Anna Sikharulidze

Weighted fuzzy averages in fuzzy environment: part I. Insufficient expert data and fuzzy averages

Three new versions of the most typical value (MTV)1,2 of the population (generalized weighted averages) are introduced. The first version, WFEVg, is a generalization of the weighted fuzzy expected value (WFEV)3 for any fuzzy measure g on a finite set and it coincides with the WFEV when a sampling probability distribution is used. The second and the third version are respectively the weighted fuzzy expected intervals WFEI and WFEIg which are generalizations of the WFEV, namely, MTVs of the population for a sampling distribution and for any fuzzy measure g on a finite set, respectively, when the fuzzy expected interval (FEI)4 exists but the fuzzy expected value (FEV)4 does not. The construction process is based on the Friedman-Schneider-Kandel (FSK)3 principle and results in the new MTVs called the WFEI and the WFEIg when the combinatorial interval extension of a function5 is used.

Fuzzy-probabilistic aggregations in the discrete covering problem

In this paper, a new criterion is introduced for the discrete covering problem. In this criterion, the a priori information represented by a fuzzy measure and a misbelief distribution on alternatives are condensed by aggregation instruments. Using the Dempster–Shafer belief structure and representations of fuzzy measures through associated probabilities, several variants of a new criterion for the discrete covering problem are constructed based on aggregations by two types of the most typical value, namely, monotone expectation and fuzzy expected value. A bicriterial problem is obtained using one of the variants of the new criterion and the criterion of average price minimisation. The example on the application of a new criterion is presented, where the possibility distribution on the optimal choice of the candidates (alternatives) is represented by expert valuations.

Temporalized Structure of Bodies of Evidence in the Multi-Criteria Decision-Making Model

In this paper, we perform the analysis of temporalized structure of bodies of evidence to construct more precise decisions based on the mathematical model of experts’ evaluations. The relation of information precision is defined on a monotone sequence of the bodies of evidence. For determining of a body of evidence the maximum principles of nonspecificity measure, the Shannon and Shapley entropies are applied. Corresponding mathematical programming problems are constructed. A new approach for the numerical solution of these problems is developed. The temporalized structure of bodies of evidence is used for precising the decision in the well-known Kaufmann’s theory of expertons. A measure of increase of decision precision is introduced, which takes into account all steps of temporalization. The temporalized method of expertons is applied to the problem of decision risk management, where the investment fund expert commission provides evaluation of competition results. In our specially created decision-making model, the goal of the expert technology is to aggregate and refine subjective evaluations provided by the expert commission members. The model performs as an adviser that assists the expert commission in selecting of decision with a minimum risks. The results of developed method are then compared with other well-known methods and aggregation operators such as: mean, median, ordered weighed averaging (OWA) and method of expertons.

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).

Dempster-Shafer temporalized belief structure on expert knowledge streams: Part I. Theoretical foundations

In this paper we perform the analysis of Dempster-Shafer temporalized structure for the construction of more precise decisions based on the expert knowledge valuations. The relation of information precision is defined on the bodies of evidence. Negative inaccuracy is defined as the stream of rational expert knowledge in Dempster-Shafer temporalized structure. The principle of negative inaccuracy is developed, as the maximum principle of non-specificity measure of a body of evidence. Corresponding mathematical programming problem is constructed.

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.

Possibilistic aggregation in the discrete covering problems based on the expert valuations

In this paper a new criterion is introduced for the discrete covering problem. Using the representation of a possibility measure through associated probabilities, a new criterion for discrete covering problem is constructed based on aggregation by the Monotone Expectation (ME) (or Choquet integral). In this criterion the a priori information represented by a possibility measure and a misbelief distribution on alternatives are condensed by aggregation instrument. A bicriterial problem is obtained using a new criterion and the criterion of average price minimization. The example on the application of a new criterion is presented, where the possibility distribution on the optimal choice of the alternatives (candidates) is represented by expert valuations.