---
title: "IFFuzzyStats: Intuitionistic Fuzzy Statistics in R"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{IFFuzzyStats: Intuitionistic Fuzzy Statistics in R}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(collapse = TRUE, comment = "#>")
library(IFFuzzyStats)
```

## Intuitionistic fuzzy values

An intuitionistic fuzzy value (IFV) is a pair $(\mu, \nu)$ with
$\mu+\nu \le 1$; hesitation is $\pi = 1-\mu-\nu$.

```{r}
a <- ifv(0.6, 0.3)
a
if_pi(a)
if_score(a)
```

## Aggregation

Xu (2007) weighted averaging / geometric operators plus ordered and
hybrid variants:

```{r}
x <- ifv(c(0.6, 0.5, 0.7), c(0.3, 0.2, 0.1))
ifwa(x, c(0.5, 0.3, 0.2))
ifwg(x, c(0.5, 0.3, 0.2))
ifowa(x, c(0.5, 0.3, 0.2))
```

## Entropy, distance, similarity

```{r}
if_entropy(x, "szmidt")
if_entropy(x, "vlachos")
b <- ifv(c(0.5, 0.4, 0.6), c(0.3, 0.3, 0.2))
if_dist(x, b, "hamming")
if_dist(x, b, "euclidean")
if_sim(x, b, "ye_cosine")
if_sim(x, b, "dice")
```

## Clustering

```{r}
set.seed(1)
mu <- runif(30, 0.3, 0.7); nu <- runif(30, 0.05, 0.25)
d <- ifv(mu, nu)
r <- ifcmeans(d, k = 2, nstart = 2, maxit = 20)
table(r$cluster)
r$centers
```

## Inference and TOPSIS

Max-min composition and the compositional rule of inference:

```{r}
R <- ifv(c(0.6, 0.3, 0.8, 0.2), c(0.2, 0.5, 0.1, 0.6))
fact <- ifv(c(0.8, 0.2), c(0.1, 0.7))
if_infer(fact, R, nx = 2, ny = 2)
```

IF-TOPSIS for a 3-alternative, 2-criterion problem:

```{r}
m <- ifv(c(0.6, 0.5, 0.7, 0.4, 0.5, 0.6), c(0.2, 0.3, 0.1, 0.4, 0.3, 0.2))
if_topsis(m, nalt = 3, ncrit = 2, w = c(0.6, 0.4))
```