wiki:normalization

Version 11 (modified by 231175, 15 hours ago) ( diff )

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Формална анализа и доказ за нормализација на Shifter

1. Дефиниција на универзалната релација

Тргнуваме од една единствена универзална релација која ги содржи сите атрибути од доменот. 

Universal_Relation_Shifter(
user_id, user_name, user_email, user_login_provider, user_password_hash, user_verified, user_profile_complete, user_used_free_consultation, user_company_size, user_work_position, user_points,
meeting_reminder_id, meeting_at, meeting_scheduled_at, meeting_sent, meeting_link,
expert_id, expert_name, expert_email, expert_login_provider, expert_password_hash,
course_id, course_image_url, course_color, course_difficulty, course_duration_minutes, course_price,
course_version_id, version_number, version_creation_date, version_active,
enrollment_id, enrollment_status, enrollment_purchase_date, enrollment_activation_date, enrollment_completion_date,
payment_id, payment_amount, payment_date, payment_method, payment_status,
review_id, review_rating, review_comment, review_date,
course_translate_id, course_translate_language, course_title_short, course_title, course_description_short, course_description, course_description_long,
course_what_will_be_learned,
course_content_id, content_position,
course_content_translate_id, content_translate_title, content_translate_language,
course_lecture_id, lecture_duration_minutes, lecture_position, lecture_content_type,
course_lecture_translate_id, lecture_title, lecture_language, lecture_content_file_name, lecture_description, lecture_content_text,
user_course_progress_id, progress_completed, progress_completed_at,
verification_token_uuid, token_created_at, token_expired_at,
tag_id, tag_type,
tag_translate_id, tag_translate_language, tag_value
)

2. Функционални зависности

Ги идентификуваме сите функционални зависности што важат во универзалната релација:

F = {

  • FD1: user_id → user_name, user_email, user_login_provider, user_password_hash, user_verified, user_profile_complete, user_used_free_consultation, user_company_size, user_work_position, user_points
  • FD2: verification_token_uuid → token_created_at, token_expired_at, user_id
  • FD3: meeting_reminder_id → meeting_at, meeting_scheduled_at, meeting_sent, meeting_link, user_id
  • FD4: expert_id → expert_name, expert_email, expert_login_provider, expert_password_hash
  • FD5: course_id → course_image_url, course_color, course_difficulty, course_duration_minutes, course_price
  • FD6: enrollment_id → enrollment_status, enrollment_purchase_date, enrollment_activation_date, enrollment_completion_date, user_id, course_version_id, payment_id, review_id
  • FD7: payment_id → payment_amount, payment_date, payment_method, payment_status, enrollment_id
  • FD8: review_id → review_rating, review_comment, review_date, enrollment_id
  • FD9: tag_id → tag_type
  • FD10: tag_translate_id → tag_translate_language, tag_value, tag_id
  • FD11: course_version_id → version_number, version_creation_date, version_active, course_id
  • FD12: course_translate_id → course_translate_language, course_title_short, course_title, course_description_short, course_description, course_description_long, course_id
  • FD13: course_content_id → content_position, course_version_id
  • FD14: course_content_translate_id → content_translate_title, content_translate_language, course_content_id
  • FD15: course_lecture_id → lecture_duration_minutes, lecture_position, lecture_content_type, course_content_id
  • FD16: course_lecture_translate_id → lecture_title, lecture_language, lecture_content_file_name, lecture_description, lecture_content_text, course_lecture_id
  • FD17: user_course_progress_id → progress_completed, progress_completed_at, enrollment_id, course_lecture_id
  • FD18: user_email → user_id
  • FD19: expert_email → expert_id
  • FD20: (course_id, version_number) → course_version_id
  • FD21: (course_id, course_translate_language) → course_translate_id
  • FD22: (course_lecture_id, lecture_language) → course_lecture_translate_id
  • FD23: (course_content_id, content_translate_language) → course_content_translate_id
  • FD24: (tag_id, tag_translate_language) → tag_translate_id
  • FD25: (enrollment_id, course_lecture_id) → user_course_progress_id
  • FD26: (course_version_id, content_position) → course_content_id
  • FD27: (course_content_id, lecture_position) → course_lecture_id
  • FD28: (course_translate_id, course_what_will_be_learned) → ∅

}

3. Кандидат клучеви и примарен клуч

3.1 Определување на кандидат клучеви

За да најдеме кандидат клуч, треба да најдеме минимално множество атрибути чиј затворач ги содржи сите атрибути на релацијата.

3.2 Класификација на атрибути (Лева / Десна страна)

Атрибут Лева страна Десна страна Класификација
user_id ✓ (FD1) ✓ (FD2, FD3, FD6, FD18) и лево и десно
user_name ✗ ✓ (FD1) десно
user_email ✓ (FD18) ✓ (FD1) и лево и десно
user_login_provider ✗ ✓ (FD1) десно
user_password_hash ✗ ✓ (FD1) десно
user_verified ✗ ✓ (FD1) десно
user_profile_complete ✗ ✓ (FD1) десно
user_used_free_consultation ✗ ✓ (FD1) десно
user_company_size ✗ ✓ (FD1) десно
user_work_position ✗ ✓ (FD1) десно
user_points ✗ ✓ (FD1) десно
verification_token_uuid ✓ (FD2) ✗ лево
token_created_at ✗ ✓ (FD2) десно
token_expired_at ✗ ✓ (FD2) десно
meeting_reminder_id ✓ (FD3) ✗ лево
meeting_at ✗ ✓ (FD3) десно
meeting_scheduled_at ✗ ✓ (FD3) десно
meeting_sent ✗ ✓ (FD3) десно
meeting_link ✗ ✓ (FD3) десно
expert_id ✓ (FD4) ✓ (FD19) и лево и десно
expert_name ✗ ✓ (FD4) десно
expert_email ✓ (FD19) ✓ (FD4) и лево и десно
expert_login_provider ✗ ✓ (FD4) десно
expert_password_hash ✗ ✓ (FD4) десно
course_id ✓ (FD5, FD20, FD21) ✓ (FD11, FD12) и лево и десно
course_image_url ✗ ✓ (FD5) десно
course_color ✗ ✓ (FD5) десно
course_difficulty ✗ ✓ (FD5) десно
course_duration_minutes ✗ ✓ (FD5) десно
course_price ✗ ✓ (FD5) десно
enrollment_id ✓ (FD6, FD25) ✓ (FD7, FD8, FD17) и лево и десно
enrollment_status ✗ ✓ (FD6) десно
enrollment_purchase_date ✗ ✓ (FD6) десно
enrollment_activation_date ✗ ✓ (FD6) десно
enrollment_completion_date ✗ ✓ (FD6) десно
payment_id ✓ (FD7) ✓ (FD6) и лево и десно
payment_amount ✗ ✓ (FD7) десно
payment_date ✗ ✓ (FD7) десно
payment_method ✗ ✓ (FD7) десно
payment_status ✗ ✓ (FD7) десно
review_id ✓ (FD8) ✓ (FD6) и лево и десно
review_rating ✗ ✓ (FD8) десно
review_comment ✗ ✓ (FD8) десно
review_date ✗ ✓ (FD8) десно
tag_id ✓ (FD9, FD24) ✓ (FD10) и лево и десно
tag_type ✗ ✓ (FD9) десно
tag_translate_id ✓ (FD10) ✓ (FD24) и лево и десно
tag_translate_language ✓ (FD24) ✓ (FD10) и лево и десно
tag_value ✗ ✓ (FD10) десно
course_version_id ✓ (FD11, FD26) ✓ (FD6, FD13, FD20) и лево и десно
version_number ✓ (FD20) ✓ (FD11) и лево и десно
version_creation_date ✗ ✓ (FD11) десно
version_active ✗ ✓ (FD11) десно
course_translate_id ✓ (FD12) ✓ (FD21) и лево и десно
course_translate_language ✓ (FD21) ✓ (FD12) и лево и десно
course_title_short ✗ ✓ (FD12) десно
course_title ✗ ✓ (FD12) десно
course_description_short ✗ ✓ (FD12) десно
course_description ✗ ✓ (FD12) десно
course_description_long ✗ ✓ (FD12) десно
course_what_will_be_learned ✓ (FD28) ✗ лево
course_content_id ✓ (FD13, FD23, FD27) ✓ (FD14, FD15, FD26) и лево и десно
content_position ✓ (FD26) ✓ (FD13) и лево и десно
course_content_translate_id ✓ (FD14) ✓ (FD23) и лево и десно
content_translate_title ✗ ✓ (FD14) десно
content_translate_language ✓ (FD23) ✓ (FD14) и лево и десно
course_lecture_id ✓ (FD15, FD22, FD25) ✓ (FD16, FD17, FD27) и лево и десно
lecture_duration_minutes ✗ ✓ (FD15) десно
lecture_position ✓ (FD27) ✓ (FD15) и лево и десно
lecture_content_type ✗ ✓ (FD15) десно
course_lecture_translate_id ✓ (FD16) ✓ (FD22) и лево и десно
lecture_title ✗ ✓ (FD16) десно
lecture_language ✓ (FD22) ✓ (FD16) и лево и десно
lecture_content_file_name ✗ ✓ (FD16) десно
lecture_description ✗ ✓ (FD16) десно
lecture_content_text ✗ ✓ (FD16) десно
user_course_progress_id ✓ (FD17) ✓ (FD25) и лево и десно
progress_completed ✗ ✓ (FD17) десно
progress_completed_at ✗ ✓ (FD17) десно

3.3 Атрибути кои се појавуваат САМО на лева страна

  • verification_token_uuid - мора да биде дел од секој кандидат клуч
  • meeting_reminder_id - мора да биде дел од секој кандидат клуч
  • course_what_will_be_learned - мора да биде дел од секој кандидат клуч

3.4 Пресметка на затворач

Чекор 1: Започнуваме со {verification_token_uuid, meeting_reminder_id, course_what_will_be_learned} и пресметуваме затворач: 

{verification_token_uuid, meeting_reminder_id, course_what_will_be_learned}⁺:
- Од FD2 (verification_token_uuid →): добиваме token_created_at, token_expired_at, user_id
- Од FD3 (meeting_reminder_id →): добиваме meeting_at, meeting_scheduled_at, meeting_sent, meeting_link, user_id
- Од FD1 (user_id →): добиваме user_name, user_email, user_login_provider, user_password_hash, user_verified, user_profile_complete, user_used_free_consultation, user_company_size, user_work_position, user_points
- Од FD18 (user_email →): добиваме user_id

{verification_token_uuid, meeting_reminder_id, course_what_will_be_learned}⁺ ≠ Universal_Relation_Shifter

Недостасуваат: expert_id, expert_name, expert_email, expert_login_provider, expert_password_hash, course_id, course_image_url, course_color, course_difficulty, course_duration_minutes, course_price, course_version_id, version_number, version_creation_date, version_active, enrollment_id, enrollment_status, enrollment_purchase_date, enrollment_activation_date, enrollment_completion_date, payment_id, payment_amount, payment_date, payment_method, payment_status, review_id, review_rating, review_comment, review_date, course_translate_id, course_translate_language, course_title_short, course_title, course_description_short, course_description, course_description_long, course_content_id, content_position, course_content_translate_id, content_translate_title, content_translate_language, course_lecture_id, lecture_duration_minutes, lecture_position, lecture_content_type, course_lecture_translate_id, lecture_title, lecture_language, lecture_content_file_name, lecture_description, lecture_content_text, user_course_progress_id, progress_completed, progress_completed_at, tag_id, tag_type, tag_translate_id, tag_translate_language, tag_value

Чекор 2: Додаваме user_course_progress_id: 

{verification_token_uuid, meeting_reminder_id, course_what_will_be_learned, user_course_progress_id}⁺:
- Сè од претходно, плус:
- Од FD6 (user_course_progress_id →): добиваме progress_completed, progress_completed_at, enrollment_id, course_lecture_id
- Од FD15 (course_lecture_id →): добиваме lecture_duration_minutes, lecture_position, lecture_content_type, course_content_id
- Од FD13 (course_content_id →): добиваме content_position, course_version_id
- Од FD6 (enrollment_id →): добиваме enrollment_status, enrollment_purchase_date, enrollment_activation_date, enrollment_completion_date, user_id, course_version_id, payment_id, review_id
- Од FD7 (payment_id →): добиваме payment_amount, payment_date, payment_method, payment_status, enrollment_id
- Од FD8 (review_id →): добиваме review_rating, review_comment, review_date, enrollment_id
- Од FD11 (course_version_id →): добиваме version_number, version_creation_date, version_active, course_id
- Од FD5 (course_id →): добиваме course_image_url, course_color, course_difficulty, course_duration_minutes, course_price

{verification_token_uuid, meeting_reminder_id, course_what_will_be_learned, user_course_progress_id}⁺ ≠ Universal_Relation_Shifter

Недостасуваат: expert_id, expert_name, expert_email, expert_login_provider, expert_password_hash, course_translate_id, course_translate_language, course_title_short, course_title, course_description_short, course_description, course_description_long, course_content_translate_id, content_translate_title, content_translate_language, course_lecture_translate_id, lecture_title, lecture_language, lecture_content_file_name, lecture_description, lecture_content_text, tag_id, tag_type, tag_translate_id, tag_translate_language, tag_value

Чекор 3: Додаваме expert_id, course_lecture_translate_id, course_content_translate_id, course_translate_id, tag_translate_id: 

{verification_token_uuid, meeting_reminder_id, course_what_will_be_learned, user_course_progress_id, expert_id, course_lecture_translate_id, course_content_translate_id, course_translate_id, tag_translate_id}⁺:
- Сè од претходно, плус:
- Од FD4 (expert_id →): добиваме expert_name, expert_email, expert_login_provider, expert_password_hash
- Од FD16 (course_lecture_translate_id →): добиваме lecture_title, lecture_language, lecture_content_file_name, lecture_description, lecture_content_text, course_lecture_id
- Од FD14 (course_content_translate_id →): добиваме content_translate_title, content_translate_language, course_content_id
- Од FD12 (course_translate_id →): добиваме course_translate_language, course_title_short, course_title, course_description_short, course_description
- Од FD10 (tag_translate_id →): добиваме tag_translate_language, tag_value, tag_id
- Од FD9 (tag_id →): добиваме tag_type
- Од FD28 ({course_translate_id, course_what_will_be_learned} →): добиваме ∅

{verification_token_uuid, meeting_reminder_id, course_what_will_be_learned, user_course_progress_id, expert_id, course_lecture_translate_id, course_content_translate_id, course_translate_id, tag_translate_id}⁺ = Universal_Relation_Shifter (ги содржи сите атрибути) ✓

3.5 Проверка за минималност

Подмножество Затворач = Universal_Relation_Shifter?
{verification_token_uuid, meeting_reminder_id, course_what_will_be_learned}⁺ Недостасуваат атрибути од user_course_progress ✗ НЕ
{verification_token_uuid, meeting_reminder_id, course_what_will_be_learned, user_course_progress}⁺ Недостасуваат атрибути од expert ✗ НЕ
{verification_token_uuid, meeting_reminder_id, course_what_will_be_learned, user_course_progress_id, expert_id}⁺ Недостасуваат атрибути од course_translate ✗ НЕ
{verification_token_uuid, meeting_reminder_id, course_what_will_be_learned, user_course_progress_id, expert_id, course_translate_id}⁺ Недостасуваат атрибути од course_lecture_translate ✗ НЕ
{verification_token_uuid, meeting_reminder_id, course_what_will_be_learned, user_course_progress_id, expert_id, course_translate_id, course_lecture_translate_id}⁺ Недостасуваат атрибути од course_content_translate ✗ НЕ
{verification_token_uuid, meeting_reminder_id, course_what_will_be_learned, user_course_progress_id, expert_id, course_translate_id, course_lecture_translate_id, course_content_translate_id}⁺ Недостасуваат атрибути од tag_translate ✗ НЕ
{verification_token_uuid, meeting_reminder_id, course_what_will_be_learned, user_course_progress_id, expert_id, course_translate_id, course_lecture_translate_id, course_content_translate_id, tag_translate_id}⁺ Сите атрибути се присути ✓ ДА

Заклучок: {verification_token_uuid, meeting_reminder_id, course_what_will_be_learned, user_course_progress_id, expert_id, course_lecture_translate_id, course_content_translate_id, course_translate_id, tag_translate_id} е минимален и е кандидат клуч.

3.6 Други кандидат клучеви

Нема

3.7 Избор на примарен клуч

Избран примарен клуч: {verification_token_uuid, meeting_reminder_id, course_what_will_be_learned, user_course_progress_id, expert_id, course_lecture_translate_id, course_content_translate_id, course_translate_id, tag_translate_id}

Образложение: Ова е примарен клуч (минимален кандидат-клуч) бидејќи само со овие атрибути може да се добијат сите останати атрибути од универзалната релација преку затворање на функционалните зависности. Причината за големиот број атрибути во примарниот клуч е што универзалната релација содржи повеќе независни ентитети (корисници, експерти, курсеви, оцени, преводи, тагови) кои не се директно поврзани преку функционални зависности. Секој од овие независни ентитети бара најмалку еден идентификатор во клучот за да може да се пристапи до сите негови атрибути. Овој клуч е минимален - отстранувањето на било кој атрибут од него би довело до тоа да не може да се изведат некои од атрибутите во релацијата.

4. 1NF Декомпозиција

Чекор 4.1: Декомпозиција на релацијата Universal_Relation_Shifter

Нарушува 1NF: Релацијата не е во 1NF бидејќи атрибутот course_what_will_be_learned претставува повеќевредносен (multi-valued) атрибут. Секој course_translate може да има повеќе ставки од course_what_will_be_learned.

Декомпозиција: 

Course_What_Will_Be_Learned(course_translate_id, course_what_will_be_learned)
   PK: {course_translate_id, course_what_will_be_learned}

Universal_Relation_Shifter_Base = Universal_Relation_Shifter - {course_what_will_be_learned}

Universal_Relation_Shifter_Base(
user_id, user_name, user_email, user_login_provider, user_password_hash, user_verified, user_profile_complete, user_used_free_consultation, user_company_size, user_work_position, user_points,
meeting_reminder_id, meeting_at, meeting_scheduled_at, meeting_sent, meeting_link,
expert_id, expert_name, expert_email, expert_login_provider, expert_password_hash,
course_id, course_image_url, course_color, course_difficulty, course_duration_minutes, course_price,
course_version_id, version_number, version_creation_date, version_active,
enrollment_id, enrollment_status, enrollment_purchase_date, enrollment_activation_date, enrollment_completion_date,
payment_id, payment_amount, payment_date, payment_method, payment_status,
review_id, review_rating, review_comment, review_date,
course_translate_id, course_translate_language, course_title_short, course_title, course_description_short, course_description, course_description_long,
course_content_id, content_position,
course_content_translate_id, content_translate_title, content_translate_language,
course_lecture_id, lecture_duration_minutes, lecture_position, lecture_content_type,
course_lecture_translate_id, lecture_title, lecture_language, lecture_content_file_name, lecture_description, lecture_content_text,
user_course_progress_id, progress_completed, progress_completed_at,
verification_token_uuid, token_created_at, token_expired_at,
tag_id, tag_type,
tag_translate_id, tag_translate_language, tag_value
)
   PK: {verification_token_uuid, meeting_reminder_id, user_course_progress_id, expert_id, course_lecture_translate_id, course_content_translate_id, course_translate_id, tag_translate_id}

Проверка за lossless join: Може да се реконструира преку course_translate_id Проверка за dependency preservation: FD28 е зачувана во Course_What_Will_Be_Learned

4.2 Проверка која FD ја нарушува 2NF

За да биде во 2NF, секој не-клучен атрибут мора целосно да зависи од примарниот клуч (нема парцијални зависности).

Примарен клуч во Universal_Relation_Shifter_Base: {verification_token_uuid, meeting_reminder_id, user_course_progress_id, expert_id, course_lecture_translate_id, course_content_translate_id, course_translate_id, tag_translate_id}

Парцијални зависности (атрибути кои зависат од дел од клучот):

FD Детерминант Дел од клуч? Парцијална зависност?
FD1: user_id → user_* user_id НЕ (транзитивно преку user_course_progress_id) Не директно
FD2: verification_token_uuid → token_created_at, token_expired_at, user_id verification_token_uuid ДА (дел од примарен клуч) ДА
FD3: meeting_reminder_id → meeting_at, meeting_scheduled_at, meeting_sent, meeting_link, user_id meeting_reminder_id ДА (дел од примарен клуч) ДА
FD4: expert_id → expert_name, expert_email, expert_login_provider, expert_password_hash expert_id ДА (дел од примарен клуч) ДА
FD5: course_id → course_image_url, course_color, course_difficulty, course_duration_minutes, course_price course_id НЕ (транзитивно преку user_course_progress_id) Не директно
FD6: enrollment_id → enrollment_*, user_id, course_version_id, payment_id, review_id enrollment_id НЕ (транзитивно преку user_course_progress_id) Не директно
FD7: payment_id → payment_amount, payment_date, payment_method, payment_status, enrollment_id payment_id НЕ (транзитивно преку user_course_progress_id) Не директно
FD8: review_id → review_rating, review_comment, review_date, enrollment_id review_id НЕ (транзитивно преку user_course_progress_id) Не директно
FD9: tag_id → tag_type tag_id НЕ (транзитивно преку tag_translate_id) Не директно
FD10: tag_translate_id → tag_translate_language, tag_value, tag_id tag_translate_id ДА (дел од примарен клуч) ДА
FD11: course_version_id → version_number, version_creation_date, version_active, course_id course_version_id НЕ (транзитивно преку user_course_progress_id) Не директно
FD12: course_translate_id → course_translate_language, course_title_short, course_title, course_description_short, course_description, course_description_long, course_id course_translate_id ДА (дел од примарен клуч) ДА
FD13: course_content_id → content_position, course_version_id course_content_id НЕ (транзитивно преку course_content_translate_id) Не директно
FD14: course_content_translate_id → content_translate_title, content_translate_language, course_content_id course_content_translate_id ДА (дел од примарен клуч) ДА
FD15: course_lecture_id → lecture_duration_minutes, lecture_position, lecture_content_type, course_content_id course_lecture_id НЕ (транзитивно преку course_lecture_translate_id) Не директно
FD16: course_lecture_translate_id → lecture_title, lecture_language, lecture_content_file_name, lecture_description, lecture_content_text, course_lecture_id course_lecture_translate_id ДА (дел од примарен клуч) ДА
FD17: user_course_progress_id → progress_completed, progress_completed_at, enrollment_id, course_lecture_id user_course_progress_id ДА (дел од примарен клуч) ДА
FD18: user_email → user_id user_email НЕ Не
FD19: expert_email → expert_id expert_email НЕ Не
FD20: (course_id, version_number) → course_version_id course_id, version_number НЕ Не
FD21: (course_id, course_translate_language) → course_translate_id course_id, course_translate_language НЕ Не
FD22: (course_lecture_id, lecture_language) → course_lecture_translate_id course_lecture_id, lecture_language НЕ Не
FD23: (course_content_id, content_translate_language) → course_content_translate_id course_content_id, content_translate_language НЕ Не
FD24: (tag_id, tag_translate_language) → tag_translate_id tag_id, tag_translate_language НЕ Не
FD25: (enrollment_id, course_lecture_id) → user_course_progress_id enrollment_id, course_lecture_id НЕ Не
FD26: (course_version_id, content_position) → course_content_id course_version_id, content_position НЕ Не
FD27: (course_content_id, lecture_position) → course_lecture_id course_content_id, lecture_position НЕ Не

Заклучок: Релацијата не е во 2NF бидејќи има парцијални зависности. Атрибутите на FD2, FD3, FD4, FD10, FD12, FD14, FD16, FD17 зависат само од дел од примарниот клуч, а не од целиот клуч.

Идентификувани парцијални зависности што ја нарушуваат 2NF:

  1. FD2: verification_token_uuid → token_created_at, token_expired_at, user_id
  2. FD3: meeting_reminder_id → meeting_at, meeting_scheduled_at, meeting_sent, meeting_link, user_id
  3. FD4: expert_id → expert_name, expert_email, expert_login_provider, expert_password_hash
  4. FD10: tag_translate_id → tag_translate_language, tag_value, tag_id
  5. FD12: course_translate_id → course_translate_language, course_title_short, course_title, course_description_short, course_description, course_description_long, course_id
  6. FD14: course_content_translate_id → content_translate_title, content_translate_language, course_content_id
  7. FD16: course_lecture_translate_id → lecture_title, lecture_language, lecture_content_file_name, lecture_description, lecture_content_text, course_lecture_id
  8. FD17: user_course_progress_id → progress_completed, progress_completed_at, enrollment_id, course_lecture_id

5. 2NF Декомпозиција

Чекор 5.1: Декомпозиција по FD2 (verification_token_uuid → ...)

Нарушува 2NF: verification_token_uuid е дел од примарниот клуч, а token_created_at, token_expired_at зависат само од verification_token_uuid.

Декомпозиција: 

Verification_Token(verification_token_uuid, token_created_at, token_expired_at, user_id)
   PK: verification_token_uuid

Universal_Relation_Shifter_Base_1 = Universal_Relation_Shifter_Base - {verification_token_uuid, token_created_at, token_expired_at}

Universal_Relation_Shifter_Base_1(
user_id, user_name, user_email, user_login_provider, user_password_hash, user_verified, user_profile_complete, user_used_free_consultation, user_company_size, user_work_position, user_points,
meeting_reminder_id, meeting_at, meeting_scheduled_at, meeting_sent, meeting_link,
expert_id, expert_name, expert_email, expert_login_provider, expert_password_hash,
course_id, course_image_url, course_color, course_difficulty, course_duration_minutes, course_price,
course_version_id, version_number, version_creation_date, version_active,
enrollment_id, enrollment_status, enrollment_purchase_date, enrollment_activation_date, enrollment_completion_date,
payment_id, payment_amount, payment_date, payment_method, payment_status,
review_id, review_rating, review_comment, review_date,
course_translate_id, course_translate_language, course_title_short, course_title, course_description_short, course_description, course_description_long,
course_content_id, content_position,
course_content_translate_id, content_translate_title, content_translate_language,
course_lecture_id, lecture_duration_minutes, lecture_position, lecture_content_type,
course_lecture_translate_id, lecture_title, lecture_language, lecture_content_file_name, lecture_description, lecture_content_text,
user_course_progress_id, progress_completed, progress_completed_at,
tag_id, tag_type,
tag_translate_id, tag_translate_language, tag_value
)
   PK: {meeting_reminder_id, user_course_progress_id, expert_id, course_lecture_translate_id, course_content_translate_id, course_translate_id, tag_translate_id}

Проверка за lossless join: Може да се реконструира преку user_id Проверка за dependency preservation: FD2 е зачувана во Verification_Token

Чекор 5.2: Декомпозиција по FD3 (meeting_reminder_id → ...)

Нарушува 2NF: meeting_reminder_id е дел од примарниот клуч, а meeting_at, meeting_scheduled_at, meeting_sent, meeting_link зависат само од meeting_reminder_id.

Декомпозиција: 

Meeting_Reminder(meeting_reminder_id, meeting_at, meeting_scheduled_at, meeting_sent, meeting_link, user_id)
   PK: meeting_reminder_id

Universal_Relation_Shifter_Base_2 = Universal_Relation_Shifter_Base_1 - {meeting_reminder_id, meeting_at, meeting_scheduled_at, meeting_sent, meeting_link}

Universal_Relation_Shifter_Base_2(
user_id, user_name, user_email, user_login_provider, user_password_hash, user_verified, user_profile_complete, user_used_free_consultation, user_company_size, user_work_position, user_points,
expert_id, expert_name, expert_email, expert_login_provider, expert_password_hash,
course_id, course_image_url, course_color, course_difficulty, course_duration_minutes, course_price,
course_version_id, version_number, version_creation_date, version_active,
enrollment_id, enrollment_status, enrollment_purchase_date, enrollment_activation_date, enrollment_completion_date,
payment_id, payment_amount, payment_date, payment_method, payment_status,
review_id, review_rating, review_comment, review_date,
course_translate_id, course_translate_language, course_title_short, course_title, course_description_short, course_description, course_description_long,
course_content_id, content_position,
course_content_translate_id, content_translate_title, content_translate_language,
course_lecture_id, lecture_duration_minutes, lecture_position, lecture_content_type,
course_lecture_translate_id, lecture_title, lecture_language, lecture_content_file_name, lecture_description, lecture_content_text,
user_course_progress_id, progress_completed, progress_completed_at,
tag_id, tag_type,
tag_translate_id, tag_translate_language, tag_value
)
   PK: {user_course_progress_id, expert_id, course_lecture_translate_id, course_content_translate_id, course_translate_id, tag_translate_id}

Проверка за lossless join: Може да се реконструира преку user_id Проверка за dependency preservation: FD3 е зачувана во Meeting_Reminder

Чекор 5.3: Декомпозиција по FD4 (expert_id → ...)

Нарушува 2NF: expert_id е дел од примарниот клуч, а expert_name, expert_email, expert_login_provider, expert_password_hash зависат само од expert_id.

Декомпозиција: 

Expert(expert_id, expert_name, expert_email, expert_login_provider, expert_password_hash)
   PK: expert_id

Universal_Relation_Shifter_Base_3 = Universal_Relation_Shifter_Base_2 - {expert_id, expert_name, expert_email, expert_login_provider, expert_password_hash}

Universal_Relation_Shifter_Base_3(
user_id, user_name, user_email, user_login_provider, user_password_hash, user_verified, user_profile_complete, user_used_free_consultation, user_company_size, user_work_position, user_points,
expert_id
course_id, course_image_url, course_color, course_difficulty, course_duration_minutes, course_price,
course_version_id, version_number, version_creation_date, version_active,
enrollment_id, enrollment_status, enrollment_purchase_date, enrollment_activation_date, enrollment_completion_date,
payment_id, payment_amount, payment_date, payment_method, payment_status,
review_id, review_rating, review_comment, review_date,
course_translate_id, course_translate_language, course_title_short, course_title, course_description_short, course_description, course_description_long,
course_content_id, content_position,
course_content_translate_id, content_translate_title, content_translate_language,
course_lecture_id, lecture_duration_minutes, lecture_position, lecture_content_type,
course_lecture_translate_id, lecture_title, lecture_language, lecture_content_file_name, lecture_description, lecture_content_text,
user_course_progress_id, progress_completed, progress_completed_at,
tag_id, tag_type,
tag_translate_id, tag_translate_language, tag_value
)
   PK: {user_course_progress_id, course_lecture_translate_id, course_content_translate_id, course_translate_id, tag_translate_id}

Проверка за lossless join: Може да се реконструира преку expert_id Проверка за dependency preservation: FD4 е зачувана во Expert

Чекор 5.4: Декомпозиција по FD10 (tag_translate_id → ...)

Нарушува 2NF: tag_translate_id е дел од примарниот клуч, а tag_translate_language, tag_value зависат само од tag_translate_id.

Декомпозиција: 

Tag_Translate(tag_translate_id, tag_translate_language, tag_value, tag_id)
   PK: tag_translate_id

Universal_Relation_Shifter_Base_4 = Universal_Relation_Shifter_Base_3 - {tag_translate_id, tag_translate_language, tag_value}

Universal_Relation_Shifter_Base_4(
user_id, user_name, user_email, user_login_provider, user_password_hash, user_verified, user_profile_complete, user_used_free_consultation, user_company_size, user_work_position, user_points,
expert_id,
course_id, course_image_url, course_color, course_difficulty, course_duration_minutes, course_price,
course_version_id, version_number, version_creation_date, version_active,
enrollment_id, enrollment_status, enrollment_purchase_date, enrollment_activation_date, enrollment_completion_date,
payment_id, payment_amount, payment_date, payment_method, payment_status,
review_id, review_rating, review_comment, review_date,
course_translate_id, course_translate_language, course_title_short, course_title, course_description_short, course_description, course_description_long,
course_content_id, content_position,
course_content_translate_id, content_translate_title, content_translate_language,
course_lecture_id, lecture_duration_minutes, lecture_position, lecture_content_type,
course_lecture_translate_id, lecture_title, lecture_language, lecture_content_file_name, lecture_description, lecture_content_text,
user_course_progress_id, progress_completed, progress_completed_at,
tag_id, tag_type
)
   PK: {user_course_progress_id, course_lecture_translate_id, course_content_translate_id, course_translate_id}

Проверка за lossless join: Може да се реконструира преку tag_id Проверка за dependency preservation: FD10 е зачувана во Tag_Translate

Чекор 5.5: Декомпозиција по FD12 (course_translate_id → ...)

Нарушува 2NF: course_translate_id е дел од примарниот клуч, а course_translate_language, course_title_short, course_title, course_description_short, course_description, course_description_long зависат само од course_translate_id.

Декомпозиција: 

Course_Translate(course_translate_id, course_translate_language, course_title_short, course_title, course_description_short, course_description, course_description_long, course_id)
   PK: course_translate_id

Universal_Relation_Shifter_Base_5 = Universal_Relation_Shifter_Base_4 - {course_translate_id, course_translate_language, course_title_short, course_title, course_description_short, course_description, course_description_long}

Universal_Relation_Shifter_Base_5(
user_id, user_name, user_email, user_login_provider, user_password_hash, user_verified, user_profile_complete, user_used_free_consultation, user_company_size, user_work_position, user_points,
expert_id,
course_id, course_image_url, course_color, course_difficulty, course_duration_minutes, course_price,
course_version_id, version_number, version_creation_date, version_active,
enrollment_id, enrollment_status, enrollment_purchase_date, enrollment_activation_date, enrollment_completion_date,
payment_id, payment_amount, payment_date, payment_method, payment_status,
review_id, review_rating, review_comment, review_date,
course_content_id, content_position,
course_content_translate_id, content_translate_title, content_translate_language,
course_lecture_id, lecture_duration_minutes, lecture_position, lecture_content_type,
course_lecture_translate_id, lecture_title, lecture_language, lecture_content_file_name, lecture_description, lecture_content_text,
user_course_progress_id, progress_completed, progress_completed_at,
tag_id, tag_type
)
   PK: {user_course_progress_id, course_lecture_translate_id, course_content_translate_id}

Проверка за lossless join: Може да се реконструира преку course_id Проверка за dependency preservation: FD12 е зачувана во Course_Translate

Чекор 5.6: Декомпозиција по FD14 (course_content_translate_id → ...)

Нарушува 2NF: course_content_translate_id е дел од примарниот клуч, а content_translate_title, content_translate_language зависат само од course_content_translate_id.

Декомпозиција: 

Course_Content_Translate(course_content_translate_id, content_translate_title, content_translate_language, course_content_id)
   PK: course_content_translate_id

Universal_Relation_Shifter_Base_6 = Universal_Relation_Shifter_Base_5 - {course_content_translate_id, content_translate_title, content_translate_language}

Universal_Relation_Shifter_Base_6(
user_id, user_name, user_email, user_login_provider, user_password_hash, user_verified, user_profile_complete, user_used_free_consultation, user_company_size, user_work_position, user_points,
expert_id,
course_id, course_image_url, course_color, course_difficulty, course_duration_minutes, course_price,
course_version_id, version_number, version_creation_date, version_active,
enrollment_id, enrollment_status, enrollment_purchase_date, enrollment_activation_date, enrollment_completion_date,
payment_id, payment_amount, payment_date, payment_method, payment_status,
review_id, review_rating, review_comment, review_date,
course_content_id, content_position,
course_lecture_id, lecture_duration_minutes, lecture_position, lecture_content_type,
course_lecture_translate_id, lecture_title, lecture_language, lecture_content_file_name, lecture_description, lecture_content_text,
user_course_progress_id, progress_completed, progress_completed_at,
tag_id, tag_type
)
   PK: {user_course_progress_id, course_lecture_translate_id}

Проверка за lossless join: Може да се реконструира преку course_content_id Проверка за dependency preservation: FD14 е зачувана во Course_Content_Translate

Чекор 5.7: Декомпозиција по FD16 (course_lecture_translate_id → ...)

Нарушува 2NF: course_lecture_translate_id е дел од примарниот клуч, а lecture_title, lecture_language, lecture_content_file_name, lecture_description, lecture_content_text зависат само од course_lecture_translate_id.

Декомпозиција: 

Course_Lecture_Translate(course_lecture_translate_id, lecture_title, lecture_language, lecture_content_file_name, lecture_description, lecture_content_text, course_lecture_id)
   PK: course_lecture_translate_id

Universal_Relation_Shifter_Base_7 = Universal_Relation_Shifter_Base_6 - {course_lecture_translate_id, lecture_title, lecture_language, lecture_content_file_name, lecture_description, lecture_content_text}

Universal_Relation_Shifter_Base_7(
user_id, user_name, user_email, user_login_provider, user_password_hash, user_verified, user_profile_complete, user_used_free_consultation, user_company_size, user_work_position, user_points,
expert_id,
course_id, course_image_url, course_color, course_difficulty, course_duration_minutes, course_price,
course_version_id, version_number, version_creation_date, version_active,
enrollment_id, enrollment_status, enrollment_purchase_date, enrollment_activation_date, enrollment_completion_date,
payment_id, payment_amount, payment_date, payment_method, payment_status,
review_id, review_rating, review_comment, review_date,
course_content_id, content_position,
course_lecture_id, lecture_duration_minutes, lecture_position, lecture_content_type,
user_course_progress_id, progress_completed, progress_completed_at,
tag_id, tag_type
)
   PK: {user_course_progress_id}

Проверка за lossless join: Може да се реконструира преку course_lecture_id Проверка за dependency preservation: FD16 е зачувана во Course_Lecture_Translate

Чекор 5.8: Декомпозиција по FD17 (user_course_progress_id → ...)

Нарушува 2NF: user_course_progress_id е дел од примарниот клуч, а progress_completed, progress_completed_at зависат само од user_course_progress_id.

Декомпозиција: 

User_Course_Progress(user_course_progress_id, progress_completed, progress_completed_at, enrollment_id, course_lecture_id)
   PK: user_course_progress_id

Universal_Relation_Shifter_Base_8 = Universal_Relation_Shifter_Base_7 - {user_course_progress_id, progress_completed, progress_completed_at}

Universal_Relation_Shifter_Base_8(
user_id, user_name, user_email, user_login_provider, user_password_hash, user_verified, user_profile_complete, user_used_free_consultation, user_company_size, user_work_position, user_points,
expert_id,
course_id, course_image_url, course_color, course_difficulty, course_duration_minutes, course_price,
course_version_id, version_number, version_creation_date, version_active,
enrollment_id, enrollment_status, enrollment_purchase_date, enrollment_activation_date, enrollment_completion_date,
payment_id, payment_amount, payment_date, payment_method, payment_status,
review_id, review_rating, review_comment, review_date,
course_content_id, content_position,
course_lecture_id, lecture_duration_minutes, lecture_position, lecture_content_type,
tag_id, tag_type
)
   PK: ∅

Проверка за lossless join: Може да се реконструира преку enrollment_id и course_lecture_id Проверка за dependency preservation: FD17 е зачувана во User_Course_Progress

Состојба после 2NF декомпозиција

R1(productId, product_name, product_description, product_sku, product_unit_price, product_reorder_level, categoryId, supplierId)
   PK: productId

R2(saleId, sale_date_time, sale_total_amount, userId, customerId, warehouseId)
   PK: saleId

R3(poId, po_order_date, po_expected_delivery_date, po_status, supplierId, warehouseId)
   PK: poId

R4(saleId, productId, saleitem_quantity, saleitem_unit_price_at_sale)
   PK: {saleId, productId}

R5(poId, productId, poitem_quantity, poitem_unit_cost)
   PK: {poId, productId}

U5(saleId, poId, productId, userId, user_username, user_password, user_full_name, user_email, user_role, user_is_active,
   customerId, customer_name, customer_email, customer_phone, customer_address,
   categoryId, category_name, category_description,
   supplierId, supplier_name, supplier_contact_person, supplier_phone, supplier_email, supplier_address,
   warehouseId, warehouse_name, warehouse_location, warehouse_capacity,
   stock_quantity_on_hand, stock_last_updated)
   PK: {saleId, poId, productId}

6. 3NF Декомпозиција

Проверка за транзитивни зависности во секоја релација

R1(productId, product_name, product_description, product_sku, product_unit_price, product_reorder_level, categoryId, supplierId)

Транзитивни зависности:

  • productId → categoryId → category_name, category_description?
    • category_name и category_description НЕ се во R1, па нема транзитивна зависност во оваа релација.
  • productId → supplierId → supplier_*?
    • supplier_* атрибутите НЕ се во R1.

Заклучок: R1 е во 3NF ✓

R2(saleId, sale_date_time, sale_total_amount, userId, customerId, warehouseId)

Транзитивни зависности:

  • saleId → userId → user_*?
    • user_* атрибутите НЕ се во R2.
  • saleId → customerId → customer_*?
    • customer_* атрибутите НЕ се во R2.
  • saleId → warehouseId → warehouse_*?
    • warehouse_* атрибутите НЕ се во R2.

Заклучок: R2 е во 3NF ✓

R3(poId, po_order_date, po_expected_delivery_date, po_status, supplierId, warehouseId)

Транзитивни зависности:

  • Слично како R2, supplier_* и warehouse_* не се во R3.

Заклучок: R3 е во 3NF ✓

R4(saleId, productId, saleitem_quantity, saleitem_unit_price_at_sale)

Транзитивни зависности:

  • Нема не-клучни атрибути кои одредуваат други не-клучни атрибути.

Заклучок: R4 е во 3NF ✓

R5(poId, productId, poitem_quantity, poitem_unit_cost)

Заклучок: R5 е во 3NF ✓

U5 - Проверка за транзитивни зависности

Примарен клуч на U5: {saleId, poId, productId}

Транзитивни зависности во U5:

  1. FD1 транзитивно: {saleId, poId, productId} → userId (преку R2/saleId) → user_username, user_password, user_full_name, user_email, user_role, user_is_active
    • userId не е клуч на U5, а user_* зависат од userId
    • НАРУШУВА 3NF
  1. FD4 транзитивно: {saleId, poId, productId} → customerId (преку R2/saleId) → customer_name, customer_email, customer_phone, customer_address
    • НАРУШУВА 3NF
  1. FD7 транзитивно: {saleId, poId, productId} → categoryId (преку R1/productId) → category_name, category_description
    • НАРУШУВА 3NF
  1. FD8 транзитивно: {saleId, poId, productId} → supplierId → supplier_name, supplier_contact_person, supplier_phone, supplier_email, supplier_address
    • НАРУШУВА 3NF
  1. FD9 транзитивно: {saleId, poId, productId} → warehouseId → warehouse_name, warehouse_location, warehouse_capacity
    • НАРУШУВА 3NF
  1. FD14: {warehouseId, productId} → stock_quantity_on_hand, stock_last_updated
    • warehouseId се добива транзитивно, а {warehouseId, productId} не е клуч на U5
    • НАРУШУВА 3NF

Чекор 6.1: Декомпозиција по FD1 (userId → user_*)

R6(userId, user_username, user_password, user_full_name, user_email, user_role, user_is_active)
   PK: userId

U6 = U5 - {user_username, user_password, user_full_name, user_email, user_role, user_is_active}

U6(saleId, poId, productId, userId, customerId, customer_name, customer_email, 
   customer_phone, customer_address, categoryId, category_name, category_description, 
   supplierId, supplier_name, supplier_contact_person, supplier_phone, supplier_email, 
   supplier_address, warehouseId, warehouse_name, warehouse_location, warehouse_capacity, 
   stock_quantity_on_hand, stock_last_updated)

Проверка за lossless join:

  • R6 ∩ U6 = {userId}
  • userId → R6 (FD1)
  • Lossless ✓

Чекор 6.2: Декомпозиција по FD4 (customerId → customer_*)

R7(customerId, customer_name, customer_email, customer_phone, customer_address)
   PK: customerId

U7 = U6 - {customer_name, customer_email, customer_phone, customer_address}

U7(saleId, poId, productId, userId, customerId, categoryId, category_name, 
   category_description, supplierId, supplier_name, supplier_contact_person, 
   supplier_phone, supplier_email, supplier_address, warehouseId, warehouse_name, 
   warehouse_location, warehouse_capacity, stock_quantity_on_hand, stock_last_updated)

Проверка за lossless join:

  • R7 ∩ U7 = {customerId}
  • customerId → R7 (FD4)
  • Lossless ✓

Чекор 6.3: Декомпозиција по FD7 (categoryId → category_*)

R8(categoryId, category_name, category_description)
   PK: categoryId

U8 = U7 - {category_name, category_description}

U8(saleId, poId, productId, userId, customerId, categoryId, supplierId, 
   supplier_name, supplier_contact_person, supplier_phone, supplier_email, 
   supplier_address, warehouseId, warehouse_name, warehouse_location, 
   warehouse_capacity, stock_quantity_on_hand, stock_last_updated)

Проверка за lossless join:

  • R8 ∩ U8 = {categoryId}
  • categoryId → R8 (FD7)
  • Lossless ✓

Чекор 6.4: Декомпозиција по FD8 (supplierId → supplier_*)

R9(supplierId, supplier_name, supplier_contact_person, supplier_phone, supplier_email, supplier_address)
   PK: supplierId

U9 = U8 - {supplier_name, supplier_contact_person, supplier_phone, supplier_email, supplier_address}

U9(saleId, poId, productId, userId, customerId, categoryId, supplierId, 
   warehouseId, warehouse_name, warehouse_location, warehouse_capacity, 
   stock_quantity_on_hand, stock_last_updated)

Проверка за lossless join:

  • R9 ∩ U9 = {supplierId}
  • supplierId → R9 (FD8)
  • Lossless ✓

Чекор 6.5: Декомпозиција по FD9 (warehouseId → warehouse_*)

R10(warehouseId, warehouse_name, warehouse_location, warehouse_capacity)
   PK: warehouseId

U10 = U9 - {warehouse_name, warehouse_location, warehouse_capacity}

U10(saleId, poId, productId, userId, customerId, categoryId, supplierId, warehouseId, stock_quantity_on_hand, stock_last_updated)

Проверка за lossless join:

  • R10 ∩ U10 = {warehouseId}
  • warehouseId → R10 (FD9)
  • Lossless ✓

Чекор 6.6: Декомпозиција по FD14 ({warehouseId, productId} → stock_*)

R11(warehouseId, productId, stock_quantity_on_hand, stock_last_updated)
   PK: {warehouseId, productId}

U11 = U10 - {stock_quantity_on_hand, stock_last_updated}

U11(saleId, poId, productId, userId, customerId, categoryId, supplierId, warehouseId)

Проверка за lossless join:

  • R11 ∩ U11 = {warehouseId, productId}
  • {warehouseId, productId} → R11 (FD14)
  • Lossless ✓

Анализа на U11

U11(saleId, poId, productId, userId, customerId, categoryId, supplierId, warehouseId)
   PK: {saleId, poId, productId}

Атрибутите userId, customerId, warehouseId се веќе дел од R2 (Sale). Атрибутите categoryId, supplierId се веќе дел од R1 (Product).

U11 претставува врска меѓу продажби (saleId), нарачки (poId) и продукти (productId).

Прашање: Дали оваа релација има семантичка смисла?

Во реалноста:

  • Една продажба (saleId) е независна од една нарачка (poId)
  • Нивната врска е само преку productId и warehouseId

U11 може да се декомпонира понатаму, бидејќи атрибутите userId, customerId, warehouseId зависат само од saleId (FD10), а supplierId зависи само од poId или productId.

Но бидејќи овие атрибути се веќе издвоени во R2 и R1, U11 станува редундантна и може да се отстрани бидејќи информацијата е веќе зачувана во другите релации.

Состојба после 3NF декомпозиција

Релација Атрибути Примарен клуч
R1 (Product) productId, product_name, product_description, product_sku, product_unit_price, product_reorder_level, categoryId, supplierId productId
R2 (Sale) saleId, sale_date_time, sale_total_amount, userId, customerId, warehouseId saleId
R3 (PurchaseOrder) poId, po_order_date, po_expected_delivery_date, po_status, supplierId, warehouseId poId
R4 (SaleItem) saleId, productId, saleitem_quantity, saleitem_unit_price_at_sale {saleId, productId}
R5 (PurchaseOrderItem) poId, productId, poitem_quantity, poitem_unit_cost {poId, productId}
R6 (User) userId, user_username, user_password, user_full_name, user_email, user_role, user_is_active userId
R7 (Customer) customerId, customer_name, customer_email, customer_phone, customer_address customerId
R8 (Category) categoryId, category_name, category_description categoryId
R9 (Supplier) supplierId, supplier_name, supplier_contact_person, supplier_phone, supplier_email, supplier_address supplierId
R10 (Warehouse) warehouseId, warehouse_name, warehouse_location, warehouse_capacity warehouseId
R11 (WarehouseStock) warehouseId, productId, stock_quantity_on_hand, stock_last_updated {warehouseId, productId}

7. BCNF Декомпозиција

Проверка за BCNF

За секоја релација проверуваме: за секоја нетривијална FD X → Y, дали X е суперклуч?

R1 (Product)

FD Детерминант Суперклуч?
productId → сите productId ✓ ДА
product_sku → сите (FD6) product_sku ✓ ДА (кандидат клуч)

R1 е во BCNF ✓

R2 (Sale)

FD Детерминант Суперклуч?
saleId → сите saleId ✓ ДА

R2 е во BCNF ✓

R3 (PurchaseOrder)

FD Детерминант Суперклуч?
poId → сите poId ✓ ДА

R3 е во BCNF ✓

R4 (SaleItem)

FD Детерминант Суперклуч?
{saleId, productId} → сите {saleId, productId} ✓ ДА

R4 е во BCNF ✓

R5 (PurchaseOrderItem)

FD Детерминант Суперклуч?
{poId, productId} → сите {poId, productId} ✓ ДА

R5 е во BCNF ✓

R6 (User)

FD Детерминант Суперклуч?
userId → сите userId ✓ ДА
user_username → сите (FD2) user_username ✓ ДА (кандидат клуч)
user_email → сите (FD3) user_email ✓ ДА (кандидат клуч)

R6 е во BCNF ✓

R7 (Customer)

FD Детерминант Суперклуч?
customerId → сите customerId ✓ ДА

R7 е во BCNF ✓

R8 (Category)

FD Детерминант Суперклуч?
categoryId → сите categoryId ✓ ДА

R8 е во BCNF ✓

R9 (Supplier)

FD Детерминант Суперклуч?
supplierId → сите supplierId ✓ ДА

R9 е во BCNF ✓

R10 (Warehouse)

FD Детерминант Суперклуч?
warehouseId → сите warehouseId ✓ ДА

R10 е во BCNF ✓

R11 (WarehouseStock)

FD Детерминант Суперклуч?
{warehouseId, productId} → сите {warehouseId, productId} ✓ ДА

R11 е во BCNF ✓

Заклучок: Сите релации се во BCNF.

8. Финален резултат и дискусија

8.1 Финални релации

User(userId, username, password, full_name, email, role, is_active)
  - Примарен клуч: userId
  - Кандидат клучеви: userId, username, email
  - Надворешни клучеви: -

Customer(customerId, name, email, phone, address)
  - Примарен клуч: customerId
  - Кандидат клучеви: customerId
  - Надворешни клучеви: -

Category(categoryId, name, description)
  - Примарен клуч: categoryId
  - Кандидат клучеви: categoryId
  - Надворешни клучеви: -

Supplier(supplierId, name, contact_person, phone, email, address)
  - Примарен клуч: supplierId
  - Кандидат клучеви: supplierId
  - Надворешни клучеви: -

Warehouse(warehouseId, name, location, capacity)
  - Примарен клуч: warehouseId
  - Кандидат клучеви: warehouseId
  - Надворешни клучеви: -

Product(productId, name, description, sku, unit_price, reorder_level, categoryId, supplierId)
  - Примарен клуч: productId
  - Кандидат клучеви: productId, sku
  - Надворешни клучеви: categoryId → Category, supplierId → Supplier

Sale(saleId, date_time, total_amount, userId, customerId, warehouseId)
  - Примарен клуч: saleId
  - Кандидат клучеви: saleId
  - Надворешни клучеви: userId → User, customerId → Customer, warehouseId → Warehouse

PurchaseOrder(poId, order_date, expected_delivery_date, status, supplierId, warehouseId)
  - Примарен клуч: poId
  - Кандидат клучеви: poId
  - Надворешни клучеви: supplierId → Supplier, warehouseId → Warehouse

SaleItem(saleId, productId, quantity, unit_price_at_sale)
  - Примарен клуч: {saleId, productId}
  - Кандидат клучеви: {saleId, productId}
  - Надворешни клучеви: saleId → Sale, productId → Product

PurchaseOrderItem(poId, productId, quantity, unit_cost)
  - Примарен клуч: {poId, productId}
  - Кандидат клучеви: {poId, productId}
  - Надворешни клучеви: poId → PurchaseOrder, productId → Product

WarehouseStock(warehouseId, productId, quantity_on_hand, last_updated)
  - Примарен клуч: {warehouseId, productId}
  - Кандидат клучеви: {warehouseId, productId}
  - Надворешни клучеви: warehouseId → Warehouse, productId → Product

8.2 Дискусија на разликите од моделот во Фаза P2

Преку процесот на нормализација, тргнувајќи од една универзална релација, дојдовме до истите 11 релации како во концептуалниот модел од Фаза P2. Ова покажува дека:

  1. Концептуалниот модел беше правилно дизајниран - ентитетите и нивните атрибути беа логички групирани.
  1. Процесот на нормализација го потврди дизајнот - секоја декомпозиција базирана на функционалните зависности резултираше со релација која одговара на ентитет од оригиналниот модел.
  1. Клучот на универзалната релација {saleId, poId, productId} беше идентификуван преку анализа на функционалните зависности и класификација лева/десна страна.
  1. Сите релации се во BCNF - нема функционална зависност каде детерминантот не е суперклуч.
  1. Декомпозицијата е lossless - оригиналната информација може да се реконструира.
  1. Сите функционални зависности се зачувани - секоја FD е зачувана во барем една од финалните релации.
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