Fuzzy reasoning and fuzzy relational equations
Fuzzy Sets and Systems
Inference with a single fuzzy conditional proposition
Fuzzy Sets and Systems
Fuzzy sets in approximate reasoning, part 1: inference with possibility distributions
Fuzzy Sets and Systems - Special memorial volume on foundations of fuzzy reasoning
On the semantics of fuzzy logic
International Journal of Approximate Reasoning
The effects of membership function on fuzzy reasoning
Fuzzy Sets and Systems
The generalized modus ponens and the triangular fuzzy data model
Fuzzy Sets and Systems - Special issue on fuzzy data analysis
Continuity in Zadeh's compositional rule of inference
Fuzzy Sets and Systems
On generalized modus ponens with multiple rules and a residuated implication
Fuzzy Sets and Systems - Data bases and approximate reasoning
Abductive reasoning and measures of similitude in the presence of fuzzy rules
Fuzzy Sets and Systems - Special issue: Preference modelling and applications
Compositional rule of inference as an analogical scheme
Fuzzy Sets and Systems
Comparison of fuzzy reasoning methods
Fuzzy Sets and Systems
The approximation of piecewise linear membership functions and Łukasiewicz operators
Fuzzy Sets and Systems
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In this paper we emphasize the use of sigmoid-like membership functions which take values in the open unit interval, and propose the membership driven inference (MDI) reasoning scheme. With sigmoid-like membership functions one can avoid the so-called indetermination part of the conclusion, which occur in reasoning with the compositional rule of inference (CRI). Moreover, the MDI and the min and product based CRI are closed under such membership functions. The axiomatic properties of the MDI reasoning scheme are shown, including not only the generalized modus ponens, but also the generalized modus tollens, the generalized chain rule, and more. As a special sigmoid-like function, we present the so-called squashing function by which piecewise-linear fuzzy intervals can be arbitrarily approximated. We show that by utilizing approximated fuzzy intervals in rules and premises, the MDI reasoning scheme can be efficiently calculated only by the parameters that define the fuzzy sets in the rule and the premise.