Ion Iancu

Intuitionistic fuzzy similarity measures based on Frank t-norms family☆

Abstract Intuitionistic fuzzy sets, proposed by Atanassov, have gained attention of many researches for applications in various fields. Different types of similarity measures for intuitionistic fuzzy sets were proposed and used in numerous applications. In this paper we extend some crisp cardinality measures to measures for intuitionistic fuzzy sets; the main role in this process is played by the Frank t-norm family.

Propagation of uncertainty and imprecision in knowledge-based systems

Abstract Using generalized modus ponens, we examine the values of the inferred conclusion, depending on the used implication and on the correspondence between the premise of the rule and the observed fact. The conclusion is obtained using t-norm t(x, y) = max((1 + λ)(x + y − 1) − λxy, 0), λ ⩾ − 1.

Connectives for fuzzy partitions

Abstract The fuzzy intersection and union are defined by means of a certain pair (T, S) of non-strict Archimedean operators dual with respect to a strict negation having the same additive generator as T. We prove that the equivalence between the Butnarius definition and the Ruspinis one concerning the fuzzy partitions holds if and only if the connectives for fuzzy operations are T∞ and S∞.

Intuitionistic fuzzy system for fingerprints authentication

Using a fuzzy logic control system, we propose in this paper an optimized method to reduce the points number to be used in order to identify a person using fuzzy fingerprints. Two fingerprints are similar if n out of N points from the skin are identical. We discuss a criteria to choose these points. Our method compares two matching sets and selects the optimal set from these, using a fuzzy reasoning system based on intuitionistic fuzzy numbers. The advantage of our method with respect to the classical existing methods consists in a smaller number of calculations.

Mamdani FLC with Various Implications

The task of the standard Mamdani fuzzy logic controller is to find a crisp control action from the fuzzy rule-base and from a set of crisp inputs. Because the interval inputs are frequently used in various domains (online shopping, for instance), in this paper we propose an extension of this type of controller which works with intervals as inputs and with various implication operators. For any implication we obtain a crisp value as output. Finally, these outputs are combined to obtain the overall crisp output action of the system.

Approximate Reasoning Using Fodor's Implication

Using generalized modus ponens reasoning, we examine the values of the inferred conclusion using the Fodor’s implication in order to interpret a fuzzy if-then rule with a single input single output and the T-norms t1(x, y) = min(x, y), t2(x, y) = xy and t3(x, y) = max(0, x + y − 1) for composition operation. These are the very used T-norms in generalized modus ponens reasoning.

Reasoning system with fuzzy uncertainty

Abstract In this paper we present a system of uncertain inference for expert systems which works with knowledge represented in form of production rules accompanied by uncertainty degrees expressed by fuzzy numbers. Our system generates a Turbo Prolog program which has included the operations for uncertainty management.

T-norms with threshold

In this paper, two kinds of strict negations with threshold Ca, a ϵ (0,1) and pairs (t-norm, t-conorm) Ca-dual are presented.

A method for constructing t-norms

In this paper a new type of t-operators with double thresholda,b ∈ (0,1),a ≤b, is presented, each pair (t-norm,t-conorm) consisting of two dual elements with respect to a negation with double threshold.

An Atanassov's intuitionistic fuzzy reasoning model

The task of the standard Mamdani fuzzy logic controller is to find a crisp control action from the fuzzy rule-base and from a set of crisp inputs. In this paper we modify this controller in order to work with Atanassovs intuitionistic fuzzy sets and to activate a set of rules having the same conclusion. Usually, the inference rules used in a fuzzy logic controller are given by a domain expert; in our system, these rules are automatically induced as fuzzy association rules starting from a training set. The fuzzy confidence value associated with each rule is used to obtain the fuzzy set inferred by our system.