Dynamic
(sequencing of alternatives
conditional on observed future)</p>
      </sec>
      <sec id="sec-1-4">
        <title>Uncertainty connected with the Specifying various uncertainty types</title>
      </sec>
      <sec id="sec-1-5">
        <title>EAM DMDU Support</title>
      </sec>
      <sec id="sec-1-6">
        <title>Providing the most promising policies</title>
        <p>among those being considered with
guides to adapt them when adjusting
information undetermined at their
elaborating stage</p>
      </sec>
      <sec id="sec-1-7">
        <title>Global methodologies’ Support future.</title>
      </sec>
      <sec id="sec-1-8">
        <title>Policies efficiency modeling</title>
        <p>under all possible states of the
world (scenarios)</p>
      </sec>
      <sec id="sec-1-9">
        <title>Determining the scenario space basis and multi-component policy efficiency model</title>
      </sec>
      <sec id="sec-1-10">
        <title>External threats "Red Teams" [8] best practices</title>
        <p>eliciting for exercising with the proper goal
internally provided trees for further scenario space</p>
      </sec>
      <sec id="sec-1-11">
        <title>Alternatives updating with the threats effectiveness elicited Alternatives analysis</title>
      </sec>
      <sec id="sec-1-12">
        <title>EAM DMDU Support</title>
        <p>regarding Decision implementing
conditions, alternatives parameters and
results of decision making process
interim stages.</p>
      </sec>
      <sec id="sec-1-13">
        <title>Expert assessment of Alternatives perspectivity under the worst and the best parameter values</title>
      </sec>
      <sec id="sec-1-14">
        <title>Alternatives considering for both impacting goals and their achieving means.</title>
      </sec>
      <sec id="sec-1-15">
        <title>Alternatives Perspectivity defining based</title>
        <p>on state of the art hierarchy for which</p>
      </sec>
      <sec id="sec-1-16">
        <title>Expert confirmations or refusals of</title>
        <p>reachability under conditions
given with current uncertainty determine</p>
      </sec>
      <sec id="sec-1-17">
        <title>Certainty factor in Decision objects’</title>
        <p>target state providing with given</p>
      </sec>
      <sec id="sec-1-18">
        <title>Alternatives implementing</title>
      </sec>
      <sec id="sec-1-19">
        <title>Alternatives Perspectivity assessment</title>
        <p>(optimistic and pessimistic) with
considering an option to adjust
conditions of current evidences’’
sufficiency loss for hypothesis certainty
factor assessment</p>
      </sec>
      <sec id="sec-1-20">
        <title>Considering threats that cancel inputs of some nodes within state of the art hierarchy</title>
      </sec>
      <sec id="sec-1-21">
        <title>External threats and enabling factors</title>
        <p>from the Decision frame eliciting with</p>
      </sec>
      <sec id="sec-1-22">
        <title>Critical System Thinking methods [9].</title>
      </sec>
      <sec id="sec-1-23">
        <title>Representing threats within the</title>
      </sec>
      <sec id="sec-1-24">
        <title>Robustness model that thus enhances</title>
        <p>the Perspectivity model
Evaluated for alternatives, whose expert
assessment of the prospects of a thing is
beyond the threshold value, as the
savings of the prospects in case of influx
of threats for the obvious
nonobviousness of the situation, the Decision
and the parameters of the alternatives</p>
      </sec>
      <sec id="sec-1-25">
        <title>Using Information Uncertainty Map and properties of decision-making process interim stages’ outputs for guides obtaining towards further adaptation</title>
      </sec>
      <sec id="sec-1-26">
        <title>Formal procedures using for Expert judgments integrating and aggregating with diagnostics of the consistency level</title>
      </sec>
      <sec id="sec-1-27">
        <title>Efficiency assessment or choice based on efficiency – over the entire scenario space or critical zones being elicited</title>
        <p>Being evaluated: as efficiency
loss minimum with respect to a
given efficiency basic level
under some state of the world
or as the number of world’s
states where given efficiency
threshold is achieved for
alternative</p>
      </sec>
      <sec id="sec-1-28">
        <title>Scenarios characteristics</title>
        <p>finding that are critical for
uncertainty impact</p>
      </sec>
      <sec id="sec-1-29">
        <title>Critical areas identifying within the spaces of policies and states of the world</title>
      </sec>
      <sec id="sec-1-30">
        <title>Expert involvement for experimental data analysis outputs interpretation without</title>
      </sec>
    </sec>
    <sec id="sec-2">
      <title>2. ЕАМ DMDU General Description</title>
      <p>The methodology purposes at supporting deliberative multi-stage PD Process of an adaptive
Decision forming, aimed at the Crisis situation anticipating in the future to resolve. The process model
looks like the tuple</p>
      <p>MPD =&lt; I,{ &lt; KD,MST (KD) &gt; },MUI,WUI,{MEti }i6=1 &gt; ,
where I is the common information space; KD is Decision type; MST (KD)– problem statement
model for KD -typed Decisions; MUI ,WUI are information uncertainty model characterizing data
from I that PD process uses and, respectively, selected modes of uncertainty handling within the
Process stages’ procedures; MEti is the model of i-th PD Process stage – one of its ten subsequent
stages. These are as follows: Problem situation analysis; Goals proposing for Problem situation to
impact; Assessing the goals Proposals provided; Measures proposing to achieve the Goal adopted;
Assessing the measure Proposals provided; Reference variant selecting and adaptation options
analysis.</p>
      <p>The structure of common information space I is characterized with such a tuple:</p>
      <p>I = &lt; OM,O,{DS}, { SM(KD)},P ,PM &gt; (2)
where OM is an ontological model for OMS Decisions problem area; O is the list of objects being
processed during PD process stages; DS are information sources that could be used for objects O
states identifying; SM (KD)is a frame model for a Decision with given type that identifies ontology
concept essential for procedures P from MEti based on the previous expertises retrospective data and
activity experience; P are the procedures for State of the Art concerning given objects O formal
identifying based on {DS}; PM are the procedures for SM (KD) models interpreting based on DS
information.</p>
      <p>An ontological model</p>
      <sec id="sec-2-1">
        <title>Global methodologies’ Support</title>
        <p>procedural regulations</p>
      </sec>
      <sec id="sec-2-2">
        <title>EAM DMDU Support</title>
        <p>being achieved acceptability and
potential sources of inconsistencies.</p>
        <p>Passing to deliberative procedures using
the interactions protocol and
argumentation formats being provided
when it is required
(1)
(4)
(5)</p>
        <p>OM = STR ∪ ACT∪ ENV ∪INT ∪PL∪DEC (3)
combines inter-referenced ontologies characterizing various OMS aspects: components and structure
( STR ); activity ( ACT ); factors of activity external environment ( ENV ); external stakeholders
interaction ( INT ); goals, priorities and planning programs ( PL ); strategic and operational Decisions
( DEC )..</p>
        <p>The model is based on dedicated knowledge conceptualization [10].</p>
        <p>It provides for all the concepts CEBAS from the stage models MEt (See (1)) their ontological
definitions</p>
        <p>Def(CEBAS ) = {(Ri ,CEi )}iN=B1AS ∪{PARK (CEBAS )}kM=B1AS
where CEi is a concept from OM not belonging to CEBAS ; Ri is a relation linked CEBAS and CEi ;
PARK is a concept CEBAS parameter with the values range Z(PARK ); NBAS , MBAS is the number of the
above CEBAS properties.</p>
        <p>Object O(CEBAS ) that is an information element of stage model MEt interpretation for a specific</p>
        <sec id="sec-2-2-1">
          <title>Decision is defined as INT(Def (CEBAS )) interpretation:</title>
          <p>∀ i∈(1,NBAS )INT(CEi ) = O(CEi )</p>
          <p>INT(Ri )∈(0,1); ∀i ∈(1,MBAS ) INT(PARK )∈ Z(PARK )
where ST(Ri ) = 0 means that object O(CEBAS ) has not the property mentioned.</p>
          <p>The state of object O at a fixed moment t</p>
          <p>S(O,t ) = INTt (Def (CEBAS )) (6)
is thus defined through the states at moment t of those objects and relations that constitute CEBAS
properties and also current values of their parameters.</p>
          <p>Based on (4)-(6) one could define the Sate of the Art for the set of objects {O} at moment t</p>
        </sec>
        <sec id="sec-2-2-2">
          <title>SS({O},t ,DSa ) being informationally confirmed as follows:</title>
          <p>S(O,t ) = INTt (Def (CEBAS )) . (7)
Informational DSa - confirmation is made with the P procedure from (2) or with Expert statement by
means of mapping</p>
          <p>({O},{ DSa (t )}, ) → { S(O,t )} (8)
where DSa ⊆ DS is a subset of information sources representing data concerning objects O.
Procedure PM from (2) semantics is given with the mapping</p>
          <p>PM : ( SM(KD),dec ,t ,DSdec (t )) → ISM(dec ,t ) (9)
where SM is the Decision Frame model for KD -typed Decisions with the composition of
SM = {C C ∈ OM} corresponding the subset of ontological model concepts representing current
conditions for those Decisions making and implementing stages; dec is a KD -typed Decision; t is a
time moment; DSdec (t ) ⊆ DS is a subset of information sources containing information about the state
of Def(dec) objects valid at t moment; ISM(dec ,t ) is a State of the Art SS({OI },t ,DSa ) concerning
the set of objects OI that interpret SM according to the rules (5).</p>
          <p>The Problem Statement model from (1) looks like</p>
          <p>MST(KD) =&lt; MCR,{ &lt; CTRi ,CPi , CONTi &gt;}i6=1 &gt;,
where MCR is an anticipated crisis model:</p>
          <p>MCR =&lt; CCr ,ICr , SCr &gt;,
where CCr is a set of those ontology concepts that their states interrelations constitute an anticipated
crisis contradiction; ICr are information sources to CCr characterize; SCr are ontologically specified
States of the Art being considered as crisis symptoms; CTRi are acceptance conditions of i-th stage
results; CPi are the requirements for the stage expert group; CONTi is an information context
recommended for the stage.</p>
          <p>The structure of the stage model from (1) is as follows:</p>
          <p>MEti = {Eij } 1j=01 ,
(10)
(11)
where the j-th type of i-th stage element Eij is as follows: Ei1 – output information structures from (1),
(2), (10) models and the previous stages results; Ei2 – an information context; E i3 – Expert judgment
structure and argumentation reference model; Ei4 – procedures for source data automated preparing;
E i5– procedures for Problem Statement and Expert judgments reference model deliberative
enhancing; Ei6 – procedures for individual expert judgments providing and arguing support; Ei7 –
procedures for expert judgments formal integrating and aggregating; E i8 – the stage result and its
properties; E i9 – Information Uncertainty Map for the result; Ei10 – procedures for commonly
acceptable result deliberative forming with iterative identifying of 8th and 9th element types.</p>
        </sec>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>3. Perspectivity and Robustness Models of Decision Element Proposal</title>
      <p>The tools for knowledge (related to various aspects of Decision problem area and pertaining to
various sources and holders) interaction, alignment and agreement are proposed to be dedicated
Models of Decision element Proposal, namely its Robustness with respect to external threats and
Perspectivity.</p>
      <p>With these Models Proposals are considered for two Decision elements such as the Goal of
Problem Situation impacting (Res3 within Et3 stage model) and the Way to achieve this Goal (Res5
within Et5 stage model), See (11).</p>
      <p>Let’s define the result of decision dec (modeled with (1)) making process completed at time
moment t as a sequence
where Re si is E i8 element of the i-th stage model (see (11)), considered as SS (Oi8 , t, PR) (See (7)),
PR∈{DS} – decision execution protocol і ∀o ∈Oi8 o = INT(Def (Resi )) (See (5)).</p>
      <sec id="sec-3-1">
        <title>The perspectivity PER ( ALij ,EX k ) of j-th Proposal ALij being considered over i-th stage within</title>
        <p>6
{Re si }i=1</p>
        <p>CF (HO | Arg(EX k ))
expert EXk knowledge is defined as the level of certainty
for hypothesis</p>
        <p>Ho : (Re si →Re si−2 )
based on argumentation given by the Expert EX k .
(12)
(13)
(14)
(16)</p>
        <p>The perspectivity model MPERSiKD (і – stage number, KD – Decision type) constructively clarifies
its representation (13) using the Stanford fuzzy inference method based on certainty factor [11].</p>
      </sec>
      <sec id="sec-3-2">
        <title>Let's define the facilitation ratio RH( X1 , X 2 ) between the States of the Art X1 , X 2 with the metrics</title>
        <p>of certainty factor for the hypothesis</p>
        <p>X1 → X 2 (15)
X1 = SS (O1, t1, D1); X 2 = SS (O2,t2, D2); O1,O2 ⊆ ISM (dec,T ) (See (9)); T is the period Decision
making; t1, t2 ∈T ; D1, D2 – information sources from {DS} in (2).</p>
        <p>The Perspectivity model is proposed to be the tuple</p>
        <p>MPERS = &lt; PER ,{ &lt; Aj , TRj &gt;} Nj=1 , Sc &gt;
where PER is an integral perspectivity indicator corresponding the target State of the Art; Aj – j-th
perspectivity aspect related with k-th ontology from (3); TR j is the States of the Art hierarchy that
specializes aspect Aj as a sub-goals tree for target State of the Art achieving where the elements are
in turn represented as the States of the Art for corresponding objects; Sc is a verbal scale used to
evaluate both PER and other model nodes as certainty factor [11] for corresponding State of the Art.</p>
        <p>The scale is characterized in table 2.</p>
        <p>(clk ∈CL) = &lt; ndir ,s1 ,{ nd( r−1),s2 }sS2=1 ,CFk &gt;
(nd(r−1), s2 ∈(NDI ∪ NDL)) ∧ RH(nd(r−1), s2, ndir,s1)
where ndir ,s1 ∈NDI is the root of a bush; nd is a node of the bush that specifies a State of the Art
satisfying the condition (See (15)); S is the nodes’ number; CFk is an optional element of clk
definition setting the condition</p>
        <p>CF k({e ∈ISM(dec ,T ) ∪ def ( ALT )}), (18)
formalizing the set { nd( r−1),s2 }sS2=1 non-validity as the rational for the estimate of certainty factor
related to hypothesis regarding the State of the Art ndir,s1 .</p>
        <p>The perspectivity model thus defined with (16) – (18) is assumed to be elaborated beyond the PD
Process (1) for further multiple reuse concerning certain class of Decisions (specified with ontological
classes of concepts from the Crisis model within (10) and/or the measures proposed class).</p>
        <p>An individual expert estimate of certainty factor being provided during PD Process (1) for a</p>
      </sec>
      <sec id="sec-3-3">
        <title>MPERS leaf Li by Expert Ek concerning the Proposal ALj is a triple</title>
        <p>EASijk = &lt; ASiOjkP , ASiPjk , Argijk &gt;</p>
        <p>Arg = { DE , OCH , ONTK(OCH , AL), &lt; UI , Z OP , Z P &gt;}
where AS OP and AS P are both the estimates up to Table 2 scale corresponding the most and
respectively the least appropriate meanings of CON and EB from (17) elements being incompletely
defined; Arg is the argumentation; DE is a context element being used; OCH ⊆{O}, O is pertinent to
the State of the Art Li definition; ONTK denotes the ontological relationships determining the
elements interdependencies used by Expert; UI is DE ’s information uncertainty type; Z OP , Z P are
respectively the best and the worst DE ’s suitable meanings.</p>
        <p>Individual estimate of integral perspectivity indicator PER from (16) is proposed to obtain through
estimates EASijk (19) integrating under k , j being fixed up to the rule [12] of certainty factor
estimates multiplying for the set of independent evidences of the same hypothesis validity.</p>
        <p>For the root ndm of a bush with S leaves being estimated with { ASi }iS=1</p>
        <p>ASm = (( AS1 ∗ AS2 ) ∗ AS3 ) ∗ ...) ∗ ASS )
where operation ∗ semantics is as follows:</p>
        <p>ASS1 ∗ ASS2 = ASS1 + ASS2 – ASS1 ⋅ ASS2 , AS1, AS2 &gt; 0</p>
        <p>ASS1 ∗ ASS2 = ASS1 + ASS2 – ASS1 ⋅ ASS2 , AS1, AS2 &lt; 0</p>
        <p>ASS1 ∗ ASS2 =( ASS1 + ASS2 ) / (1− min( ASS1 , ASS2 ) otherwise</p>
        <p>Those Proposals being evaluated for which at least one optimistic expert estimate of integral
perspectivity indicator under 0.3 or no its pessimistic estimates over 0.3 is obtained are eliminated
from further considering as unacceptable.</p>
      </sec>
      <sec id="sec-3-4">
        <title>Considering ndm as a node of an interim bush rooted with ndm−1 and using its estimate obtained</title>
        <p>ASm the estimates of interim root ndm−1 are further calculated and so on in such a way up to the root
Aj of the tree TR j and finally – an individual estimate of integral perspectivity indicator PER for ALj
Proposal.</p>
        <p>Performing the above described procedure twice – for both optimistic and pessimistic estimates of
all the nodes of the Perspectivity model (see (19)) – provides the pair of estimates
&lt; AS OjkP , AS Pjk &gt;
(19)
(20)
(21)
(22)</p>
      </sec>
      <sec id="sec-3-5">
        <title>An input of CFS into the estimate AS jk due conditions violation of the evidences sufficiency for</title>
        <p>the s-th bush root (18) is calculated in such a way.</p>
      </sec>
      <sec id="sec-3-6">
        <title>During integrating the direct leaves’ estimates according to the rule (21) CFS validity is verified</title>
        <p>under the current values of its operands (18). Validity confirmation provides for nd S an input 0
regardless of the bush nodes estimates.</p>
        <p>The estimates AS OjP , AS Pj (being the results of corresponding individual estimates (22)
generalizing through averaging with respect to Experts list) are proposed to further subject the
procedure of collective Expert approval. In case of objections and/or inconsistencies the deliberative
procedure is performed based on the principles of iterative Delphi process proposed earlier in [13] and
estimates’ argumentation elements (19), (20) considering.</p>
        <p>The Perspectivity model (16) – (18) could be enhanced with external threats specification that
cancel the node ndm of the tree Tj from (16) validity as an evidence concerning the certainty factor of
predecessor node. The corresponding specification is represented with the tuple:</p>
        <p>&lt; {THFmr , { F F ∈OM}, C r ({ SS (F ,t ,{ Argik }kK=1 }rR=1 ) &gt; (23)
where THFrm is the r -th threat to ndm node being an event not necessarily pertain to OM ontology;
F ∈ SM is a factor influencing THFrm actualization; t is a time moment; Argik is an argumentation
provided by the Expert k for i -th leave assessment serving as an information source about State of
the Art concerning Fr factor; Cr is a condition of Fr actualization.</p>
        <p>Then the estimate of integral perspectivity indicator PER from (16) for AL being calculated with
considering CF conditions could be modified by assigning the value –1 to all the nodes ndm
satisfying at least one of Cr conditions.</p>
        <p>Let’s denote PER OjkP , PER Pjk and PER ∗jkOP , PER ∗jkP the estimates of ALj Proposal by k -th Expert,
integrated without and, respectively, with considering C and CF conditions.</p>
      </sec>
      <sec id="sec-3-7">
        <title>Then the robustness indicator of the generalized estimate for ALj proposal is proposed to define as</title>
        <p>a pair:</p>
        <p>K K (24)
ROBj =&lt;1/ K ∑ PER∗jkOP − PEROjkP , 1/ K ∑ PER∗jkP − PERPjk &gt;</p>
        <p>k =1 k =1</p>
        <p>The estimates obtained of perspectivity and robustness are used at the stages of proposals
assessment:
• To initiate the procedure of individual estimates deliberative agreement;
• As input data for this procedure and the procedure of unacceptable Proposals screening.</p>
        <p>At the stage of final selecting the Decision option these estimates are used for both merely
selecting and Decision adaptive capabilities analyzing.</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Uncertainty Handling</title>
      <p>Information uncertainty with various causes and forms concerning various elements of PD
process for reference Decision forming (See (1)) is one of inspiring factors PD process to support.
The most important information structures of this process for which elements definition
incompleteness impacts the input data and performing modes of procedures at the process stages are
as follows: Assessment context, Alternative Proposal Specification and argumentation and Operands
of conditions pertinent to Perspectivity model.</p>
      <p>Element’s current information uncertainty is characterized with a pair</p>
      <p>&lt; UR , UF &gt; (25)
where UR is the cause of uncertainty, one of the following: 1 – available facts unawareness, 2 –
processes operation volatility and dynamicity, 3 – stakeholders’ viewpoints conflicts, 4 –the system of
business interests and viewpoints instability; UF is an information presentation format, namely: 1 –
information array with gaps, 2 – a set of options pertinent to various business groups, 3 – a set of
meaning versions equally plausible at the forming time; 4 – element representation with some
conceptual components being omitted; 5 – meaning interval localization.</p>
      <p>The modes of data with information uncertainty represented by means of a given format and
localized within the above-mentioned information structures operating within three basic procedures
of PD process are characterized with Table 3.</p>
      <p>Information about each information element used for reference Decision elaborating is proposed to
represent by means of the Uncertainty Map UCARD , as an essential component of PD Process results.
Within UCARD , an information element EL is characterized with a structured tuple:</p>
      <sec id="sec-4-1">
        <title>Alternative</title>
      </sec>
      <sec id="sec-4-2">
        <title>Proposals individual assessment</title>
        <p>UCH(El ) = { &lt; Et i ,UF ,UR, { &lt; ZKOPT (EL), ZKPES (EL) &gt;}KK=1 ,&lt; ZGOPT (EL),ZGPES (EL) &gt;,N1 ,N2 ,N3 ,N4 }iI=1
(26)
where Et i is the stage where the information is used in procedures; UF , UR correspond (24);
Z OPT , ZKPES are the most and the least appropriate EL ’s meanings accepted by k -th Expert; Z OPT , ZGPES</p>
        <p>K G
are the corresponding meanings being formed by deliberative procedures; N1 is the relative frequency
of using EL by Experts; N 2 is the proportion of model MPERS leaves being assessed with EL ;
N3 ,N4 are respectively the proportions of C and CF conditions from MPERS (See (18)), for which
EL is actual.</p>
        <p>Uncertainty map is used during Analytical Review of reference Decision engineering for its further
operational use. Recommendations within Analytical Review addresses:
• Conditions of PD process results direct using and the list of their suitable constituents;
• Results’ elements requiring adaptation as well as operations necessary for it;
• Knowledge components represented with the elements of reference Decision, suitable for reuse
over DMDU processes with MPD model (1).</p>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>5. Adaptive Reference Decision Elaborating</title>
      <p>Previous sections specify PD Process of forming an adaptive Decision within DMDU EAM
methodology as:
• The sequence of stages and their execution information environment (see (1), (2));
• The set of informational and procedural elements with prescribed types as constituents of the
Process stage (see (11));
• The way of Expert knowledge organizing used for the analysis of Proposals perspectivity
property and this property Robustness under the conditions of available information uncertainty of
various forms.</p>
      <p>This section provides a high-level and integrated description of activities sequence over this
Process based on aspects considered with previous sections and further detailizes some stages and
procedures.</p>
      <p>The sequence of PD Process stages is linear, but allowes for iterative cycles within the stages.
The First Stage.</p>
      <p>Deliberative procedure of the Problem Statement provided analysis with clarifying and accepting
the Crisis situation Model. Formal definition the class Decision is pertinent to and searching for
analogues being explored. Deliberative procedure of Decision frame description and Information
Uncertainty Map for the information elements accepted.</p>
      <p>The Second Stage.</p>
      <p>Proposals creating related to the goal of the Crisis situation impacting (direct or indirect) with
identifying the impact’s object and its current state. Proposal’s argumentation forming in terms of
used ontological relationships and precedents as well as relevant professional and domain experience.</p>
      <p>The Third Stage.</p>
      <p>Reference Perspectivity model updating for the impacting goal. Revising sub-goals considered in
reference Perspectivity model. Eliciting additional conditions for given sub-nodes of the hierarchy
nodes sufficiency properties violation. Update the set of external threats to sub-goals represented with
the hierarchy nodes. Supplement the Sates of the Art being assessed directly and recommended
assessment context.</p>
      <p>Individual and group procedures of critical system thinking [9] are used for the activities above as
well as deliberative procedure of Perspectivity model Harmonized version forming.</p>
      <p>Providing optimistic and pessimistic meanings of information context undefined elements.</p>
      <p>Procedure performing of certainty factor extreme values individual expert assessment for the
States of the Art corresponding the leaves of Perspectivity model Harmonized version. Identifying the
individual assessment contexts and their elements meanings: optimistic and pessimistic.</p>
      <p>Individual assessment of coefficients of certainty. Information Uncertainty Map updating.</p>
      <p>Integrating estimates formally up to the States of the Art hierarchy. Obtaining the pair of
individual estimates for Proposal ALj &lt; PER OjkP ,PER Pjk &gt;.</p>
      <p>Calculation the pair of estimates &lt; PER ∗jkOP ,PER ∗jkP &gt; formally considering all the limitations and
conditions from the Harmonized version of Perspectivity model.</p>
      <p>Formal analysis of individual perspectivity estimates and their generalization with respect to
Experts list: screening unacceptable Proposals and obtaining estimate’s pair &lt; PER OjP ,PER Pj &gt; for
those Proposals that are recognized as acceptable. Formal calculation the Perspectivity’s robustness
estimate for accepted Proposals.</p>
      <p>Adjusting generalized integrated results by the members of expert group. Approval these or
passing to the participatory procedure of adjusting.</p>
      <p>Participatory procedure of the Perspectivity and Robustness estimates adjusting through Delphi
process with expert estimates and their arguments in a tour [13] and also providing the Experts with
the results of previous procedures at this stage. Optional iteration the stage procedures being
performed unsatisfactorily using the information expertly updated.</p>
      <p>The activities above benefit in concordant estimates obtaining, alternative Proposals eliminated
from consideration identifying, optional interrupting the Process to obtain additional information.</p>
      <p>The stage results are as follows: the set of acceptable Proposals regarding the goal of impacting the
Crisis situation; pessimistic and optimistic estimates of these Proposals Perspectivity and Robustness
with their informational arguments; updated Information Uncertainty Map.</p>
      <p>The Fourth Stage.</p>
      <p>Proposals creating related to the measure the goal of impacting the Crisis situation to support.
The Proposal is formed as a quintuple</p>
      <p>PRAij =&lt; Gi , Aij ,Rij , Sij , Argij &gt;
where Gi is one of those impacting goals being recognized as acceptable at the Stage 3; Aij is the j -th
kind of measures (actions); Rij is the description of necessary resources; Sij denotes performing
subjects; Argij is the Proposal argumentation.</p>
      <p>This argumentation provides success precedents for similar target objects, characteristics of
possible side effects and their consequences, resources availability under current Decision frame etc.</p>
      <p>If the measure parameters are set with information uncertainty the Information Uncertainty Map is
respectively updated.</p>
      <p>The Results are represented with the Proposal array {{PRAij }i=1 Mj=1i, where N is the number of
N }
Proposals related to the impact goal being considered; Mi is the number of Proposals concerning the
impact measure provided for Gi .</p>
      <p>The Fifth Stage.</p>
      <p>The sequence of actions being performed at the stage is in whole identical to Stage 3. The
difference is just handling with the reference Perspectivity model for the impacting measures. Besides
that Proposal related to the impacting goal Gi for which all Mi proposals related to the measure
proved to be unacceptable is removed from the list of acceptable ones.</p>
      <p>The Stage results are as follows:
M
{{&lt; PERiOjP ,PERiPj &gt;,&lt; PERi∗jOP ,PERi∗jP &gt;,&lt; ROBiOjP ,ROBiPj &gt;}iN=1 } j=1i
(27)
The Sixth Stage.</p>
      <p>At the stage the following tasks are solved:
• Final selecting the goal of the Crisis situation impacting and the means to achieve it – in
accordance with the current priorities and expectations system;
• Preparing options that are the most acceptable under alternative situation evolving;
• Providing analytical rational for further adaptive usage of the Process results;
• Saving the results for reuse over the further coping of similar Crisis situations.</p>
      <p>The procedure of optimal final selecting uses one of the target function prescribed forms where the
operands are the set (27) elements depending on the Experts answers provided to the check list
questions regarding the essence and weight of their preferences related to such the oppositions: goal
effectiveness/way of goal achieving effectiveness; Perspectivity/Robustness; benefit maximization/
risk minimization; effectiveness under external threats absence/resilience to threats.</p>
      <p>The results of optimization being performed using all the target functions (selected based on each
preferences collection being provided) are submitted to expert group for deliberative adjusting the
final result, namely the «Goal – Way» pair.</p>
      <p>Decision Analytical review that is also pertinent to the stage results is created by means of the
formal procedure using the data from the Information Uncertainty Map.</p>
      <p>Analytical review includes:
• Effectiveness estimate of uncertainty presenting formats and operating modes being used over
PD process (from the perspective of changes being adopted in new iterations and the level of
using by Experts the information provided);
• Level of definability losses estimate being caused with the information uncertainty of a certain
Process element assessment for the Perspectivity estimates;
• Recommendations for using these analytical data to determine: the conditions of the reference
results direct usage, the suitability of certain operations to adapt the reference results, the
appropriate corrections of the process elements for reuse when making similar Decisions.</p>
      <p>Thus PD Process creates knowledge about the Decision and handles it through harmonized
application of formal procedures, individual expert assessment procedures and procedures for
deliberative engineering the process model elements.</p>
      <p>Creating the common information space ensures equal information awareness of participants,
unified format for expert judgments and their argumentation providing as well as storing and possible
re-use of all the knowledge obtained during the Process execution.</p>
      <p>For subsequent reference results obtained adapting over immediate preparing for their operational
use the analytical Recommendations are purposed that enable the Process elements to be revised
determining and adaptation performing subject to the information changes made.</p>
    </sec>
    <sec id="sec-6">
      <title>6. Conclusion and Future work</title>
      <p>The ultimate goal of DMDU EAM methodology elaboration is engineering the tools to support its
formal mechanisms and human-machine procedures information and technological environment that
will allow for DMDU EAM tailoring for the specific OMS domain and management relationships.</p>
      <p>Necessary functional components of appropriate support tools include foremost:
• Software packages (SP) to administer individual and group expertises using the Perspectivity
and Robustness models and enabling typified argumentation analysis;
• Ontological support tools to maintain and align the processes of strategic and anticipatory
anticrisis OMS decisions reference making and adapting;
• Tools to administer the common information environment;
• Components to support multi-stage and iterative Decision life cycle process;
• Techniques to organize and perform human-machine procedures;
• Tools to visualize the processes operation and OMS Decisions system current state.</p>
      <p>Preliminary corresponding work being focused on defense resource management domain is now
performing in the Institute of Software Systems of the National Academy of Sciences (SSI of NAS) of
Ukraine.</p>
      <p>It concerns further development of SP "Diagnostic expertise" [14] that supports handling the
expert evaluation hierarchical multi-criteria model and uses production rules to diagnose the state of
explored object with recommendations providing about suitable further actions with it based on a
comprehensive analysis of individual and aggregated criteria estimates.</p>
      <p>The authors’ rational for complex coordination of logistic Decisions system within the Armed
Forces of Ukraine is characterized in [15].</p>
      <p>The special efforts are currently purposed at including NATO basic logistics software LOGFAS
into the expert-analytical decision-making processes [16]. Corresponding work was launched during
LOGFAS national extension engineering in SSI of NAS of Ukraine.
[1] V. A. Marchau, W. Walker, P. Bloemen, Decision Making Under Deep Uncertainty. From Theory
to Practice, Springer, 2019. doi:10.1007/978-3-030-05252-2.
[2] N. N. Taleb, The Black Swan: The Impact of the Highly Improbable, Kolibri, Moscow, Russia,
2018. [in Russian].
[3] R. J. Lempert, S. V. Popper, D. G. Groves, Making Good Decisions Without Predictions: Robust
Decision Making for Planning Under Deep Uncertainty, CA: RAND, RB-9701. Santa Monica,
2013.
[4] J. H. Kwakkel, W. E. Walker, V. A. Marchau, Adaptive airport strategic planning, Europ. J. of
Transport and Infrastructure Research 10 (2010) 249–273. URL:
https://www.researchgate.net/publication/235428145_Adaptive_Airport_Strategic_Planning.
[5] M. Haasnoot, J. H. Kwakkel, W. E. Walker, J. terMaat, Dynamic adaptive policy pathways: A
method for crafting robust decisions for a deeply uncertain world, Global Environmental Change.
23 (2013) 485–498. URL:
https://www.sciencedirect.com/science/article/pii/S095937801200146X.
[6] What is a DeliberativeProcess?, URL:
[https://www.ncchpp.ca/docs/DeliberativeDoc1_EN_pdf.pdf.
[7] O. Renn, The challenge of integrating deliberation and expertise. Risk analysis and society, in: An
interdisciplinary characterisation of the field, 2004, pp. 289-366. doi:
[8] M. Zenko, Red Team: How to succeed by thinking like the enemy, Basic Books, 2015. URL:
[9] The Applied Critical Thinking Handbook. V.7.0, . University of Foreign Military and Cultural</p>
      <p>Studies, 2015. URL: https://nsiteam.com/the-applied-critical-thinking-handbook-7-0/.
[10] E. P. Ilina, Methods and Models for Employment of the Expert Analytical Knowledge in
Organization Decision Making. Part I. Decisions Knowledge Models, Problems in Programming
1 (2016) 89–101. doi: https://doi.org/10.15407/pp2016.01.089 [In Russian].
[11] D. Heckerman, The Certainty-Factor Model, 1992. URL:.</p>
      <p>http://heckerman.com/david/H92encyclopedia.pdf.
[12] L. Torgo, Rule Combination in Inductive Learning, 2001. URL:
https://www.dcc.fc.up.pt/~ltorgo/Papers/RCIL/RCIL.html.
[13] E. P. Ilina, The Functions and the Methods for the modern paradigms of the Delphi method
support, Problems in Programming 1 (2009) 36–52. URI:
http://dspace.nbuv.gov.ua/handle/123456789/2952 [In Russian].
[14] I. P. Sinitsyn et al., Computer Support of decision making in the fundamental scientific research
programs management using the expert methodology, Preprint, Software Systems Institute of
NAS of Ukraine, Kiev, 2011. [In Russian].
[15] I. P. Sinitsyn, E.P. .Ilina, Models and methods for automated analytic support of the organization
decisions field, Problems in Programming 3 (2017) 93–107. doi:
https://doi.org/10.15407/pp2017.03.113 [In Russian].
[16] I. Yu. Havrylyuk, .M. Yu. Stepanyuk, I. P. Sinitsyn, O. V. Kotelya, About NATO Logistics
System implementation in Ukraine, 2019. URL:
http://defpol.org.ua/index.php/aleia-heroiv/481shchodo-vprovadzhennya-lohistychnoyi-systemy-nato-v-ukrayini [In Ukrainian].</p>
    </sec>
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