diff --git a/backend/Dockerfile b/backend/Dockerfile
index b862b2b..3639ea9 100644
--- a/backend/Dockerfile
+++ b/backend/Dockerfile
@@ -2,6 +2,10 @@ FROM python:3.10-slim
 
 WORKDIR /app
 
-RUN pip install fastapi uvicorn
+COPY requirements.txt .
 
-CMD ["uvicorn", "api.routes:app", "--host", "0.0.0.0", "--port", "8000", "--reload"]
\ No newline at end of file
+RUN pip install --no-cache-dir -r requirements.txt
+
+COPY . .
+
+CMD ["uvicorn", "api.main:app", "--host", "0.0.0.0", "--port", "8000", "--reload"]
diff --git a/backend/api/database/mongodb.py b/backend/api/database/mongodb.py
new file mode 100644
index 0000000..fbe5848
--- /dev/null
+++ b/backend/api/database/mongodb.py
@@ -0,0 +1,9 @@
+from motor.motor_asyncio import AsyncIOMotorClient
+
+MONGO_URL = "mongodb://mongo:27017"
+DB_NAME = "deckofcards"
+
+client = AsyncIOMotorClient(MONGO_URL)
+db = client[DB_NAME]
+
+users_collection = db["users"]
diff --git a/backend/api/main.py b/backend/api/main.py
new file mode 100644
index 0000000..1edd7e5
--- /dev/null
+++ b/backend/api/main.py
@@ -0,0 +1,41 @@
+from fastapi import FastAPI
+from fastapi.middleware.cors import CORSMiddleware
+from contextlib import asynccontextmanager
+from api.database.mongodb import db
+
+# Routers
+from api.routers.test_mongo import router as test_mongo_router
+from api.routers.value_function import router as value_router
+from api.routers.docmf_build import router as docmf_build_router
+from api.routers.docmf_evaluate import router as docmf_eval_router
+from api.routers.docmf_simple_validation import router as simple_validation_router
+from api.routers.docmf_validation import router as validation_router
+from api.routers.auth import router as auth_router
+from api.routers.history import router as history_router
+from api.routers.test_mongo import router as test_mongo_router
+
+@asynccontextmanager
+async def lifespan(app: FastAPI):
+    # Aquí podrías hacer comprobaciones si quieres
+    yield
+    # No hace falta cerrar nada con Motor
+
+app = FastAPI(lifespan=lifespan)
+
+app.add_middleware(
+    CORSMiddleware,
+    allow_origins=["*"],
+    allow_credentials=True,
+    allow_methods=["*"],
+    allow_headers=["*"],
+)
+
+app.include_router(test_mongo_router, prefix="/api")
+app.include_router(value_router, prefix="/api/criteria/doc")
+app.include_router(docmf_build_router, prefix="/api/criteria/doc-mf")
+app.include_router(docmf_eval_router, prefix="/api/criteria/doc-mf")
+app.include_router(simple_validation_router, prefix="/api/criteria/doc-mf")
+app.include_router(validation_router, prefix="/api/criteria/doc-mf")
+app.include_router(test_mongo_router, prefix="/api")
+app.include_router(auth_router, prefix="/api")
+app.include_router(history_router, prefix="/api")
\ No newline at end of file
diff --git a/backend/api/models/docmf_models.py b/backend/api/models/docmf_models.py
new file mode 100644
index 0000000..0cf9342
--- /dev/null
+++ b/backend/api/models/docmf_models.py
@@ -0,0 +1,47 @@
+from pydantic import BaseModel, field_validator
+from typing import List, Tuple
+
+class DoCMFRequest(BaseModel):
+    term: str
+    core: Tuple[float, float]
+    support: Tuple[float, float]
+    left_nodes_x: List[float]
+    left_blank_cards: List[int]
+    right_nodes_x: List[float]
+    right_blank_cards: List[int]
+
+    @field_validator("term")
+    def term_not_empty(cls, v):
+        if not v.strip():
+            raise ValueError("El término no puede estar vacío.")
+        return v
+
+    @field_validator("core")
+    def core_valid(cls, v):
+        a, b = v
+        if a > b:
+            raise ValueError("El núcleo debe cumplir a <= b.")
+        return v
+
+    @field_validator("support")
+    def support_valid(cls, v, info):
+        c, d = v
+        if c >= d:
+            raise ValueError("El soporte debe cumplir c < d.")
+
+        core = info.data.get("core")
+        if core:
+            a, b = core
+            if not (c <= a < b <= d):
+                raise ValueError("El núcleo debe estar dentro del soporte.")
+        return v
+
+    @field_validator("left_blank_cards", "right_blank_cards")
+    def cards_valid(cls, v):
+        if any(c < 0 for c in v):
+            raise ValueError("Las cartas no pueden ser negativas.")
+        return v
+
+
+class DoCMFMultiRequest(BaseModel):
+    levels: List[DoCMFRequest]
diff --git a/backend/api/models/docmf_simple_validation_models.py b/backend/api/models/docmf_simple_validation_models.py
new file mode 100644
index 0000000..246e5d5
--- /dev/null
+++ b/backend/api/models/docmf_simple_validation_models.py
@@ -0,0 +1,24 @@
+from pydantic import BaseModel, field_validator
+from typing import List, Tuple
+
+class SimpleLevelDefinition(BaseModel):
+    core: Tuple[float, float]
+    support: Tuple[float, float]
+
+    @field_validator("core")
+    def validate_core(cls, v):
+        a, b = v
+        if a >= b:
+            raise ValueError("El núcleo debe cumplir a < b.")
+        return v
+
+    @field_validator("support")
+    def validate_support(cls, v):
+        c, d = v
+        if c >= d:
+            raise ValueError("El soporte debe cumplir c < d.")
+        return v
+
+
+class SimpleValidationRequest(BaseModel):
+    levels: List[SimpleLevelDefinition]
diff --git a/backend/api/models/docmf_validation_models.py b/backend/api/models/docmf_validation_models.py
new file mode 100644
index 0000000..e62907d
--- /dev/null
+++ b/backend/api/models/docmf_validation_models.py
@@ -0,0 +1,37 @@
+from pydantic import BaseModel, field_validator
+from typing import List, Tuple
+
+class LevelDefinition(BaseModel):
+    core: Tuple[float, float]
+    support: Tuple[float, float]
+    left_nodes: List[Tuple[float, float]]
+    right_nodes: List[Tuple[float, float]]
+
+    @field_validator("core")
+    def validate_core(cls, v):
+        a, b = v
+        if a >= b:
+            raise ValueError("El núcleo debe cumplir a < b.")
+        return v
+
+    @field_validator("support")
+    def validate_support(cls, v):
+        c, d = v
+        if c >= d:
+            raise ValueError("El soporte debe cumplir c < d.")
+        return v
+
+    @field_validator("left_nodes", "right_nodes")
+    def validate_nodes(cls, v):
+        if len(v) < 2:
+            raise ValueError("Debe haber al menos 2 nodos.")
+        xs = [p[0] for p in v]
+        if xs != sorted(xs):
+            raise ValueError("Los nodos deben estar ordenados por x.")
+        if len(xs) != len(set(xs)):
+            raise ValueError("Los nodos no pueden tener valores x duplicados.")
+        return v
+
+
+class ValidationRequest(BaseModel):
+    levels: List[LevelDefinition]
diff --git a/backend/api/models/evaluation_models.py b/backend/api/models/evaluation_models.py
new file mode 100644
index 0000000..ca18221
--- /dev/null
+++ b/backend/api/models/evaluation_models.py
@@ -0,0 +1,35 @@
+from pydantic import BaseModel, field_validator
+from typing import List, Tuple
+
+class EvaluationRequest(BaseModel):
+    x: float
+    core: Tuple[float, float]
+    support: Tuple[float, float]
+    left_nodes: List[Tuple[float, float]]
+    right_nodes: List[Tuple[float, float]]
+
+    @field_validator("core")
+    def core_valid(cls, v):
+        a, b = v
+        if a > b:
+            raise ValueError("El núcleo debe cumplir a <= b.")
+        return v
+
+    @field_validator("support")
+    def support_valid(cls, v, info):
+        c, d = v
+        if c >= d:
+            raise ValueError("El soporte debe cumplir c < d.")
+
+        core = info.data.get("core")
+        if core:
+            a, b = core
+            if not (c <= a < b <= d):
+                raise ValueError("El núcleo debe estar dentro del soporte.")
+        return v
+
+    @field_validator("left_nodes", "right_nodes")
+    def nodes_valid(cls, v):
+        if len(v) < 2:
+            raise ValueError("Debe haber al menos 2 nodos.")
+        return v
diff --git a/backend/api/models/user_models.py b/backend/api/models/user_models.py
new file mode 100644
index 0000000..c611c6f
--- /dev/null
+++ b/backend/api/models/user_models.py
@@ -0,0 +1,44 @@
+from typing import List, Optional
+from pydantic import BaseModel, EmailStr, Field
+from datetime import datetime
+
+
+class FuzzyTerm(BaseModel):
+    term: str
+    core: List[float]
+    support: List[float]
+    left_nodes: List[List[float]]
+    right_nodes: List[List[float]]
+
+
+class HistoryItem(BaseModel):
+    id: Optional[str] = Field(default=None, alias="_id")
+    name: str
+    created_at: datetime
+    results: List[FuzzyTerm]
+
+
+class HistoryCreateRequest(BaseModel):
+    name: str
+    results: List[FuzzyTerm]
+
+
+class UserCreate(BaseModel):
+    username: str
+    email: EmailStr
+    password: str
+
+
+class UserLogin(BaseModel):
+    email: EmailStr
+    password: str
+
+
+class UserInDB(BaseModel):
+    id: Optional[str] = Field(default=None, alias="_id")
+    username: str
+    email: EmailStr
+    password_hash: str
+    token: Optional[str] = None
+    history: List[HistoryItem] = []
+
diff --git a/backend/api/models/value_function_models.py b/backend/api/models/value_function_models.py
new file mode 100644
index 0000000..66aaed5
--- /dev/null
+++ b/backend/api/models/value_function_models.py
@@ -0,0 +1,36 @@
+from pydantic import BaseModel, field_validator
+from typing import List, Dict
+
+class ValueFunctionRequest(BaseModel):
+    criterion_name: str
+    levels: List[str]
+    blank_cards: List[int]
+    references: Dict[str, float]
+
+    @field_validator("criterion_name")
+    def name_not_empty(cls, v):
+        if not v.strip():
+            raise ValueError("El nombre no puede estar vacío.")
+        return v
+
+    @field_validator("levels")
+    def levels_not_empty(cls, v):
+        if len(v) < 2:
+            raise ValueError("Debe haber al menos 2 niveles.")
+        return v
+
+    @field_validator("blank_cards")
+    def cards_valid(cls, v, info):
+        if any(c < 0 for c in v):
+            raise ValueError("Las cartas no pueden ser negativas.")
+
+        levels = info.data.get("levels")
+        if levels and len(v) != len(levels) - 1:
+            raise ValueError("Debe haber uno menos de número de cartas blancas que de niveles.")
+        return v
+
+    @field_validator("references")
+    def refs_valid(cls, v):
+        if len(v) != 2:
+            raise ValueError("Debe haber 2 referencias.")
+        return v
diff --git a/backend/api/routers/auth.py b/backend/api/routers/auth.py
new file mode 100644
index 0000000..2287379
--- /dev/null
+++ b/backend/api/routers/auth.py
@@ -0,0 +1,89 @@
+from fastapi import APIRouter, HTTPException, status
+from api.database.mongodb import users_collection
+from api.models.user_models import UserCreate, UserLogin
+from api.utils.security import hash_password, verify_password, generate_token
+from bson import ObjectId
+
+router = APIRouter(prefix="/auth", tags=["auth"])
+
+
+@router.post("/register")
+async def register_user(user: UserCreate):
+    existing_username = await users_collection.find_one({"username": user.username})
+    if existing_username:
+        raise HTTPException(
+            status_code=status.HTTP_400_BAD_REQUEST,
+            detail="El nombre de usuario ya está en uso",
+        )
+
+    existing_email = await users_collection.find_one({"email": user.email})
+    if existing_email:
+        raise HTTPException(
+            status_code=status.HTTP_400_BAD_REQUEST,
+            detail="El email ya está registrado",
+        )
+
+    token = generate_token()
+
+    user_doc = {
+        "username": user.username,
+        "email": user.email,
+        "password_hash": hash_password(user.password),
+        "token": token,
+        "history": [],
+    }
+
+    result = await users_collection.insert_one(user_doc)
+
+    return {
+        "message": "Usuario registrado correctamente",
+        "user_id": str(result.inserted_id),
+        "token": token,
+    }
+
+
+@router.post("/login")
+async def login_user(credentials: UserLogin):
+    user = await users_collection.find_one({"email": credentials.email})
+    if not user:
+        raise HTTPException(
+            status_code=status.HTTP_401_UNAUTHORIZED,
+            detail="Credenciales inválidas",
+        )
+
+    if not verify_password(credentials.password, user["password_hash"]):
+        raise HTTPException(
+            status_code=status.HTTP_401_UNAUTHORIZED,
+            detail="Credenciales inválidas",
+        )
+
+    new_token = generate_token()
+
+    await users_collection.update_one(
+        {"_id": user["_id"]},
+        {"$set": {"token": new_token}}
+    )
+
+    return {
+        "message": "Login correcto",
+        "user_id": str(user["_id"]),
+        "username": user["username"],
+        "token": new_token,
+    }
+
+
+@router.post("/logout/{user_id}")
+async def logout_user(user_id: str):
+    user = await users_collection.find_one({"_id": ObjectId(user_id)})
+    if not user:
+        raise HTTPException(
+            status_code=status.HTTP_404_NOT_FOUND,
+            detail="Usuario no encontrado",
+        )
+
+    await users_collection.update_one(
+        {"_id": ObjectId(user_id)},
+        {"$set": {"token": None}}
+    )
+
+    return {"message": "Sesión cerrada correctamente"}
diff --git a/backend/api/routers/docmf_build.py b/backend/api/routers/docmf_build.py
new file mode 100644
index 0000000..24467c4
--- /dev/null
+++ b/backend/api/routers/docmf_build.py
@@ -0,0 +1,12 @@
+from fastapi import APIRouter, HTTPException
+from api.models.docmf_models import DoCMFMultiRequest
+from api.services.docmf_build_service import build_docmf_multi
+
+router = APIRouter()
+
+@router.post("/build")
+def build(request: DoCMFMultiRequest):
+    try:
+        return build_docmf_multi(request)
+    except Exception as e:
+        raise HTTPException(status_code=400, detail=str(e))
diff --git a/backend/api/routers/docmf_evaluate.py b/backend/api/routers/docmf_evaluate.py
new file mode 100644
index 0000000..3024fe8
--- /dev/null
+++ b/backend/api/routers/docmf_evaluate.py
@@ -0,0 +1,12 @@
+from fastapi import APIRouter, HTTPException
+from api.models.evaluation_models import EvaluationRequest
+from api.services.docmf_evaluate_service import evaluate_docmf
+
+router = APIRouter()
+
+@router.post("/evaluate")
+def evaluate(request: EvaluationRequest):
+    try:
+        return evaluate_docmf(request)
+    except Exception as e:
+        raise HTTPException(status_code=400, detail=str(e))
diff --git a/backend/api/routers/docmf_simple_validation.py b/backend/api/routers/docmf_simple_validation.py
new file mode 100644
index 0000000..425384a
--- /dev/null
+++ b/backend/api/routers/docmf_simple_validation.py
@@ -0,0 +1,38 @@
+from fastapi import APIRouter, HTTPException
+from api.models.docmf_simple_validation_models import SimpleValidationRequest
+from api.services.docmf_simple_validation_service import validate_simple_levels
+
+router = APIRouter()
+
+@router.post("/validate-simple")
+def validate_simple_docmf(request: SimpleValidationRequest):
+    results = validate_simple_levels(request.levels)
+    invalid = [r for r in results if not r["valid"]]
+
+    # Caso: un solo nivel
+    if len(request.levels) == 1:
+        if invalid:
+            raise HTTPException(
+                status_code=400,
+                detail={
+                    "message": "El nivel es incorrecto.",
+                    "errors": invalid[0]["errors"]
+                }
+            )
+        return {
+            "message": "El nivel es correcto.",
+            "details": results[0]
+        }
+
+    # Caso: varios niveles
+    if invalid:
+        return {
+            "message": "Validación completada.",
+            "valid_levels": [r for r in results if r["valid"]],
+            "invalid_levels": invalid
+        }
+
+    return {
+        "message": "Todos los niveles son correctos.",
+        "results": results
+    }
diff --git a/backend/api/routers/docmf_validation.py b/backend/api/routers/docmf_validation.py
new file mode 100644
index 0000000..92eda8d
--- /dev/null
+++ b/backend/api/routers/docmf_validation.py
@@ -0,0 +1,39 @@
+from fastapi import APIRouter, HTTPException
+from api.models.docmf_validation_models import ValidationRequest
+from api.services.docmf_validation_service import validate_levels
+
+router = APIRouter()
+
+@router.post("/validate")
+def validate_docmf_levels(request: ValidationRequest):
+    results = validate_levels(request.levels)
+
+    invalid = [r for r in results if not r["valid"]]
+
+    if len(request.levels) == 1:
+        # Caso de un solo nivel
+        if invalid:
+            raise HTTPException(
+                status_code=400,
+                detail={
+                    "message": "El nivel es incorrecto.",
+                    "errors": invalid[0]["errors"]
+                }
+            )
+        return {
+            "message": "El nivel es correcto.",
+            "details": results[0]
+        }
+
+    # Caso de varios niveles
+    if invalid:
+        return {
+            "message": "Validación completada.",
+            "valid_levels": [r for r in results if r["valid"]],
+            "invalid_levels": invalid
+        }
+
+    return {
+        "message": "Todos los niveles son correctos.",
+        "results": results
+    }
diff --git a/backend/api/routers/history.py b/backend/api/routers/history.py
new file mode 100644
index 0000000..fadd769
--- /dev/null
+++ b/backend/api/routers/history.py
@@ -0,0 +1,62 @@
+from fastapi import APIRouter, HTTPException, status
+from typing import List
+from datetime import datetime
+from bson import ObjectId
+
+from api.database.mongodb import users_collection
+from api.models.user_models import FuzzyTerm, HistoryCreateRequest
+
+router = APIRouter(prefix="/history", tags=["history"])
+
+
+@router.post("/{user_id}/add")
+async def add_history_item(user_id: str, data: HistoryCreateRequest):
+    user = await users_collection.find_one({"_id": ObjectId(user_id)})
+    if not user:
+        raise HTTPException(
+            status_code=status.HTTP_404_NOT_FOUND,
+            detail="Usuario no encontrado",
+        )
+
+    history_item_id = ObjectId()
+
+    history_item = {
+        "_id": history_item_id,
+        "name": data.name,  # ← nuevo campo
+        "created_at": datetime.utcnow(),
+        "results": [r.dict() for r in data.results],
+    }
+
+    await users_collection.update_one(
+        {"_id": ObjectId(user_id)},
+        {"$push": {"history": history_item}},
+    )
+
+    return {
+        "message": "Elemento añadido al historial",
+        "history_item_id": str(history_item_id),
+    }
+
+
+
+@router.delete("/{user_id}/delete/{history_item_id}")
+async def delete_history_item(user_id: str, history_item_id: str):
+    user = await users_collection.find_one({"_id": ObjectId(user_id)})
+    if not user:
+        raise HTTPException(
+            status_code=status.HTTP_404_NOT_FOUND,
+            detail="Usuario no encontrado",
+        )
+
+    result = await users_collection.update_one(
+        {"_id": ObjectId(user_id)},
+        {"$pull": {"history": {"_id": ObjectId(history_item_id)}}},
+    )
+
+    if result.modified_count == 0:
+        raise HTTPException(
+            status_code=status.HTTP_404_NOT_FOUND,
+            detail="Elemento de historial no encontrado",
+        )
+
+    return {"message": "Elemento eliminado del historial"}
diff --git a/backend/api/routers/test_mongo.py b/backend/api/routers/test_mongo.py
new file mode 100644
index 0000000..43dd15d
--- /dev/null
+++ b/backend/api/routers/test_mongo.py
@@ -0,0 +1,12 @@
+from fastapi import APIRouter
+from api.database.mongodb import db
+
+router = APIRouter()
+
+@router.get("/test-mongo")
+async def test_mongo():
+    try:
+        await db.command("ping")
+        return {"status": "ok", "message": "Conexión a MongoDB correcta"}
+    except Exception as e:
+        return {"status": "error", "message": str(e)}
diff --git a/backend/api/routers/value_function.py b/backend/api/routers/value_function.py
new file mode 100644
index 0000000..0dfc5a4
--- /dev/null
+++ b/backend/api/routers/value_function.py
@@ -0,0 +1,19 @@
+from fastapi import APIRouter, HTTPException
+from api.models.value_function_models import ValueFunctionRequest
+from api.services.value_function_service import compute_value_function, compute_points
+
+router = APIRouter()
+
+@router.post("/value-function")
+def value_function(request: ValueFunctionRequest):
+    try:
+        return compute_value_function(request)
+    except Exception as e:
+        raise HTTPException(status_code=400, detail=str(e))
+
+@router.post("/value-function/points")
+def value_function_points(request: ValueFunctionRequest):
+    try:
+        return compute_points(request)
+    except Exception as e:
+        raise HTTPException(status_code=400, detail=str(e))
diff --git a/backend/api/routes.py b/backend/api/routes.py
deleted file mode 100644
index 10544bc..0000000
--- a/backend/api/routes.py
+++ /dev/null
@@ -1,210 +0,0 @@
-from fastapi import FastAPI
-from pydantic import BaseModel
-from typing import List, Dict, Tuple
-from fastapi.middleware.cors import CORSMiddleware 
-
-app = FastAPI()
-
-# Configuración CORS para permitir peticiones desde React
-app.add_middleware(
-    CORSMiddleware,
-    allow_origins=["*"],  # Permite cualquier origen (perfecto para desarrollo local)
-    allow_credentials=True,
-    allow_methods=["*"],  # Permite POST, GET, OPTIONS, etc.
-    allow_headers=["*"],  # Permite cualquier cabecera
-)
-
-# -----------------------------
-# MODELOS
-# -----------------------------
-
-class ValueFunctionRequest(BaseModel):
-    criterion_name: str
-    levels: List[str]
-    blank_cards: List[int]
-    references: Dict[str, float]
-
-class DoCMFRequest(BaseModel):
-    term: str
-    core: Tuple[float, float]      # [a, b]
-    support: Tuple[float, float]   # [c, d]
-    left_nodes_x: List[float]
-    left_blank_cards: List[int]
-    right_nodes_x: List[float]
-    right_blank_cards: List[int]
-
-class EvaluationRequest(BaseModel):
-    x: float
-    left_nodes: List[Tuple[float, float]]
-    right_nodes: List[Tuple[float, float]]
-    core: Tuple[float, float]
-    support: Tuple[float, float]
-
-
-# -----------------------------
-# ENDPOINT 1: FUNCIÓN DE VALOR DoC
-# -----------------------------
-
-@app.post("/api/criteria/doc/value-function")
-def calcular_value_function(request: ValueFunctionRequest):
-    levels = request.levels
-    cards = request.blank_cards
-    refs = request.references
-
-    ref_indices = sorted(int(k) for k in refs)
-    p, q = ref_indices
-    up, uq = refs[str(p)], refs[str(q)]
-
-    total_units = sum(cards[i] + 1 for i in range(p, q))
-    alpha = (uq - up) / total_units if total_units else 0
-
-    values = [0] * len(levels)
-    values[p] = up
-
-    for i in range(p + 1, len(levels)):
-        units = sum(cards[r] + 1 for r in range(p, i))
-        values[i] = up + alpha * units
-
-    for i in range(p - 1, -1, -1):
-        units = sum(cards[r] + 1 for r in range(i, p))
-        values[i] = up - alpha * units
-
-    return {
-        "criterion_name": request.criterion_name,
-        "values": {levels[i]: round(values[i], 4) for i in range(len(levels))}
-    }
-
-
-# -----------------------------
-# ENDPOINT 2: CONSTRUIR DoC-MF
-# -----------------------------
-
-@app.post("/api/criteria/doc-mf/build")
-def build_doc_mf(request: DoCMFRequest):
-
-    a, b = request.core
-    c, d = request.support
-
-    # ---- LADO IZQUIERDO ----
-    left_x = request.left_nodes_x
-    left_e = request.left_blank_cards
-
-    TL = sum(e + 1 for e in left_e)
-    YL = 1 / TL if TL else 0
-
-    left_nodes = []
-    acc = 0
-    for i in range(len(left_x)):
-        if i == 0:
-            left_nodes.append((left_x[i], 0.0))
-        else:
-            acc += (left_e[i-1] + 1)
-            left_nodes.append((left_x[i], round(acc * YL, 4)))
-
-    # ---- LADO DERECHO ----
-    right_x = request.right_nodes_x
-    right_e = request.right_blank_cards
-
-    TR = sum(e + 1 for e in right_e)
-    YR = 1 / TR if TR else 0
-
-    right_nodes = []
-    acc = 0
-    for i in range(len(right_x)):
-        if i == 0:
-            right_nodes.append((right_x[i], 1.0))
-        else:
-            acc += (right_e[i-1] + 1)
-            right_nodes.append((right_x[i], round(1 - acc * YR, 4)))
-
-    return {
-        "term": request.term,
-        "core": request.core,
-        "support": request.support,
-        "left_nodes": left_nodes,
-        "right_nodes": right_nodes
-    }
-
-
-# -----------------------------
-# ENDPOINT 3: EVALUAR UN VALOR x
-# -----------------------------
-
-def linear_interpolation(x, nodes):
-    for i in range(len(nodes) - 1):
-        x0, y0 = nodes[i]
-        x1, y1 = nodes[i+1]
-        if x0 <= x <= x1:
-            t = (x - x0) / (x1 - x0)
-            return y0 + t * (y1 - y0)
-    return 0.0
-
-@app.post("/api/criteria/doc-mf/evaluate")
-def evaluate_doc_mf(request: EvaluationRequest):
-    x = request.x
-    a, b = request.core
-    c, d = request.support
-
-    if x < c or x > d:
-        return {
-            "membership": 0.0,
-            "explanation": "El valor está fuera del soporte, por eso la pertenencia es 0."
-        }
-
-    if a <= x <= b:
-        return {
-            "membership": 1.0,
-            "explanation": "El valor está dentro del núcleo, por eso la pertenencia es 1."
-        }
-
-    if c <= x < a:
-        mu = linear_interpolation(x, request.left_nodes)
-        return {
-            "membership": mu,
-            "explanation": "El valor está en el lado izquierdo y se interpola entre nodos."
-        }
-
-    if b < x <= d:
-        mu = linear_interpolation(x, request.right_nodes)
-        return {
-            "membership": mu,
-            "explanation": "El valor está en el lado derecho y se interpola entre nodos."
-        }
-
-    return {
-        "membership": 0.0,
-        "explanation": "No se pudo determinar la pertenencia."
-    }
-
-
-# -----------------------------
-# ENDPOINT 4: PUNTOS (x,y) DE LA FUNCIÓN DE VALOR
-# -----------------------------
-
-@app.post("/api/criteria/doc/value-function/points")
-def value_function_points(request: ValueFunctionRequest):
-    levels = request.levels
-    cards = request.blank_cards
-    refs = request.references
-
-    ref_indices = sorted(int(k) for k in refs)
-    p, q = ref_indices
-    up, uq = refs[str(p)], refs[str(q)]
-
-    total_units = sum(cards[i] + 1 for i in range(p, q))
-    alpha = (uq - up) / total_units if total_units else 0
-
-    values = [0] * len(levels)
-    values[p] = up
-
-    for i in range(p + 1, len(levels)):
-        units = sum(cards[r] + 1 for r in range(p, i))
-        values[i] = up + alpha * units
-
-    for i in range(p - 1, -1, -1):
-        units = sum(cards[r] + 1 for r in range(i, p))
-        values[i] = up - alpha * units
-
-    points = [{"x": i, "y": round(values[i], 4)} for i in range(len(levels))]
-
-    return {"points": points}
diff --git a/backend/api/services/docmf_build_service.py b/backend/api/services/docmf_build_service.py
new file mode 100644
index 0000000..7c88660
--- /dev/null
+++ b/backend/api/services/docmf_build_service.py
@@ -0,0 +1,45 @@
+def build_single_docmf(request):
+    a, b = request.core
+    c, d = request.support
+
+    # LEFT
+    TL = sum(e + 1 for e in request.left_blank_cards)
+    YL = 1 / TL
+    left_nodes = []
+    acc = 0
+
+    for i, x in enumerate(request.left_nodes_x):
+        if i == 0:
+            left_nodes.append((x, 0.0))
+        else:
+            acc += request.left_blank_cards[i-1] + 1
+            left_nodes.append((x, round(acc * YL, 4)))
+
+    # RIGHT
+    TR = sum(e + 1 for e in request.right_blank_cards)
+    YR = 1 / TR
+    right_nodes = []
+    acc = 0
+
+    for i, x in enumerate(request.right_nodes_x):
+        if i == 0:
+            right_nodes.append((x, 1.0))
+        else:
+            acc += request.right_blank_cards[i-1] + 1
+            right_nodes.append((x, round(1 - acc * YR, 4)))
+
+    return {
+        "term": request.term,
+        "core": request.core,
+        "support": request.support,
+        "left_nodes": left_nodes,
+        "right_nodes": right_nodes
+    }
+
+
+def build_docmf_multi(request):
+    results = []
+    for level in request.levels:
+        result = build_single_docmf(level)
+        results.append(result)
+    return {"results": results}
diff --git a/backend/api/services/docmf_evaluate_service.py b/backend/api/services/docmf_evaluate_service.py
new file mode 100644
index 0000000..5b31eb0
--- /dev/null
+++ b/backend/api/services/docmf_evaluate_service.py
@@ -0,0 +1,22 @@
+from api.utils.interpolation import linear_interpolation
+
+def evaluate_docmf(request):
+    x = request.x
+    a, b = request.core
+    c, d = request.support
+
+    if x < c or x > d:
+        return {"membership": 0.0, "explanation": "Fuera del soporte."}
+
+    if a <= x <= b:
+        return {"membership": 1.0, "explanation": "Dentro del núcleo."}
+
+    if c <= x < a:
+        mu = linear_interpolation(x, request.left_nodes)
+        return {"membership": mu, "explanation": f"El valor x={x} se interpola entre los nodos {request.left_nodes} del lado izquierdo."}
+
+    if b < x <= d:
+        mu = linear_interpolation(x, request.right_nodes)
+        return {"membership": mu, "explanation": f"El valor x={x} se interpola entre los nodos {request.right_nodes} del lado derecho."}
+
+    raise ValueError("No se pudo evaluar el valor.")
diff --git a/backend/api/services/docmf_simple_validation_service.py b/backend/api/services/docmf_simple_validation_service.py
new file mode 100644
index 0000000..253f910
--- /dev/null
+++ b/backend/api/services/docmf_simple_validation_service.py
@@ -0,0 +1,25 @@
+def validate_simple_level(level: dict):
+    errors = []
+
+    a, b = level["core"]
+    c, d = level["support"]
+
+    # Validación: núcleo dentro del soporte
+    if not (c <= a < b <= d):
+        errors.append("El núcleo debe estar completamente dentro del soporte.")
+
+    return errors
+
+
+def validate_simple_levels(levels):
+    results = []
+
+    for idx, level in enumerate(levels):
+        errors = validate_simple_level(level.dict())
+        results.append({
+            "level_index": idx,
+            "valid": len(errors) == 0,
+            "errors": errors
+        })
+
+    return results
diff --git a/backend/api/services/docmf_validation_service.py b/backend/api/services/docmf_validation_service.py
new file mode 100644
index 0000000..97ccfa5
--- /dev/null
+++ b/backend/api/services/docmf_validation_service.py
@@ -0,0 +1,39 @@
+def validate_single_level(level: dict):
+    errors = []
+
+    a, b = level["core"]
+    c, d = level["support"]
+
+    # Core dentro del soporte
+    if not (c <= a < b <= d):
+        errors.append("El núcleo debe estar completamente dentro del soporte.")
+
+    # Nodos cubren correctamente el soporte
+    left = level["left_nodes"]
+    right = level["right_nodes"]
+
+    if left[0][0] != c:
+        errors.append("El primer nodo izquierdo debe coincidir con el inicio del soporte.")
+    if left[-1][0] != a:
+        errors.append("El último nodo izquierdo debe coincidir con el inicio del núcleo.")
+
+    if right[0][0] != b:
+        errors.append("El primer nodo derecho debe coincidir con el final del núcleo.")
+    if right[-1][0] != d:
+        errors.append("El último nodo derecho debe coincidir con el final del soporte.")
+
+    return errors
+
+
+def validate_levels(levels):
+    results = []
+
+    for idx, level in enumerate(levels):
+        errors = validate_single_level(level.dict())
+        results.append({
+            "level_index": idx,
+            "valid": len(errors) == 0,
+            "errors": errors
+        })
+
+    return results
diff --git a/backend/api/services/value_function_service.py b/backend/api/services/value_function_service.py
new file mode 100644
index 0000000..07039b0
--- /dev/null
+++ b/backend/api/services/value_function_service.py
@@ -0,0 +1,38 @@
+def compute_value_function(request):
+    levels = request.levels
+    cards = request.blank_cards
+    refs = request.references
+
+    p, q = sorted(int(k) for k in refs)
+    up, uq = refs[str(p)], refs[str(q)]
+
+    if len(levels) < 3:
+        raise ValueError("Mínimo debe haber 3 niveles para esta funcionalidad.")
+
+    total_units = sum(cards[i] + 1 for i in range(p, q))
+    if total_units == 0:
+        raise ValueError("Las cartas no pueden generar 0 unidades.")
+
+    alpha = (uq - up) / total_units
+
+    values = [0] * len(levels)
+    values[p] = up
+
+    for i in range(p + 1, len(levels)):
+        units = sum(cards[r] + 1 for r in range(p, i))
+        values[i] = up + alpha * units
+
+    for i in range(p - 1, -1, -1):
+        units = sum(cards[r] + 1 for r in range(i, p))
+        values[i] = up - alpha * units
+
+    return {
+        "criterion_name": request.criterion_name,
+        "values": {levels[i]: round(values[i], 4) for i in range(len(levels))}
+    }
+
+
+def compute_points(request):
+    result = compute_value_function(request)
+    values = list(result["values"].values())
+    return {"points": [{"x": i, "y": values[i]} for i in range(len(values))]}
diff --git a/backend/api/utils/interpolation.py b/backend/api/utils/interpolation.py
new file mode 100644
index 0000000..ccfc35f
--- /dev/null
+++ b/backend/api/utils/interpolation.py
@@ -0,0 +1,8 @@
+def linear_interpolation(x, nodes):
+    for i in range(len(nodes) - 1):
+        x0, y0 = nodes[i]
+        x1, y1 = nodes[i+1]
+        if x0 <= x <= x1:
+            t = (x - x0) / (x1 - x0)
+            return y0 + t * (y1 - y0)
+    return 0.0
diff --git a/backend/api/utils/security.py b/backend/api/utils/security.py
new file mode 100644
index 0000000..6dd73c5
--- /dev/null
+++ b/backend/api/utils/security.py
@@ -0,0 +1,16 @@
+import secrets
+from passlib.context import CryptContext
+
+pwd_context = CryptContext(schemes=["bcrypt"], deprecated="auto")
+
+
+def hash_password(password: str) -> str:
+    return pwd_context.hash(password)
+
+
+def verify_password(plain_password: str, hashed_password: str) -> bool:
+    return pwd_context.verify(plain_password, hashed_password)
+
+
+def generate_token() -> str:
+    return secrets.token_hex(32)  # 64 caracteres seguros
diff --git a/backend/requirements.txt b/backend/requirements.txt
new file mode 100644
index 0000000..26ebe6e
--- /dev/null
+++ b/backend/requirements.txt
@@ -0,0 +1,7 @@
+fastapi
+uvicorn
+motor
+pydantic
+passlib
+bcrypt==4.0.1
+email-validator
diff --git a/docker-compose.yaml b/docker-compose.yaml
index 38e74c6..f0fa360 100644
--- a/docker-compose.yaml
+++ b/docker-compose.yaml
@@ -1,17 +1,35 @@
+version: "3.9"
+
 services:
   backend:
     build: 
       context: ./backend
+    container_name: backend
     ports:
       - "8000:8000"
     volumes:
       - ./backend:/app
+    depends_on:
+      - db
 
   frontend:
     build:
       context: ./frontend
+    container_name: frontend
     ports:
       - "5173:5173"
     volumes:
       - ./frontend:/app
-      - /app/node_modules
\ No newline at end of file
+      - /app/node_modules
+
+  db:
+    image: mongo:6
+    container_name: mongo
+    restart: always
+    ports:
+      - "27018:27017"
+    volumes:
+      - mongo_data:/data/db
+
+volumes:
+  mongo_data: