Intuitionistic Fuzzy Statistics

Provides constructors and arithmetic for intuitionistic fuzzy values (intuitionistic fuzzy value, IFV) for intuitionistic fuzzy sets (Atanassov (1986) ), including aggregation operators of Xu (2007) and Xu and Yager (2006) : intuitionistic fuzzy weighted averaging (IFWA), intuitionistic fuzzy weighted geometric (IFWG), intuitionistic fuzzy ordered weighted averaging (IFOWA), intuitionistic fuzzy ordered weighted geometric (IFOWG), intuitionistic fuzzy hybrid averaging (IFHA), intuitionistic fuzzy hybrid geometric (IFHG), and Einstein operators; entropy (Szmidt and Kacprzyk (2000) ; Vlachos and Sergiadis (2007) ) and distance and similarity measures, including Ye (2011) cosine similarity and Hamming, Euclidean and Hausdorff distances; intuitionistic fuzzy c-means and k-means clustering; approximate reasoning via compositional inference; and multi-criteria decision support via intuitionistic fuzzy Technique for Order of Preference by Similarity to Ideal Solution (IF-TOPSIS) (Boran et al. (2009) ) and score ranking. All computations use only base R with fully vectorised implementations.

IFFuzzyStats: Intuitionistic Fuzzy Statistics Toolkit

Intuitionistic fuzzy sets (Atanassov, 1986) carry membership $\mu$, non-membership $\nu$ ($\mu+\nu\le 1$) and hesitation $\pi=1-\mu-\nu$. IFFuzzyStats is a zero-dependency (base-R only) toolkit covering:

ifv() constructor + if_add(), if_mul(), if_scalar_mul(), if_pow() (Xu arithmetic) and Einstein variants
aggregation: ifwa(), ifwg(), ifowa(), ifowg(), ifha(), ifhg(), if_einstein_wa(), if_einstein_wg()
entropy: if_entropy() (Burillo, Szmidt-Kacprzyk, Vlachos-Sergiadis, Zeng-Li)
distance: if_dist() (Hamming, Euclidean, Hausdorff, Ye, Ye-cosine, Park)
similarity: if_sim() (Chen, Hong-Kim, Ye cosine/weighted, Jaccard/Deng, Dice)
inference: if_compose(), if_infer(), if_rule_block()
clustering: ifcmeans(), ifkmeans()
decisions: if_topsis(), if_rank(), if_rank_df()
converters: if_fuzzify(), if_defuzzify(), if_score()

Install

# from local source
install.packages("/path/to/IFFuzzyStats_0.1.0.tar.gz", repos = NULL, type = "source")

Quick start

library(IFFuzzyStats)
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))
if_entropy(x, "szmidt")
if_sim(x, ifv(c(0.5, 0.4, 0.6), c(0.3, 0.3, 0.2)), "ye_cosine")

References

Atanassov (1986) Fuzzy Sets and Systems 20(1); Xu (2007) IEEE TFS 15(6); Szmidt & Kacprzyk (2000) FSS 114(3); Vlachos & Sergiadis (2007) PRL 28(2); Ye (2011) MCM 53(1-2); Boran et al. (2009) ESWA 36(8).