Images of fuzzy sets under fuzzy relations have been investigated mainly in two contexts: On the one hand, mostly under the term “full image” [5], they can be regarded as very general tools for fuzzy inference, leading to the so-called “compositional rule of inference” [1, 5]. On the other hand, under the term “extensional hull”, the image of a fuzzy set under a fuzzy equivalence relation yield...

We contribute to the theory of implications and conjunctions related by adjointness, in multiple-valued logics. We suggest their use in Zadeh s compositional rule of inference, to interpret generalized modus ponens inference schemata. We provide new complete characterizations of implications that distinguish left arguments, implications that satisfy the exchange principle, divisible conjunction...

The exploration for oil and gas requires real-time petrophysical expertise to interpret measurement data acquired in boreholes and to recommend further steps. High time pressure and the far reaching nature of these decisions, as well as the limited opportunity to gain in depth petrophysical experience suggests that a decision support system that can aid the petrophysicist will be very useful. I...

This is an author produced version of a conference paper. The paper has been peer-reviewed but may not include the final publisher proof-corrections or pagination of the proceedings. Abstract: The compositional rule of inference, grounded on the modus ponens law, is one of the most effective fuzzy systems. We modify the classical version of the rule (Zadeh, 1973, 1979) to propose an original mo...

It is well known that a fuzzy rule base is a characterization of a partially given mapping (fuzzy function) between fuzzy universes. For practical applications, it is desirable to interpolate that function in order to compute its values at points (fuzzy or crisp) other than fuzzy sets (nodes) in antecedents of the rule base. Moreover, interpolation requires that in the case of coincidence betwe...

compositional rule of inference to a fuzzy input X* E F ( X ) we obtain a fuzzy output Y* E F(Y): We propose an enhancement of MamY * = X * o T R , (1) dani fuzzy controllers. We tested it on l.e., a simple control task and verified that it outperforms the traditional approach. VY E Y : Y*(Y) = SUPT(X*(X),R(X,Y)) , (2) xEX

We present a kind of fuzzy reasoning, dependent on a measure of fulfilment of the antecedent clause, that captures all the expressiveness of the traditional approximate reasoning methodology based on the Compositional Rule of Inference (CRI) and at the same time rules out a good deal of its inherent complexity. We also argue why this approach offers a more genuine solution to the implementation...

Many researches dealt with the problem of induction motors fault detection and diagnosis. The major difficulty is the lack of an accurate model that describes a fault motor. Moreover, experienced engineers are often required to interpret measurement data that are frequently inconclusive. A fuzzy logic approach may help to diagnose induction motor faults. In fact, fuzzy logic is reminiscent of h...

The “fuzzy dot” (or fuzzy relation) representation of fuzzy rules in fuzzy rule based systems, in case of classical fuzzy reasoning methods (e.g. the Zadeh-MamdaniLarsen Compositional Rule of Inference (CRI) (Zadeh, 1973) (Mamdani, 1975) (Larsen, 1980) or the Takagi Sugeno fuzzy inference (Sugeno, 1985) (Takagi & Sugeno, 1985)), are assuming the completeness of the fuzzy rule base. If there are...

This paper provides a logical basis for manipulation with fuzzy IF-THEN rules. Our theory is wide enough and it encompasses not only finding a conclusion by means of the compositional rule of inference due to Lotfi A. Zadeh but also other kinds of approximate reasoning methods, e.g. perception-based deduction, provided that there exists a possibility to characterize them within a formal logical...