Fuzzy Quantities Research Articles

COPING WITH UNCERTAINTY FOR KNOWLEDGE ACQUISITION AND INFERENCE MECHANISM

A problem of handling fuzzy quantities in a process of knowledge acquisition and deriving an inference mechanism by means of fuzzy relation equations is studied in extensive way. It is clearly pointed out that both of them are closely related and correspond to various types of fuzzy relation equations that are considered. Their relevance to the form of knowledge collected is also indicated. A problem of dimension reduction of a knowledge base is considered as well. Two modes of the use of the knowledge base (goal‐, and data‐driven) are also studied.

Ranking of Fuzzy Alternatives in Electrocardiography

A system for computerized electrocardiography, where the final classification of the ECG is obtained through a fuzzy decision, is briefly described. The arising problem of ranking fuzzy utilities is explored. Different methods for ordering fuzzy quantities are applied to the simulation of a diagnosis of inferior myocardial infarction, in order to test the validity of the results. It is concluded that in general all methods are comparable, possibly with a slight preference in this practical context for the “center of gravity” suggested by Yager.

Fuzzy quantities in networks

One of possible applications of the fuzzy sets theory in network analysis is described and discussed. It is shown that the uncertainty connected with the length of activities forming the network can be represented by fuzzy quantities. Summing these fuzzy quantities, it is possible to derive the uncertainty connected with more complex paths and reserves. An illustrative numerical example is presented at the end of the paper.

Rating and ranking of multiple-aspect alternatives using fuzzy sets

A method is proposed to deal with multiple-alternative decision problems under uncertainty. It is assumed that all the alternatives in the choice set can be characterized by a number of aspects, and that information is available to assign weights to these aspects and to construct a rating scheme for the various aspects of each alternative. The method basically consists of computing weighted final ratings for each alternative and comparing the weighted final ratings. The uncertainty that is assumed to be inherent in the assessments of the ratings and weights is accounted for by considering each of these variables as fuzzy quantities, characterized by appropriate membership functions. Accordingly, the final evaluation of the alternatives consists of a degree of membership in the fuzzy set of alternatives ranking first. A practical method is given to compute membership functions of fuzzy sets induced by mappings, and applied to the problem at hand. A number of examples are worked out. The method is compared to another one proposed by Kahne who approaches the problem probabilistically.

Rating and Ranking of Multiple-Aspect Alternatives Using Fuzzy Sets

A method is proposed to deal with multiple-alternative decision problems under uncertainty, It is assumed that all the alternatives in the choice set can be characterized by a number of aspects, and that information is available to assign weights to these aspects and to construct a rating scheme for the various aspects of each alternative. The method basically consists of computing we ighted final ratings for each alternative and comparing the weighted final ratings. The uncertainty that is assumed to be inherent in the assessments of the ratings ‘and weights is accounted for by considering each of these variables as fuzzy quantities, characterized by appropriate membership functions. Accordingly, the final evaluation of the alternatives consists of a degree of membership in the fuzzy set of alternatives ranking first, A prac tical method is given to compute memberschip functions of fuzzy sets induced by mappings, and applied to the problem at hand. A number o f examples are worked out. The method is compared to another one proposed by Kahne [1], [2] who approaches the problem probabilistically.