API reference

One page per module. Every public name is listed here with its one-line summary and a link to its full entry (signature, arguments, exceptions and runnable examples). The table is generated from the package at build time, so it cannot fall out of date.

The fuzzy number classes are also importable from the package root (from bulanik import TFN); everything else is imported from its module (from bulanik.mcdm import topsis).

Module	Contents
bulanik.numbers	Fuzzy number types: triangular, orthopair, three-part, interval-valued and interval type-2
bulanik.aggregate	Weighted average, weighted geometric mean, expert aggregation
bulanik.sets	Membership functions, linguistic variables, t-norms
bulanik.scales	Linguistic scales and the built-in ones
bulanik.inference	Rules, Mamdani, Sugeno and Tsukamoto systems
bulanik.type2	Interval type-2 sets, systems and type reduction
bulanik.anfis	Adaptive neuro-fuzzy inference
bulanik.mcdm	Weighting, ranking, outranking, DEMATEL and fuzzy ranking
bulanik.lumix	LumiX bridge (lumix extra)
bulanik.sezgi	sezgi bridge (sezgi extra)
bulanik.plot	Figures (plot extra)

bulanik.numbers

Full entries: bulanik.numbers

Name	Kind	Summary
FFN	class	Fermatean fuzzy number \((\mu, \nu)\) with \(\mu^3 + \nu^3 \le 1\) (q = 3, Senapati and Yager 2020).
FuzzyNumber	class	Common interface of fuzzy numbers.
IFN	class	Intuitionistic fuzzy number \((\mu, \nu)\) with \(\mu + \nu \le 1\) (q = 1, Atanassov 1986).
IT2TrFN	class	Interval type-2 trapezoidal fuzzy number \((\tilde A^U, \tilde A^L)\).
IVFFN	class	Interval-valued Fermatean fuzzy number with \(\mu_U^3 + \nu_U^3 \le 1\) (q = 3, Jeevaraj 2021).
IVIFN	class	Interval-valued intuitionistic fuzzy number with \(\mu_U + \nu_U \le 1\) (q = 1, Atanassov and Gargov 1989).
IVNeutrosophicFN	class	Interval neutrosophic number \(\langle [t_L, t_U], [i_L, i_U], [f_L, f_U] \rangle\).
IVPFN	class	Interval-valued Pythagorean fuzzy number with \(\mu_U^2 + \nu_U^2 \le 1\) (q = 2, Peng and Yang 2016).
IVQROFN	class	Interval-valued q-rung orthopair fuzzy number \(([\mu_L, \mu_U], [\nu_L, \nu_U])\).
NeutrosophicFN	class	Single-valued neutrosophic number \((t, i, f)\), each part in \([0, 1]\).
PFN	class	Pythagorean fuzzy number \((\mu, \nu)\) with \(\mu^2 + \nu^2 \le 1\) (q = 2, Yager 2013).
PictureFN	class	Picture fuzzy number \((\mu, \eta, \nu)\) with \(\mu + \eta + \nu \le 1\).
QROFN	class	q-rung orthopair fuzzy number \((\mu, \nu)\) with \(\mu^q + \nu^q \le 1\).
SphericalFN	class	Spherical fuzzy number \((\mu, \nu, \pi)\) with \(\mu^2 + \nu^2 + \pi^2 \le 1\).
TFN	class	Triangular fuzzy number \((l, m, u)\) with \(l \le m \le u\).
TrFN	class	Trapezoidal fuzzy number \((a, b, c, d)\) with \(a \le b \le c \le d\).

bulanik.aggregate

Full entries: bulanik.aggregate

Name	Kind	Summary
aggregate_experts	function	Aggregate expert ratings indexed [expert][alternative][criterion].
wa	function	Weighted average \(\sum_i w_i A_i\) with the type's own operators.
wg	function	Weighted geometric mean \(\prod_i A_i^{w_i}\) with the type's own operators.

bulanik.sets

Full entries: bulanik.sets

Name	Kind	Summary
bell	function	Generalized bell \(\dfrac{1}{1 + \lvert (x - c)/a \rvert^{2b}}\) with \(a > 0\), \(b > 0\).
gaussian	function	Gaussian \(\exp\!\left(-\frac{(x - \text{mean})^2}{2\sigma^2}\right)\) with \(\sigma > 0\).
linear_decreasing	function	Ramp down: 1 for x <= a, 0 for x >= b, linear in between (a < b).
linear_increasing	function	Ramp up: 0 for x <= a, 1 for x >= b, linear in between (a < b).
LinguisticVariable	class	A named variable on a universe (lo, hi) with named fuzzy terms.
MembershipFunction	class	A membership function \(\mu: \mathbb{R} \to [0, 1]\) of a named kind.
sigmoid	function	Sigmoid \(\dfrac{1}{1 + e^{-\text{slope}\,(x - \text{center})}}\) with \(\text{slope} \ne 0\).
SIGMOID_EPS	constant	Sigmoid memberships never reach exactly 0 or 1, so inverse of a sigmoid clamps alpha into \([\varepsilon, 1 - \varepsilon]\) with \(\varepsilon = 10^{-9}\) instead of returning \(\pm\infty\).
t_conorm	function	Fuzzy OR (t-conorm): "max" \(\max(a, b)\) or "probor" \(a + b - ab\).
t_norm	function	Fuzzy AND (t-norm): "min" \(\min(a, b)\) or "prod" \(a\,b\).
trapezoidal	function	Trapezoid with plateau [b, c] (a <= b <= c <= d, a < d).
triangular	function	Triangle with feet a, c and peak b (a <= b <= c, a < c).

bulanik.scales

Full entries: bulanik.scales

Name	Kind	Summary
EXAMPLE_IFN_5	constant	Example 5-term intuitionistic scale (VL, L, M, H, VH); illustrative values with no source.
EXAMPLE_IFN_7	constant	Example 7-term intuitionistic scale (EL, VL, L, M, H, VH, EH); illustrative values with no source.
EXAMPLE_TFN_7	constant	Example 7-term triangular rating scale on 0-10 (VP, P, MP, F, MG, G, VG); illustrative values with no source.
FUZZY_BWM_TFN	constant	The fuzzy best-worst method scale of Guo and Zhao (2017, Knowledge-Based Systems 121:23-31): equally (EI), weakly (WI), fairly (FI), very (VI) and absolutely (AI) important, as triangular numbers.
LinguisticScale	class	An ordered set of linguistic terms, all fuzzy numbers of one type.
SAATY_TFN	constant	Saaty's 1-9 scale as triangular numbers: "1" = (1,1,1), "k" = (k-1,k,k+1) for k = 2..8, "9" = (9,9,9).

bulanik.inference

Full entries: bulanik.inference

Name	Kind	Summary
And	class	Conjunction of antecedents (AND); nested conjunctions are flattened.
Antecedent	constant	An antecedent expression: a Term, or an And / Or of antecedents.
defuzzify_samples	function	Crisp value of a sampled fuzzy set.
Explanation	class	Everything behind one evaluation: degrees, rule activations and outputs.
firing_strength	function	Degree to which an antecedent holds.
Linear	class	First-order Sugeno consequent \(c_0 + \sum_i c_i x_i\) over named inputs.
MamdaniFIS	class	Mamdani fuzzy inference system (Mamdani and Assilian 1975).
NoRuleFiredError	class	No rule fired for an output and no default value was given.
Or	class	Disjunction of antecedents (OR); nested disjunctions are flattened.
parse_rule	function	Parse rule text IF ... THEN ... [WITH w] into a Rule.
Rule	class	IF antecedent THEN consequents [WITH weight].
rule_terms	function	All Term leaves of an antecedent, left to right.
RuleActivation	class	A rule's firing level: weight times antecedent degree.
SugenoFIS	class	Sugeno fuzzy inference system (Takagi and Sugeno 1985).
SugenoOutput	class	Output variable whose terms are constants (zero-order) or Linear (first-order).
Term	class	The atom variable IS term, or variable IS NOT term when negated.
TsukamotoFIS	class	Tsukamoto fuzzy inference system (Tsukamoto 1979).

bulanik.type2

Full entries: bulanik.type2

Name	Kind	Summary
gaussian_uncertain_mean	function	Gaussian with a mean anywhere in \([m_1, m_2]\) (Mendel 2001).
gaussian_uncertain_sigma	function	Gaussian with a width anywhere in \([\sigma_1, \sigma_2]\).
IT2LinguisticVariable	class	A named variable on a universe (lo, hi) with interval type-2 terms.
IT2MamdaniFIS	class	Interval type-2 Mamdani system with the centroid type reducer.
IT2MF	class	Interval type-2 membership function bounded by two type-1 functions.
IT2SugenoFIS	class	Interval type-2 Sugeno system with the centre-of-sets type reducer.
NoLowerFiringError	class	bmm type reduction needs a positive lower weight and every one is 0.
scaled_triangle	function	Triangle \(\operatorname{tri}(a, b, c)\) over a lower triangle \(h \cdot \operatorname{tri}(a, b, c)\).
type_reduce	function	Reduce points ys with interval weights [lower, upper] to a crisp value.
TypeReduced	class	Type-reduced interval [left, right] and the crisp output.

bulanik.anfis

Full entries: bulanik.anfis

Name	Kind	Summary
ANFIS	class	Grid-partition first-order Sugeno ANFIS (Jang 1993).
ExtrapolationWarning	class	ANFIS.predict was asked about inputs outside the trained ranges.
MIN_B	constant	Training floors the bell exponent b at MIN_B.
MIN_WIDTH	constant	Training floors a width (Gaussian sigma, bell a) at MIN_WIDTH * (hi - lo) of its input.

bulanik.mcdm

Full entries: bulanik.mcdm

Name	Kind	Summary
ahp	function	Saaty's AHP: principal-eigenvector weights and consistency ratio.
ahp_fuzzy_numbers	function	AHP over a comparison matrix of any one fuzzy number kind.
ahp_interval_valued	function	Interval-valued AHP over a comparison matrix of one IVQROFN kind.
BWMResult	class	Best-worst method weights (ranking is best first).
cocoso	function	CoCoSo (Yazdani et al. 2019): combined compromise solution.
codas	function	CODAS (Keshavarz Ghorabaee et al. 2016): distances from the negative-ideal point.
copras	function	COPRAS (Zavadskas, Kaklauskas & Sarka 1994): complex proportional assessment.
critic	function	CRITIC objective weights (Diakoulaki, Mavrotas & Papayannakis 1995).
DecisionMatrix	class	Expert ratings [expert][alternative][criterion] of one fuzzy number kind.
dematel	constant	DEMATEL: crisp and fuzzy (CFCS) influence analysis.
DEMATELResult	class	DEMATEL influence analysis: total-relation matrix, cause/effect groups and weights.
edas	function	EDAS (Keshavarz Ghorabaee et al. 2015): distance from the average solution.
electre	function	ELECTRE I (Roy 1968) with a complete ranking from net concordance and discordance.
entropy	function	Shannon-entropy objective weights from a decision matrix.
fuzzy_ahp	function	Buckley's fuzzy AHP (geometric mean of rows) with TFN judgements.
fuzzy_cocoso	function	CoCoSo on fuzzy numbers: weighted sum and weighted product as numbers, scored, then compromised.
fuzzy_codas	function	CODAS on fuzzy numbers: distances of the weighted numbers from the negative-ideal numbers.
fuzzy_topsis	function	Fuzzy TOPSIS of Chen (2000) on triangular fuzzy numbers.
fuzzy_waspas	function	WASPAS on fuzzy numbers: weighted sum and weighted product combined as numbers, then scored.
marcos	function	MARCOS (Stevic et al. 2020): measurement of alternatives and ranking according to compromise solution.
piprecia	function	PIPRECIA (Stanujkic et al. 2017) and its fully fuzzy form (Stevic et al. 2018).
rank_fuzzy	function	Aggregate experts, score the fuzzy numbers, then rank with a crisp method.
RankingResult	class	Alternative scores and their ranking (ranking is best first).
swara	function	SWARA (Kersuliene et al. 2010); criteria are listed most important first.
topsis	function	TOPSIS (Hwang & Yoon 1981) with vector normalisation, Euclidean distance.
vikor	function	VIKOR (Opricovic & Tzeng 2004); v is the weight of group utility.
waspas	function	WASPAS (Zavadskas et al. 2012): lam * WSM + (1 - lam) * WPM.
WeightingResult	class	Criteria weights from a weighting method (ranking is best first).
wisp	function	WISP (Stanujkic et al. 2023): integrated simple weighted sum product method.

bulanik.mcdm.bwm

Full entries: bulanik.mcdm.bwm

Name	Kind	Summary
bwm_consistency_index	function	Rezaei's (2015) consistency index for a best-over-worst comparison.
fuzzy_bwm_consistency_index	function	Guo & Zhao's (2017) consistency index for a fuzzy best-over-worst comparison.
resolve_best_worst	function	Validate BWM comparison vectors and resolve the best and worst criteria.

bulanik.lumix

Full entries: bulanik.lumix

Name	Kind	Summary
bwm_linear	function	Linear best-worst method (Rezaei 2016, Omega 64:126-130).
FuzzyGoal	class	A fuzzy goal on a linear expression \(z\) (Zimmermann 1978).
ScoreRecord	class	One scored item.
scores_as_data	function	MCDM scores as records for LXVariable(...).from_data(records).
solve_zimmermann	function	Build the Zimmermann model on model and solve it.
zimmermann	function	Add Zimmermann's max-min fuzzy goal rows to model and return it.
ZimmermannResult	class	Outcome of solve_zimmermann.

bulanik.sezgi

Full entries: bulanik.sezgi

Name	Kind	Summary
ANFISProblem	class	Training RMSE of an ANFIS as a sezgi problem.
ANFISTrainResult	class	Outcome of train_anfis.
BWMProblem	class	Rezaei's (2015, Omega 53:49-57) nonlinear best-worst method.
FuzzyBWMProblem	class	Guo & Zhao's (2017, Knowledge-Based Systems 121:23-31) fuzzy best-worst method.
train_anfis	function	Train a deep copy of anfis with sezgi; anfis itself is untouched.

bulanik.plot

Full entries: bulanik.plot

Name	Kind	Summary
alpha_cuts	function	The \(\alpha\)-cuts of a number as stacked horizontal intervals.
current_theme	function	The tokens of the active theme, as a read-only mapping.
defuzzification	function	A number with markers at the crisp values of its score functions.
dematel	function	DEMATEL cause-effect diagram: prominence against relation, with the strong influences.
it2_number	function	Interval type-2 trapezoidal numbers: upper and lower trapezoids and the footprint between them.
it2_set	function	Footprint of uncertainty of interval type-2 sets.
iv_orthopair	function	Interval-valued orthopair numbers as rectangles in the \(\mu\)–\(\nu\) plane.
mamdani_output	function	How a Mamdani system reaches its crisp output for one set of inputs.
membership	function	Membership functions of triangular and trapezoidal numbers on one axis.
neutrosophic	function	Neutrosophic numbers as \(T\)/\(I\)/\(F\) radar triangles.
orthopair	function	Orthopair numbers as points in the \(\mu\)–\(\nu\) plane with their feasible regions.
PALETTE	constant	The categorical palette: eight hues in a fixed order, one tuple per theme.
picture	function	Picture fuzzy numbers on the \(\mu\)–\(\eta\)–\(\nu\) ternary simplex.
ranking	function	Alternatives sorted best first, as a dot plot of their scores.
spherical	function	Spherical fuzzy numbers inside the positive octant of the unit sphere.
surface	function	Input-output map of a fuzzy system: a 3-D surface (2 inputs) or a curve (1 input).
theme	function	Context manager that applies the house style in a light or dark variant.
variable	function	Every term of a linguistic variable or scale, direct-labelled.
weights	function	Criteria weights as horizontal bars, largest first, value at each tip.