Tatiana Kiseliova

Generation of Representative Symptoms Based on Fuzzy Concept Lattices

It is very challenging and interesting task in medicine to find a set of representative symptoms for the disease, i.e., the set of symptoms that best characterizes a disease. In this paper we propose a method for constructing such representative symptoms for a particular disease, based on the data taken from the patient-records. The method uses a closure operator on the base of which a (one-sided) fuzzy concept lattice is defined.

A generalized time quantifier approach to approximate reasoning

Abstract In this paper, a rather expressive fuzzy temporal logic for linear time is introduced. First, this logic is a multivalued generalization (Lukasiewicz style) of a two-valued linear-time temporal logic based on, e.g., the “until” operator. Second, it is obtained by introducing a generalized time quantifier (a generalization of the partition operator investigated by Shen) applied to fuzzy time sets. In this fuzzy temporal logic, generalized compositional rules of inference, suitable for approximate reasoning in a temporal setting, are presented as valid formulas. Some medical examples illustrate our approach.

Towards application of FML in suspicion of non-common diseases

In this paper we present the preliminary results of application of Fuzzy Markup Language (FML) to suspect a non-common disease. Under non-common diseases we understand rare diseases. From the broad point of view this problem belongs to the computer-assisted decision support in medical diagnostics and can be supported by fuzzy logic controllers. We can use conventional methods to diagnose a rare disease if it can be exhibited by outstanding symptoms. For example, there are several search machines and data banks that allow to find a rare disease clearly exhibited by a patients symptoms/signs. But it is very difficult to diagnose a rare disease if it masks as a common disease. Diagnostic of rare diseases is connected with lack, uncertainty and imprecision of knowledge, medical mistake and even medical failure. Additionally, very often a common disease is also established with some degree of belief, thus, the expressions such as “it is possible that a patient has a particular disease” rather often present in the daily medical practice. It is clear that if we would know the common diseases, then deviations from them can be considered as a sign of non-common diseases. In this paper we investigate such deviations with the help of FML. We show how FML mechanism can be adjusted to suspect a rare disease, and discuss the appropriateness of the available operators.

Decision Making in Diagnosis of Oral Mucosa Lesions

The problem of decision making in diagnoses of oral mucosa lesions is considered. It is shown that computer-assisted diagnosis systems can be very helpful for clinicians in this branch. In the case of the presented problem for oral mucosa lesions an expert knowledge is used in formalizing the initial information, as well as in the estimation of indicants of the patient. The presented method is used as an alternative to avoid many problems associated with probabilistic and statistical approaches. It handles the expert information in a natural way. The diagnosis is made considering the weight of each symptom. It is shown how the proposed method can be explained from the theory of fuzzy relations point of view.

Investigation of heat waves with fuzzy methods

Abstract The paper concerns influences of global warming on health of the population. We consider an important parameter of global warming – a heat index – that is a characteristics of a human thermal comfort and represents a combination of air temperature and relative humidity. Based on the heat indexes, we propose a new approach – the fuzzy methods – to investigate heat waves which, if defined properly, can be used to assess the potential impacts of climate change on human health, e.g., in the heat-health warning systems. We find typical characteristics of heat indexes during different time periods, using most typical fuzzy expected values. We use these typical characteristics to process heat waves. Our results are applied on the data collected in the Ministry of Preservation of the Environment of Georgia during 1955–1970 and 1990–2007 years as well as free accessible meteorological data of air temperature and relative humidity during August 2003 in Paris (France) and Tbilisi (Georgia).

Free and Projective Bimodal Symmetric Gödel Algebras

Gödel logic (alias Dummett logic) is the extension of intuitionistic logic by the linearity axiom. Symmetric Gödel logic is a logical system, the language of which is an enrichment of the language of Gödel logic with their dual logical connectives. Symmetric Gödel logic is the extension of symmetric intuitionistic logic (L. Esakia, C. Rauszer). The proof-intuitionistic calculus, the language of which is an enrichment of the language of intuitionistic logic by modal operator was investigated by Kuznetsov and Muravitsky. Bimodal symmetric Gödel logic is a logical system, the language of which is an enrichment of the language of Gödel logic with their dual logical connectives and two modal operators. Bimodal symmetric Gödel logic is embedded into an extension of (bimodal) Gödel–Löb logic (provability logic), the language of which contains disjunction, conjunction, negation and two (conjugate) modal operators. The variety of bimodal symmetric Gödel algebras, that represent the algebraic counterparts of bimodal symmetric Gödel logic, is investigated. Description of free algebras and characterization of projective algebras in the variety of bimodal symmetric Gödel algebras is given. All finitely generated projective bimodal symmetric Gödel algebras are infinite, while finitely generated projective symmetric Gödel algebras are finite.

Investigation of heat waves based on the most typical fuzzy expected values with corresponding trapezoidal membership functions.

In this paper we continue to investigate the important parameter of global warming - a heat wave - that has no unique definition and represents the constellation of different factors such as e.g., heat index (temperature + humidity), time periods of excessive heat, etc. We find typical characteristics of heat indexes during different time periods, using most typical fuzzy expected values. Trapezoidal fuzzy sets are used to represent that characteristics. The results are compared with previous work based on the corresponding step-wise functions. We use the data collected in the Ministry of Preservation of the Environment of Georgia during 1955-1970 and 19902007.

“Fuzzy” in Georgian is “aramkapio”

It was always interesting however not always understandable for me how professional historians estimate a past event. Even two persons observing the same scene can give it different characteristics. Not going deep into philosophic discussions, I would like to point out here, that my intend to write about “fuzzy + Lotfi Zadeh + Georgia” is considered only from my subjective point of view. Such courage to speak about this theme is based on my rather long stay in the fuzzy society, which integrates scientists from Georgia and many countries all over the world.

Fuzzy Logic in Diagnostics of Rare Diseases

Background. Rare disease (RD) is any disease that affects a small percentage of the population, with a prevalence of about 1 in every 2000 people. Diagnostic of RDs is hindered by the lack of knowledge predetermined by the multitude of these diseases, which can lead to medical mistake and even medical failure. It may also occasion the omission of the necessary investigations and vice-versa – the prescription of a multitude of unnecessary and potentially hazardous invasive diagnostic interventions and/or delay in performing them. Quite frequently the correct diagnosis is belated, sometimes it is not made at all. The generally accepted way for RD diagnosing is usage of search machines, but this way is reasonable only when some outstanding symptoms/signs, like dismorphological signs, mental retardation, etc. occur. Very often the RDs mask as common diseases. In such cases the problem is to suspect the RD. There are no special algorithms which give rise to a suspicion for the RD. Objective. Elaboration of the model/algorithmfor revealing cases suspicious of RDs (if they present under the mask of a common disease). Methods. We need to have an approach which will help us to suspect the RD to use the search machines afterwards as usually. We assume to suspect a RD when the clinical picture and course of a disease are atypical. But the point is that the border between typical (normal) and atypical (abnormal) is not crisp: the fuzzy methodologies can be used here. Results. We present an algorithmic approach for the implementation within a framework of a computer program, that would allow to suspect RD, and therefore serve as a basis of a decision support system. Examples from medical practice illustrate our approach. Conclusions. For the group of common diseases (syndromes), e.g. pneumonia, bronchitis, rheumatic fever, etc., we propose to prepare medical electronic records (including complains, anamnesis aegroti/vitae, anamnesismorbi, status presence, etc.), which would reveal the signs/symptoms which deviate from the normal clinical course (by frequency, intensity, time of manifestation, duration, etc.). When deviation reaches some level, the program would signal that there is some suspicion of the non-common disease (e.g., RD) which masks as a common one.