Utendaji wa jumla wa solid oxide fuel cell stacks unategemea many interrelated characteristics kama power, open-circuit voltage, gas tightness, electrical efficiency, fuel utilization, start-up time na cycle durability. Kuzichukulia characteristics hizi zote kuwa equally important kunaweza kutowakilisha reliability na durability ya stack kwa usahihi. Study hii inapendekeza new entropy-based Best-Worst Method, yaani entropy-based Best-Worst Method approach, ili kuhesabu relative importance ya performance criteria kutoka evaluations za multiple experts.

Katika classical BWM decision maker kwanza anabainisha most important na least important criterion; kisha anacompare best criterion na other criteria, na other criteria na worst criterion kwa scale ya 1-9. Extension iliyopendekezwa na study badala ya kucombine directly individual BWM results za five evaluators kwa equal average, inahesabu deviation- na entropy-based importance weight kwa kila evaluator. Evaluations zinazochukuliwa kuwa closer to group result na carrying more discriminative information zinapata higher weight.

Katika SOFC example application eight electrical and operational criteria zilitathminiwa. Kulingana na final group weights, most important criterion ni gas tightness yenye %22,42. Inafuatiwa na power yenye %20,62 na open-circuit voltage yenye %17,09. Lowest weight %5,02 ilitolewa kwa start-up time. Weights za five evaluators hazikuwa equal; fourth evaluator alikuwa na largest influence katika group result kwa %45,95.

Average-measure intraclass correlation coefficient kati ya individual evaluations na final group weights ilihesabiwa 0,949 na %95 confidence interval ikapatikana 0,862-0,988. Researchers wana-interpret hii kama high group consistency. Similar ranking ya criteria katika five repeated evaluations pia imewasilishwa kama indicator of stability ya method.

Hata hivyo, study inategemea only five evaluators, eight preselected criteria na single example application. Identities, expertise levels, independence na selection method za evaluators hazijaelezwa. Pia hakuna measured data kutoka actual SOFC stacks wala alternative stack ranking. Kwa hiyo research inaonyesha sampled applicability ya proposed weighting-combination algorithm; haithibitishi kwamba method ni superior katika all sectors au kwamba determined weights ni universal kwa all SOFC designs.

Tatizo kuu la utafiti ni nini?

Solid oxide fuel cell ni electrochemical energy technology inayotumika kuzalisha electricity kutoka chemical energy ya fuel. Main component ya SOFC power system ni fuel-cell stack yenye many cells na interconnect elements. Kulingana na starting approach ya study, performance ya stack inaathiri directly reliability na service life ya whole power-generation system.

Performance ya SOFC stack haiwezi kuelezwa kwa single number. Power inaweza kuwa high huku gas tightness ikiwa insufficient; electrical efficiency inaweza kuwa high huku thermal-cycle durability ikibaki low. Kwa hiyo comprehensive evaluation inahitaji two questions:

1. Ni features zipi zinapaswa kuingizwa katika evaluation?
2. Kila feature inapaswa kuathiri kwa kiasi gani overall performance result?

Second question katika multi-criteria decision-making methods inaelezwa kama “criteria weighting”. Giving high weight to a criterion means performance on that criterion ina stronger effect kwenye final evaluation score.

Main methodological problem ambayo study inajaribu kutatua ni: When multiple evaluators assign different importance weights to same criteria, how can these individual preferences be combined into one group weight fairly, consistently, and while considering information content?

Components za SOFC stack performance

Figure 1 on page 4 ya PDF inaonyesha SOFC stack performance katika five main groups:

Stack schematic upande wa kulia wa figure inaonyesha cathode, electrolyte, anode, anode support na interconnect layers. Fuel flow inaendelea upande wa anode na air flow upande wa cathode. Ndani ya structure hii, gas tightness inachukuliwa kama central performance criterion kwa keeping fuel na oxidant flows katika designed channels.

Kwa nini multi-criteria decision-making method inahitajika?

Multi-criteria decision making ni family of methods inayoruhusu joint evaluation ya multiple na sometimes conflicting criteria. Kwanza importance weights za criteria zinabainishwa; kisha scores za alternatives kwenye criteria zinaweza kucombinewa na weights hizi.

Katika SOFC context, stack haiwezi kuonekana best kwa sababu tu inatoa highest power. Ikiwa long-term durability, gas tightness au thermal-cycle behavior ni weak, high initial power inaweza kutowakilisha superiority katika whole service period. Weighting method inaeleza jinsi different characteristics hizi zinachangia kwenye single comprehensive evaluation.

Classes za criteria-weighting methods

Study inatathmini weighting methods katika three general classes:

• Subjective methods: Generate weights through preferences of experts or decision makers.
• Objective methods: Generate weights through variability, amount of information or intercriterion correlation in data for alternatives.
• Combined methods: Use subjective and objective weights together.

Table 1 katika PDF inalinganisha advantages na limitations za Delphi, AHP, ANP, DEMATEL, BWM, entropy weighting, PCA, CRITIC na various deviation-based methods.

Analytic Hierarchy Process

AHP inaorganize decision objective, criteria na alternatives katika hierarchical layers. Method ni understandable na widely used, lakini inaweza kuhitaji many pairwise comparisons; consistency test inahitajika, na relationships among criteria hazirepresentiwi kila mara.

Figure 2 on page 5 ya PDF inaonyesha target, criterion na alternative layers za AHP. Number ya criteria na alternatives inapoongezeka, comparison connections kati ya layers zinaongezeka rapidly.

Analytic Network Process na DEMATEL

ANP inaweza kurepresent more complex network relationships ambapo criteria at same level zinaathiriana. Hata hivyo, model setup na calculation process ni difficult zaidi.

DEMATEL inalenga visualizing cause-effect relations na interactions among criteria. Hata hivyo, inaweza kutofaa ikiwa criteria hazina clear interaction au ikiwa number ya criteria ni small.

Objective weighting methods

Entropy weighting inatathmini how much different information criterion data contain. Criterion inayotoa greater discrimination among alternatives inaweza kupata higher weight. Hata hivyo, approach hii inategemea data distribution badala ya engineering meaning ya criterion.

PCA inapunguza dimensions kwa kutumia correlations among criteria, lakini resulting components si identical to original criteria. CRITIC inazingatia both data variability na conflict au correlation among criteria.

Kwa nini study ilichagua BWM?

Best-Worst Method inatumia two special comparison vectors badala ya kuhitaji decision maker compare every pair of criteria separately:

1. Importance of best criterion relative to all other criteria,
2. Importance of all other criteria relative to worst criterion.

Structure hii inahitaji fewer judgments kuliko AHP inayotumia full pairwise comparison matrix. Study pia inasisitiza kwamba special comparison structure ya BWM inaweza kutoa more consistent results.

Hata hivyo, classical BWM inabadilisha preferences za one decision maker kuwa weights. Katika real engineering evaluations, views za different experts zinaweza kutumika. Katika case hiyo, si criterion weights pekee bali pia influence ya experts au decision makers kwenye group result lazima ibainishwe.

Critique ya Bayesian BWM

Study inasema Bayesian BWM iliyotengenezwa previously kwa group decision making inamodel pairwise comparisons kwa multinomial distribution. Authors wanakritiki distributional assumption hii kwa kusema importance ratings 1-9 hazichaguliwi na decision makers kwa equal probability na independently.

Hii ndiyo methodological rationale ya paper. Hata hivyo, study haifanyi comprehensive accuracy au predictive comparison kati ya Bayesian BWM na proposed entropy-based method kwenye same data. Kwa hiyo general superiority over Bayesian BWM haijaonyeshwa directly na example application hii.

Classical BWM steps

Step one: Define criteria

Decision maker anabainisha n criteria zitakazoshiriki katika evaluation:

\[ C = \{c_1,c_2,\ldots,c_n\} \]

Step two: Select best and worst criterion

Decision maker anachagua most important criterion kama c_B na least important criterion kama c_W.

Step three: Build two comparison vectors

Superiority ya best criterion over others inawakilishwa na “Best-to-Others” vector:

\[ A_B = (a_{B1},a_{B2},\ldots,a_{Bn}) \]

Superiority ya other criteria over worst criterion ni “Others-to-Worst” vector:

\[ A_W = (a_{1W},a_{2W},\ldots,a_{nW})^T \]

Comparisons zinafanywa from 1 to 9:

• 1: Equal importance,
• 9: Extremely more important.

Step four: Calculate criterion weights

Ideally weight ratios zinatarajiwa ku-match provided pairwise comparisons:

\[ \frac{w_B}{w_j}=a_{Bj} \]

\[ \frac{w_j}{w_W}=a_{jW} \]

Kwa sababu equalities hizi zinaweza kutosatisfied exactly katika real judgments, optimization inayominimize deviation inasolvewa. Linear BWM iliyotumika katika example application ni:

\[ \min \xi^L \]

\[ |w_B-a_{Bj}w_j|\leq \xi^L,\quad j=1,\ldots,n \]

\[ |w_j-a_{jW}w_W|\leq \xi^L,\quad j=1,\ldots,n \]

\[ \sum_{j=1}^{n}w_j=1 \]

\[ w_j\geq0 \]

• w_B: Weight ya best criterion,
• w_W: Weight ya worst criterion,
• w_j: Weight ya criterion j,
• ξ^L: Optimized value ya maximum deviation kati ya comparisons na weights.

ξ^L inapokaribia zero, internal consistency ya judgments inachukuliwa kuongezeka.

Consistency ratio

Katika classical BWM consistency ratio inafafanuliwa kama:

\[ CR=\frac{\xi^*}{CI} \]

• ξ*: Inconsistency value obtained from optimization,
• CI: Consistency index depending on comparison value between best and worst criteria.

Table 2 katika PDF inatoa CI values 0,00; 0,44; 1,00; 1,63; 2,30; 3,00; 3,73; 4,47 na 5,23 wakati comparison value inaongezeka kutoka 1 hadi 9. CR inapokaribia zero, comparisons zinachukuliwa kuwa more consistent.

Multiplicative BWM

Study pia inawasilisha multiplicative BWM inayotumia logarithms za comparison values pamoja na classical na linear models. Baada ya logarithmic weights kuhesabiwa katika optimization, original criterion weights zinapatikana kwa exponential transformation na normalization:

\[ w_i=\frac{\exp(v_i)}{\sum_{j=1}^{n}\exp(v_j)} \]

Katika first stage ya proposed entropy-based group approach, classical, linear au multiplicative BWM yoyote inaweza kutumika. Linear model ilichaguliwa katika SOFC example application.

Structure ya entropy-based group BWM

Proposed method ina three main stages:

1. Calculate each decision maker's personal criterion weights with BWM,
2. Calculate each decision maker's importance weight within group,
3. Combine personal criterion weights with iterative model based on relative entropy.

Deviation weight ya decision maker

Total squared deviation kati ya personal weights za decision maker k na group weights katika iteration d inahesabiwa kama:

\[ R_k^d=\sum_{j=1}^{n}(W_j^d-W_j^k)^2 \]

• W_j^d: Group weight at iteration d,
• W_j^k: Personal weight assigned by decision maker k,
• R_k^d: Total deviation between personal decision and group result.

Deviation inapoongezeka, deviation-based weight ya decision maker inapungua. Normalized deviation weight ni:

\[ r_k^d=\frac{1/R_k^d}{\sum_{k=1}^{m}(1/R_k^d)} \]

Hivyo evaluation closer to group result inapata higher deviation weight.

Entropy weight ya decision maker

Entropy component inatumika kuwakilisha information content ya decision maker's preference distribution over criteria. Katika PDF, entropy ya decision maker imejengwa kutoka normalized distribution ya ratios za personal weights relative to group weights.

Normalized entropy value kwa ujumla inaelezwa kama:

\[ s_k^d=\frac{E_k^d}{E_k^{\max}}=\frac{E_k^d}{\log_2 n} \]

Kisha entropy weight ni:

\[ e_k^d=\frac{1-s_k^d}{m-\sum_{k=1}^{m}s_k^d} \]

.

• E_k^d: Entropy ya decision maker katika relevant iteration,
• n: Number of criteria,
• m: Number of decision makers,
• s_k^d: Normalized entropy,
• e_k^d: Entropy-based decision-maker weight.

Kulingana na interpretation ya study, less discriminative na more similar preferences across criteria zinaonyesha greater disorder au entropy. Entropy weight inalenga kuaccount for discriminative information carried by decision maker's preference distribution kwa group.

Final decision-maker weight

Deviation na entropy weights zinacombinewa linearly:

\[ U_k^d=\alpha r_k^d+\beta e_k^d \]

Katika SOFC application:

\[ \alpha=0{,}6 \]

\[ \beta=0{,}4 \]

zilichaguliwa. Kwa hiyo %60 ya decision-maker weight inabainishwa na closeness to group result na %40 na entropy component.

Study inasema coefficients hizi zinaweza kuchaguliwa na decision makers kulingana na characteristics za problem. Hata hivyo, kwa nini α = 0,6 na β = 0,4 ni more appropriate than other possible pairs haijaonyeshwa kwa experimental au theoretical optimization.

Combining personal weights into group weight

Criterion weights za decision makers zinahesabiwa kwa weighted geometric aggregation iliyoexponentiwa kwa decision-maker importance:

\[ W_j^d= \frac{\prod_{k=1}^{m}(W_j^k)^{U_k^d}} {\sum_{j=1}^{n}\prod_{k=1}^{m}(W_j^k)^{U_k^d}} \]

Katika formula hii, each decision maker's personal criterion weight ina influence kulingana na group-importance weight ya decision maker huyo. Denominator inahakikisha sum ya all criterion weights equals one.

Stopping iteration

Kwa sababu decision-maker weights zinategemea group result na group result inategemea decision-maker weights, calculation ni iterative. Process inastop wakati group weights katika two successive iterations zinakuwa sufficiently close:

\[ \sqrt{\sum_{j=1}^{n}(W_j^d-W_j^{d-1})^2}<\varepsilon \]

Katika SOFC example stopping threshold ilikuwa:

\[ \varepsilon=0{,}001 \]

.

Figure 6 on page 22 ya PDF inaonyesha algorithm loop. Initially personal criterion weights na first importance weights kwa all decision makers zinachukuliwa. Group weights na decision-maker importances zinarecalculatewa; convergence condition isiposatisfied, process inarudia kutoka previous group result.

Ni criteria gani zilitumika katika SOFC application?

Katika example application ya study eight criteria zilichaguliwa:

Some features shown in Figure 1, kama internal reforming efficiency, pressure difference, allowable operating pressure na electrical insulation, hazikuingizwa katika eight criteria za example application. Study haielezi kwa detail ni systematic selection au elimination process gani ilitumika kuchagua eight criteria hizi.

Best na worst criterion choices za five evaluators

All evaluators walichagua start-up time kama least important criterion. Kwa upande mwingine, three different approaches zilionekana kwa best criterion: two evaluators walichagua power, one evaluator open-circuit voltage na two evaluators gas tightness.

Pairwise comparison data

Table 4 on page 24 ya PDF inaonyesha superiority ya best criterion selected by each evaluator over other criteria. Table 5 inatoa superiority ya other criteria over commonly selected worst criterion, start-up time.

Kwa mfano, first evaluator alichagua power kama best criterion na akahukumu power kuwa nine times more important than start-up time. Fourth evaluator alichagua gas tightness kama best na akahukumu criterion hii seven times more important than start-up time.

Values hizi si physical measurements. Phrase “nine times more important” inalingana na score 9 kwenye BWM verbal importance scale; haimaanishi ninefold increase katika actual engineering quantity.

Personal weights za each evaluator

Power weights za first two evaluators zilikuwa respectively %29,26 na %32,61. Third evaluator alitoa %24,65 kwa open-circuit voltage; fourth na fifth evaluators walitoa respectively %24,46 na %29,24 kwa gas tightness.

Start-up time ilibaki around %4,4-%5,5 katika all evaluations. Hii inaonyesha complete agreement katika selection ya worst criterion pia ilireflectiwa katika personal weights.

Final importance weights za decision makers

Fourth evaluator alone alipata approximately %46 weight. Kwa hiyo final group result ni substantially different kutoka equal-weighted average ya five experts.

Fourth evaluator kuchagua gas tightness kama best criterion na kuaccount for almost half of group weight kulichangia strongly gas tightness ranking first. Kwa upande wa method, hii si error; method imeundwa kutoa higher influence kwa some evaluators kutokana na group-result proximity na entropy measures.

Hata hivyo, concentration around %46 inahitaji separate examination ya effect ya decision-maker weighting kwenye result. PDF haielezi kwa personal background au independent competency data kwa nini fourth evaluator ni more reliable au expert than others. Weight imetokana entirely na mathematical preference agreement.

Final combined weights za SOFC criteria

Figure 7 on page 29 ya PDF inaonyesha final weights kama donut chart. Three largest slices ni gas tightness, power na open-circuit voltage. Together three criteria hizi zinaunda:

\[ 22{,}42+20{,}62+17{,}09=60{,}13\% \]

ya total weight. Kwa maneno mengine, roughly three-fifths ya total evaluation influence katika model imeconcentrate katika three criteria hizi.

Total weight ya two durability criteria ni:

\[ 10{,}65+9{,}18=19{,}83\% \]

wakati sum ya electrical efficiency na fuel utilization ni:

\[ 8{,}27+6{,}74=15{,}01\% \]

.

Gas tightness ranking first ina maana gani?

Result inaonyesha kwamba ndani ya decision structure ya evaluators walioshiriki study, gas tightness ina higher total importance kuliko other seven criteria. Result hii:

• Haimaaanishi gas tightness always has %22,42 importance in every SOFC application,
• Haimaaanishi power au durability ni secondary,
• Haimaaanishi start-up time ni practically unimportant.

haimaanishi hivyo.

Weights ni product ya comparisons za specific five evaluators, specific eight criteria na method parameters α = 0,6 na β = 0,4. Application purpose, SOFC type, fuel, operating temperature au mission profile zikibadilika, decision preferences na resulting weights zinaweza pia kubadilika.

ICC consistency validation

Study ilitathmini agreement kati ya personal weights za five evaluators na final combined weights kwa intraclass correlation coefficient.

Study iliinterpret ICC above 0,75 kama high consistency. Average-measure ICC ya 0,949 inaonyesha high agreement kati ya common average ya five evaluators na combined weight structure.

Katika conclusion ICC value imeandikwa rounded kama 0,94. Main validation text na Table 8 zinatoa more precise value 0,949.

High ICC alone haionyeshi criterion weights zinapredict accurately real SOFC performance. ICC hapa inapima similarity ya weighting structure among evaluators; haipimi external validity au accuracy katika predicting actual stack failures.

Stability au sensitivity validation

Criterion weights katika five separate comprehensive evaluation tests zinaonyeshwa katika Figure 8 on page 31 ya PDF kama five horizontal bar charts.

Katika first three tests:

• Gas tightness,
• Open circuit voltage,
• Power

zilibaki top three positions. Katika fourth na fifth tests, open-circuit voltage ilianguka hadi fourth place na thermal-cycle durability ikapanda into top three.

Electrical efficiency, fuel utilization na start-up time zilibaki bottom three katika all tests. Researchers waliinterpret overall ranking stability hii kama sensitivity au stability validation ya method.

Hata hivyo, analysis hii si broader mathematical sensitivity analysis yenye systematic variation ya α na β coefficients, removing one evaluator, au adding error to comparison scores. Inategemea ranking similarity across five repeated weighting exercises.

Nguvu za utafiti

• Inapendekeza clear iterative algorithm ya ku-extend classical BWM kwa multiple decision makers.
• Haiassume automatically equal weights kwa decision makers.
• Inatumia distance from group result na information content ya preference distribution kama separate components.
• Inarecalculate decision-maker weights na criterion weights jointly mpaka convergence.
• Inatoa all core formulas na algorithm flow ya proposed method.
• Inaripoti all personal comparisons na weights za five evaluators katika tables.
• Inatoa final criterion weights na decision-maker weights explicitly.
• Inatathmini quantitatively within-group consistency kwa ICC.
• Inawasilisha visually ranking changes katika five repeat tests.
• Method ina general group multi-criteria decision-making structure isiyolimited only to SOFCs.

Mapungufu ya utafiti

• Study ni preprint ambayo haijapitia peer review.
• Uploaded PDF haina title page yenye author na affiliation information.
• PDF haina author-contribution, funding, conflict-of-interest au data-access statements.
• Only five evaluators walitumika.
• Identities, education, SOFC experience na selection method za evaluators hazijaelezwa.
• Evaluators wameassumiwa kufanya decisions independently; independence haikutestwa directly.
• Selection na elimination method ya eight criteria haijaelezwa in detail.
• Si all SOFC performance features shown in Figure 1 zilizoingizwa katika example application.
• Method haikutestwa na measured performance data from actual SOFC stacks.
• Multiple real stack alternatives hazikurankiwa wala best stack kuchaguliwa.
• Haijaonyeshwa kwamba determined weights zinaboresha prediction ya failure, service life au field performance.
• Choice ya α = 0,6 na β = 0,4 haijajustifyiwa in detail.
• Sensitivity ya convergence threshold ε = 0,001 kwa alternative values haijaonyeshwa.
• Fourth evaluator kupata %45,95 weight creates substantial concentration katika result.
• Decision-maker weight imetokana na preference-structure agreement with group result, si expertise au measurement accuracy.
• Expert opinion tofauti na group majority lakini scientifically correct inaweza kupata low deviation weight.
• Relationship ya entropy component na engineering accuracy haijavalidatewa kwa real performance data.
• Proposed method haijacomparewa comprehensively kwenye same data na Bayesian BWM, equal-weight average au other group-BWM methods.
• ICC inaonyesha inter-evaluator agreement, si external accuracy.
• Stability test si comprehensive parameter au error-propagation analysis.
• Computational behavior ya method katika large decision-maker groups haijaonyeshwa experimentally.
• Applicability kwa different industries inapendekezwa katika conclusion lakini imeillustratewa only kwa SOFC criteria.

Study inaunga mkono nini?

• Multiple personal criterion weights obtained with BWM zinaweza kucombinewa iteratively kwa entropy na deviation components.
• Unequal importance weights zinaweza assigned kwa decision makers.
• Algorithm iliconverge katika sample dataset na ikatoa final criterion weights.
• Average ICC agreement ya personal preferences za five evaluators na final group ni high.
• Katika examined sample group, gas tightness ilipata highest na start-up time lowest weight.
• Gas tightness, power na open-circuit voltage zinaunda approximately %60 ya weights.
• Top na bottom criterion groups zilibaki generally stable across five repeated evaluations.
• Proposed method inatoa mathematical framework worth investigating kwa group-based engineering evaluations.

Study haithibitishi nini?

• Haijathibitishwa kwamba gas tightness universally carries %22,42 importance katika all SOFC stacks.
• Haijaonyeshwa kwamba start-up time ni least important criterion katika all applications.
• Haijaonyeshwa kwamba proposed method ni superior to all existing group decision-making methods.
• Haijaonyeshwa kwamba method inatoa more accurate SOFC lifetime au reliability prediction.
• Hakuna comprehensive performance score ya real SOFC stack iliyohesabiwa.
• SOFC stacks kutoka different manufacturers hazikulinganishwa.
• Correlation ya determined weights na experimental performance outcomes haikutestwa.
• Haijathibitishwa kwamba fourth evaluator ni technically more reliable kuliko other evaluators.
• High ICC alone haithibitishi real-world accuracy ya method.
• Haijaonyeshwa kwamba results kutoka five-person sample zina-generalize kwa large expert groups.
• Haijavalidatewa experimentally kwamba method inaweza kutumika unchanged across all sectors.

Possible significance kwa SOFC engineering

Practical value ya study ni kutoa method inayoweza systematically kucombine performance priorities za different experts. Weighting system kama hii inaweza future kutumika katika:

• Comparison ya different SOFC stack designs,
• Determining which properties receive priority in test programs,
• Allocation ya product-development resources,
• Structuring quality-control criteria,
• Prioritizing maintenance and reliability indicators.

Hata hivyo, applications hizi hazikufanywa katika current study. Ili method ibadilike kuwa real engineering decision, criterion weights zinahitaji kucombinewa na actual stack performance matrix na resulting ranking ivalidatewe na field au experimental data.

Possible significance kwa multi-criteria decision-making research

General novelty ya proposed approach ni calculating decision-maker weights kutoka relationship ya individual preferences with group result badala ya assigning them externally as fixed. Hivyo group weight na decision-maker weight zinaamuliwa jointly ndani ya same iterative process.

Following validations ni muhimu kwa future studies:

• Larger na different expert groups,
• Comparison na Bayesian BWM na other group-aggregation methods,
• Systematic sensitivity analysis kwa α na β coefficients,
• Robustness analysis preserving outlier expert opinions,
• Missing au uncertain comparison data,
• External validation katika real alternative rankings,
• Repeated application katika different engineering sectors.

Mbinu na Matokeo ya Utafiti

Technical summary ya method design

Technical summary ya criterion weights

Technical summary ya decision-maker weights

Technical summary ya validation results

Technical interpretation ya figures

Figure 1: SOFC performance hierarchy

Figure inaonyesha evaluation structure extending from individual electrical na operational criteria to five main performance groups na kisha overall stack performance. Layered SOFC drawing upande wa kulia inavisualize relationship ya performance criteria na physical stack components na gas flows.

Figure 2: AHP hierarchy

Many connections kati ya decision objective, criterion layer na alternative layer zinaonyeshwa. Figure inademonstrate visually jinsi full pairwise comparisons zinavyoweza kuwa increasingly complex kadri decision problem inavyokua.

Figure 3: Use ya weighting methods katika literature

Graph yenye nested rings kwa years 2016 through July 2023 inaonyesha AHP, entropy weighting na Delphi zikiwa leading katika literature dataset examined, huku BWM use ikiwa lower but rising over time.

Graph hii si ranking ya scientific accuracy ya methods. Inaonyesha only publication-use shares according to Web of Science query used by study.

Figure 5: BWM workflow

Defining criteria, selecting best and worst criterion, forming two comparison vectors na calculating optimal weights zinaonyeshwa katika sequential boxes.

Figure 6: Combining personal preferences into group result

Personal criterion weights na initial decision-maker weights zinatengeneza first group result. Kisha decision-maker importances na group criterion weights zinarecalculatewa repeatedly; difference kati ya successive results ikishuka below 0,001, final weights zinaoutputiwa.

Figure 7: Final SOFC criterion weights

Katika donut chart largest slice ni gas tightness at %22,42 na second largest ni power at %20,62. Start-up-time slice at %5,02 ndiyo smallest.

Figure 8: Comparison ya five repeat tests

Five horizontal bar charts zinaonyesha limited position changes among top-ranked criteria. Katika first three tests gas tightness, power na open-circuit voltage ni top group. Katika fourth na fifth tests thermal-cycle durability inapita open-circuit voltage. Start-up time iko last katika all graphs.

Methodological result

Directly demonstrated result ya study ni kwamba entropy- na deviation-based decision-maker weighting inaweza applied kwa personal criterion weights kutoka BWM. Katika example problem algorithm iliconverge, ikatoa group weights na yielded high average ICC value.

Direct SOFC result ya study ni kwamba according to preferences za five participants, gas tightness, power na open-circuit voltage zilipata highest weights. Benefit ya weights hizi kwa real stack selection au field performance lazima ivalidatewe separately katika subsequent experimental na decision applications.

Maelezo ya Chanzo na Mbinu

Full original title: An entropy-based best-worst method to synthetic evaluation the performance of the solid oxide fuel cell stacks: Multi-criteria decision making approach

Authors and order in official SSRN record: Yun Luo; Xinyuan Yang; Xuqian Chen; Wenchun Jiang; Qian Zhang.

Author information in PDF: Author names na affiliations hazipo kwenye visible pages za uploaded PDF. Author list iliverifywa kutoka official SSRN bibliographic record.

Equal contribution or co-first authorship: Hakuna equal-contribution statement katika uploaded PDF au accessed SSRN record.

Contact author: Yun Luo anaonyeshwa kama “Contact Author” katika SSRN record.

Contact email: Haikuweza kuverifywa kwa sababu haikuonyeshwa openly.

Institutional affiliations

• Yun Luo: No affiliation information given in official SSRN record.
• Xinyuan Yang: No affiliation information given in official SSRN record.
• Xuqian Chen: No affiliation information given in official SSRN record.
• Wenchun Jiang: No affiliation information given in official SSRN record.
• Qian Zhang: Qingdao University of Technology, Qingdao 266033, China.

Source type: Quantitative preprint research article including method development na example engineering application.

Publication platform: SSRN.

Publication date: 15 June 2026.

Page count: 38.

DOI: 10.2139/ssrn.6946094

Official link:SSRN study record

Peer-review status: Haijapitia peer review. Pages za PDF zina warning “Preprint not peer reviewed”.

Peer-reviewed journal: No verified peer-reviewed journal version was identified katika bibliographic check dated 27 July 2026.

Original journal publisher: Hakuna kwa sababu peer-reviewed journal version haijaverifywa. Current publication platform ni SSRN.

Author contributions: Uploaded PDF haina CRediT au other author-contribution statement.

Funding: Uploaded PDF haina funding statement.

Conflict of interest: Uploaded PDF haina conflict-of-interest statement.

Data and code access: Pairwise comparisons na calculated weights za decision makers zimetolewa katika tables, lakini hakuna independent data au source-code repository iliyospecifywa.

Article preparation method: Makala hii ya Kituruki ya Verianla iliandaliwa kwa kuchunguza text, equations, tables, flowcharts, weighting graphs na results za 38-page preprint uploaded by user. No scientific finding from outside PDF was added. External sources zilitumika only kwa bibliographic verification ya author identity, author order, DOI, publication date, platform na peer-review status.

Main methodological limit: Research si performance experiment inayoscore au kurank actual SOFC stacks. Inaillustrate converting subjective importance weights assigned by five evaluators to eight criteria into group result. Relationship ya determined weights na real stack reliability, service life au failure data haijavalidatewa.

Study hii ni preprint ambayo haijapitia peer review. Proposed entropy-based BWM inatoa promising mathematical approach kwa group decision making, lakini generalizability yake, superiority to alternative methods na accuracy katika real engineering decisions zinahitaji validation kwa broader datasets.