Numerical Application 2
 ———————————-
```
*p*-(*N* ≥ 1) ←(0.037287/0.039211/0.041130)

*p* -(*N* = 0) ←(0.958870/0.960789/0.962713) *P* - ← ⎛⎝ *p*-(*N* ≥ 1) *p*-(*N* = 0) 0 *p*-(*N* ≥ 1) 0 *p*-(*N* = 0) *p*-(*N* ≥ 1) 0 *p*-(*N* = 0) ⎞⎠ *πj* ← FuzzyStationaryDistribution(*P*-) Plot *πj* for *j* = 1, 2, 3 # ———————————- # Numerical Application 4 # ———————————- *p* -(*N* = 0) ←(0.958870/0.960789/0.962713) *p* -(*N* = 1) ←(0.036583/0.038432/0.040273) *p* -(*N* ≥ 1) ←(0.037287/0.039211/0.041130) *p* -(*N* ≥ 2) ←(0.000704/0.000779/0.000858) *p* - ← ⎛⎜⎜⎜⎜⎜⎜⎝ *p*-(*N* = 0) 0 *p*-(*N* = 1) 0 0 *p*-(*N* ≥ 2) *p*-(*N* = 0) 0 0 *p*-(*N* = 1) 0 *p*-(*N* ≥ 2) 0 *p*-(*N* = 0) 0 0 *p*-(*N* = 1) *p*-(*N* ≥ 2) 0 0 *p*-(*N* = 0) 0 0 *p*-(*N* ≥ 1) 000 *p*-(*N* = 0) 0 *p*-(*N* ≥ 1) 0000 *p*-(*N* = 0) *p*-(*N* ≥ 1) ⎞⎟⎟⎟⎟⎟⎟⎠ *πj* ← FuzzyStationaryDistribution(*P*-) Plot *πj* for *j* = 1, 2, . . . , 6 **Appendix B. R Codes of Numerical Applications 2 and 4** # ———————————- # Numerical Application 2 # ———————————- library(FuzzyNumbers) library(FuzzyStatProb) a = TriangularFuzzyNumber(0.037287, 0.039210, 0.041130) b = TriangularFuzzyNumber(0.958870, 0.960790, 0.962713) zero = TriangularFuzzyNumber(0, 0, 0) allnumbers = list(a = a, b = b, zero = zero) transitions = matrix(data = c("a", "b", NA, "a", NA, "b", "a", NA, "b"), nrow = 3, byrow = T) states = c("01", "02", "03") rownames(transitions) = states colnames(transitions) = states stationary = fuzzyStationaryProb(data = transitions, options = list(regression = "linear", fuzzynumbers = allnumbers)) m <- matrix(1:3, nrow = 1, ncol = 3, byrow = TRUE) layout(mat = m, heights = c(0.25, 0.25, 0.25, 0.25)) for (state in states){ cat("State", state, "\n") fz = stationary\$fuzzyStatProb[[state]] acuts = stationary\$acuts[[state]] print(acuts[acuts\$y == 0.001,]) print(acuts[acuts\$y == 0.999,]) par(mar = c(4, 4, 2, 1)) plot(fz, col = "blue", main = paste("State", state), cex.lab = 1.1, lwd = 2, xaxt = "n") left = supp(fz)[1] right = supp(fz)[2] center = core(fz)[1]

center), digits = 4)

 right,

at =

round(c(left,

```
axis(1, at = at, labels = FALSE)
       text(x = at, y = par("usr")[3] - 0.1,
            labels = at, srt = 35, xpd = NA)
       points(acuts)
       print("—————")
     }
     # ———————————-
     # Numerical Application 4
     # ———————————-
     pN0 = TriangularFuzzyNumber(0.958870, 0.960789, 0.962713)
     pN1 = TriangularFuzzyNumber(0.036583, 0.038432, 0.040273)
     pNgt1 = TriangularFuzzyNumber(0.037287, 0.039211, 0.041130)
     pNgt2 = TriangularFuzzyNumber(0.000704, 0.000779, 0.000858)
     allnumbers2 = list(pN0 = pN0, pN1 = pN1, pNgt1 = pNgt1, pNgt2 = pNgt2)
     transitions2 = matrix(data = c("pN0", NA, "pN1", NA, NA, "pNgt2", "pN0",
NA, NA, "pN1", NA, "pNgt2", NA, "pN0", NA, NA, "pN1", "pNgt2", NA, NA,
"pN0", NA, NA, "pNgt1", NA, NA, NA, "pN0", NA, "pNgt1", NA, NA,
NA, NA, "pN0", "pNgt1"), nrow = 6, byrow = T)
     states2 = c("01", "02", "03", "04", "05", "06")
     rownames(transitions2) = states2
     colnames(transitions2) = states2
     stationary2 = fuzzyStationaryProb(data = transitions2, options = list(regression =
"linear", fuzzynumbers = allnumbers2))
     m <- matrix(1:6, nrow = 2, ncol = 3, byrow = TRUE)
     layout(mat = m, heights = c(0.25, 0.25, 0.25, 0.25))
     for (state in states2){
       cat("State", state, "\n")
       fz = stationary2$fuzzyStatProb[[state]]
       acuts = stationary2$acuts[[state]]
       print(acuts[acuts$y == 0.001,])
       print(acuts[acuts$y == 0.999,])
       par(mar = c(4, 4, 2, 1))
       plot(fz, col = "blue", main = paste("State", state),
            cex.lab = 1.1, lwd = 2, xaxt = "n")
       left = supp(fz)[1]
       right = supp(fz)[2]
       center = core(fz)[1]
       at = round(c(left, right, center), digits = 5)
       axis(1, at = at, labels = FALSE)
       text(x = at, y = par("usr")[3] - 0.1,
            labels = at, srt = 35, xpd = NA)
       points(acuts)
       print("—————")
     }
```