Edyta Mrówka

Trapezoidal approximations of fuzzy numbers---revisited

Fuzzy number approximation by trapezoidal fuzzy numbers which preserve expected interval is discussed. The previously proposed approximation operator is improved so as to always produce a well formed trapezoidal fuzzy number.

Discussion: Some notes on (Atanassov's) intuitionistic fuzzy sets

The paper contains few comments and positions the paper on (Atanasovs) intuitionistic fuzzy sets presenting points related to terminology, connections with other mathematical structures and possible interpretations.

Probability of Intuitionistic Fuzzy Events

The notion of probability measure of intuitionistic fuzzy events is investigated and basic properties of that concept are examined.

Trapezoidal approximations of fuzzy numbers

The problem of the trapezoidal approximation of fuzzy numbers is discussed. A set of criteria for approximation operators is formulated. A new nearest trapezoidal approximation operator preserving expected interval is suggested.

Designing Confidence Intervals under Vague Information

It is shown how to determine a sample size necessary for the interval estimation with vague requirements on confidence level and accuracy. Two general algorithms for computing desired sample sizes that depend on the available information (crisp or fuzzy) on the variance of the population under study are given.

Flexible querying via if-sets

The traditional query languages used in database management systems require precise and unambiguous queries only. Fuzzy querying was introduced to relax this rigidity and allow the user more natural information retrieval. In this article we suggest how to enrich fuzzy querying by the use of IF‐sets.

Optimal Process Calibration under Nonsymmetric Loss Function

A problem of process calibration for nonsymmetric loss function is considered and an optimal calibration policy is suggested. The proposed calibration method might be used e.g. when the loss caused by oversize and undersize are not equal.

The Fréchet Control Charts

A new control chart based on the Frechet distance for monitoring simultaneously the process level and spread is suggested. Our chart reveals interesting statistical properties: its behavior is comparable with traditional control charts if changes in process level only or changes in process spread only are observed, but it is much better than \( \bar X\) - S control chart under simultaneous disturbances in the process level and spread.