Mamdani and other Sugeno inference systems

[jean-demartini]

Hi all,
I'm discovering fuzzylogic module and very pleased with it. Obviously i've tried the example in the tutorial. All is OK.

But my objective is to use fuzzylogic to build a fuzzy pattern-recognition system. In that case, the consequent of a rule is better to be a crisp value (a number of a category for instance) associated with a a.k.a membership interpreted as a credence (in the Bayes logic meaning).

It seems that fuzzylogic is posed upon a Mamdani inference system well suited for control but not for patter recognition.

The tutorial is a very concise and i'm not sure if it is possible to build a Sugeno-like inference system that's to say to put a function as a consequent in a rule.

Its possible to use fuzzylogic to describe all the domains used. Its is also possible to define an inference system from ground base upon the evaluation of a domain from a value. But a full Sugeno( or others) could be more suitable.

Many thanks it somebody have an idea for that.

[amogorkon]

Hi! I'm glad you like it! It wasn't specifically designed for pattern recognition, but I did use parts of it for that purpose before. I admit I never heard of Sugeno-like fuzzy logic before, so I can't say for sure if it's possible what you imagine, but I can't see why not. The rules work with a dictionary, so it shouldn't be too hard to adapt and return arbitrary objects like functions instead. Can you give an example of what you have in mind?

[jean-demartini]

Hi Anselm, This link is an explaination of the inference systems  Mamdani of Sugeno https://www.mathworks.com/help/fuzzy/types-of-fuzzy-inference-systems.html Sugeno doesn't need a step of defuzzyfication and doesn't need only few computing ressources. It has been designed for being embarqued for process control in very small microcontrolers. It's exactly what I need. In fact, Sugeno can be considered as a Mamdani inference if consequents are singletons. With fuzzylogic, singleton is not a single point but a triangle. Then the result of the inference is not the value of the singleton but can produce intermediate values. For instance, pattern-recognition can use a Domain of only integers the corresponding Sets being only singletons. Many thanks for your interest. Jean Le mercredi 17 septembre 2025 à 07:44 -0700, Anselm Kiefner a écrit :

Hi! I'm glad you like it! It wasn't specifically designed for pattern recognition, but I did use parts of it for that purpose before. I admit I never heard of Sugeno-like fuzzy logic before, so I can't say for sure if it's possible what you imagine, but I can't see why not. The rules work with a dictionary, so it shouldn't be too hard to adapt and return arbitrary objects like functions instead. Can you give an example of what you have in mind? — Reply to this email directly, view it on GitHub [1], or unsubscribe [2]. You are receiving this because you authored the thread.Message ID: <Python-Fuzzylogic/fuzzylogic/repo- ***@***.***>

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[amogorkon]

Heh. Looking at your link, it feels like the project code was Sugeno-like at the beginning because it took a long time to get the defuzzification right.
I even had some workarounds in place to get results without the rules stuff. If you can give me some code how you expect this to work, maybe we can work out something. BTW, singletons are not triangles here.

[jean-demartini]

Hi Anselm, Using fuzzylogic as a base I've developped:  . somes domains with their fussy sets  . a method for an inference for pattern-recognition,: a set of rules which mimics the dictionnary of rules of fussylogic IF xxxx AND xxxxx THEN (<symbol>, <credence>) a dictionnary with <symbol> as key of conditions to decide is the candidate category can be accepted.  <symbol> IF <minimal credence> The second dictionnary act as an aggregator. Follow the piece of corresponding code : class FuzzyLogicEngine: # From module fuzzylogic # def _domain_info(self, dic): assert type(dic) is dict # key of the Set whose membership is maximal # key = max(dic, key=dic.get) # value of that maximal membership # val = dic[key] return (str(key), val) def _rules_builder(self, text_rules): # a very simple parsing method # rules_set = {} for rule in text_rules: # # rtx = 'IF <domaine> IS <fussy- set> AND <domaine> IS <fussy-set> THEN <catégorie>' # rtx = rule.split() premices = (rtx[1]+'.'+rtx[3], rtx[5]+'.'+rtx[7]) consequence = rtx[9] rules_set[premices] = str(consequence) return rules_set def _activations_builder(self, text_rules): # a very simple parsing method # activations_set = {} for rule in text_rules: # # rtx = '<catégorie> AS <annotation> IF <credence> WITH <ac tion>' # rtx = rule.split() categorie = rtx[0] # category annotation = rtx[2] # annotation credence = rtx[4] # minimal credence action = rtx[6] # action activations_set[categorie] = { 'credence' : float(credence), 'annotation': annotation, 'action' : action } return activations_set def __init__(self, cfg, prm): self.energ_domain = prm.fle_energ_domain self.energ_res = prm.fle_energ_res self.energ_sets = prm.fle_energ_sets self.freqy_domain = prm.fle_freqy_domain self.freqy_res = prm.fle_freqy_res self.freqy_sets = prm.fle_freqy_sets # Domain "Energ" # self.Energ = Domain( self.energ_domain[0], self.energ_domain[1], self.energ_domain[2], res=self.energ_res ) # Fuzzy-sets for "Energ" # self.Energ.low = sigmoid( 1.0, self.energ_sets['low'][0], self.energ_sets['low'][1] ) self.Energ.hig = sigmoid( 1.0, self.energ_sets['hig'][0], self.energ_sets['hig'][1] ) self.Energ.mid = ~(self.Energ.low | self.Energ.hig) # Domain "Freqy" # self.Freqy = Domain( self.freqy_domain[0], self.freqy_domain[1], self.freqy_domain[2], res=self.freqy_res ) # Fuzzy-sets for "Freqy" # self.Freqy.low = sigmoid( 1.0, self.freqy_sets['low'][0], self.freqy_sets['low'][1] ) self.Freqy.hig = sigmoid( 1.0, self.freqy_sets['hig'][0], self.freqy_sets['hig'][1] ) self.Freqy.mid = ~(self.Freqy.low | self.Freqy.hig) # Building the rules # text_rules = prm.fle_categorization_rules self.rules = self._rules_builder(text_rules) # Building the set of the contitions for activation # text_activations = prm.fle_activation_conditions self.activations = self._activations_builder(text_activations) def domains(self): return (self.Energ, self.Freqy) # Fuzzyfication # def energ_info(self, vre): return self._domain_info(self.Energ(vre)) def freqy_info(self, w): return self._domain_info(self.Freqy(w)) # Inference # def inference(self, vre, w): # Getting the key of the best result # ... for the different domains # (ekey, eval) = self._domain_info(self.Energ(vre)) (fkey, fval) = self._domain_info(self.Freqy(w)) # Inference # try: catkey = (str(ekey), str(fkey)) # key to search the can didate category categ = self.rules[catkey] # candidate category credence = min(eval, fval) # Fuzzy "and" to get th e credence except: # no candidate category in the categorization rules # categ = None credence = 0 return (categ, credence) # Validation of the result of the inference # def is_inference_validated(self, categ, credence): if categ and (categ in self.activations) and (credence > self.a ctivations[categ]['credence']): return True else: return False def get_annotation(self, categ): return self.activations[categ]['annotation'] def get_action(self, categ): return self.activations[categ]['action'] The main drawback in that implementation of the inference method is that I have not really implement a Sugeno-like inference because I use the function max() on the domain instead  iterating on the dictionnary to access at all the memberships of concern. I am on digging more deep in the API of fuzzylogic. It could be, surely, in fuzzylogic to be capable to choose the inference method to use. A parenthesis: I've experimented with : - sci-kit-fuzzy  :  very complicated to use - fuzzy-expert :  is always in alpha state  fuzzylogic is, in comparaison, very great ! Jean -- Jean DEMARTINI ***@***.***>