In this paper an approach to information quantitative measuring is offered. This information is given as a fuzzy number. It is a particular case of the fuzzy set which is defined by a membership function. It should be noted that this function is determined on the basis of some segment on the set of real numbers. Therefore, a problem changes into construction of the fuzzy number membership function. Quasiconcave membership functions of fuzzy numbers are most frequently used in economic and social problems. For this type of fuzzy numbers this paper provides an algorithm of the fuzzy numbers' membership function construction according to the expert's opinion. The algorithm is based on a segment sequential localization procedure. The fuzzy number membership function is defined by means of this segment using the expert opinion. This procedure is similar to the procedure of extremum seeking of the quasiconcave function through the instrumentality of the sequential measurements of its values. Two ways of such localization have been examined.
Rough sets theory has been considered as a useful method to model the uncertainty and has been applied successfully in many fields. And every rough set is associated with some amount of fuzziness. On the other hand, rough sets theory has been generalized with coverings instead of classical partition. So it is necessary to consider the amount of fuzziness in generalized rough sets induced by a covering. In this paper, a measure of fuzziness in generalized rough sets induced by a covering is proposed. Moreover, some characterizations and properties of this measure are shown by examples, which is every useful in future research works of generalized rough sets induced by a covering.
Some decision making applications require to encode statistics and fuzziness. In this work two frameworks are considered: coherent conditional probabilities and possibilities, which allow to give a rigorous interpretation of membership function. A comparison of the two interpretations is given to employ a general Bayesian inferential approach able to embed fuzzy information.
This paper introduces a new modeling technique of fuzziness in multivariate analysis based on subjective evaluation data. The subjective evaluation data includes diverse perceptions in the evaluators' assessment of the evaluation object. Average data of the evaluators is often used in order to send a generally accurate interpretation of the subjective data. Analyzing of the subjective evaluation data is often called the "Kansei" data analysis. In "Kansei" data analysis, the behavior of the evaluators is often focused on, because of exploring items or objects carrying weight. However, the obtained result by use of the average data does not provide such a character. The proposed modeling technique can provide the tendency of people's opinions and at the same time their diversity. This is achieved by extending the traditional multivariate statistical analysis, by use of the fuzzy-sets-theory
In this study, Fuzzy Cognitive Maps (FCMs), which are powerful tools for graphical representation of knowledge, are analyzed from an ambiguity and fuzziness perspective. In conventional FCMs the causal strengths are represented with singleton (crisp) fuzzy numbers, but recently, other researchers proposed different FCM structures where uniform (interval) or triangular fuzzy numbers are used in causal strength representation. Here, FCMs are analyzed by means of fuzziness and ambiguity measures that are proposed in literature to investigate the capability of models to represent uncertainties. In addition, two new measures, called the average ambiguity measure (AAM) and the average fuzziness measure (AFM), are proposed to indicate uncertainty representation of an FCM. A well-known FCM model of a public health system is used as a case study to show how the fuzzy weights determine the uncertainty representation of FCMs, and then the outcomes are discussed.
Scientists want to comprehend and control complex systems. Their success depends on the ability to face also the challenges of the corresponding computational complexity. A promising research line is artificial intelligence (AI). In AI, fuzzy logic plays a significant role because it is a suitable model of the human capability to compute with words, which is relevant when we make decisions in complex situations. The concept of fuzzy set pervades the natural information systems (NISs), such as living cells, the immune and the nervous systems. This paper describes the fuzziness of the NISs, in particular of the human nervous system. Moreover, it traces three pathways to process fuzzy logic by molecules and their assemblies. The fuzziness of the molecular world is useful for the development of the chemical artificial intelligence (CAI). CAI will help to face the challenges that regard both the natural and the computational complexity.
The landscape in which people live is made up of many features, which are named and have importance for cultural reasons. Prominent among these are the naming of upland features such as mountains, but mountains are an enigmatic phenomenon which do not bear precise and repeatable definition. They have a vague spatial extent, and recent research has modelled such classes as spatial fuzzy sets. We take a specifically multi-resolution approach to the definition of the fuzzy set membership of morphometric classes of landscape. We explore this idea with respect to the identification of culturally recognized landscape features of the English Lake District. Discussion focuses on peaks and passes, and the results show that the landscape elements identified in the analysis correspond to well-known landmarks included in a place name database for the area, although many more are found in the analysis than are named in the available database. Further analysis shows that a richer interrogation of the landscape can be achieved with Geographical Information Systems when using this method than using standard approaches.
The existing methods of determining an α-cut of a fuzzy set to construct its underlying shadowed set do not fully comply with the concept of shadowed sets, namely, a retention of the total amount of fuzziness and its localized redistribution throughout a universe of discourse. Moreover, no closed formula to calculate the corresponding α-cut is available. This paper proposes analytical formulas to calculate threshold values required in the construction of shadowed sets. We introduce a new algorithm to design a shadowed set from a given fuzzy set. The proposed algorithm, which adheres to the main premise of shadowed sets of capturing the essence of fuzzy sets, helps localize fuzziness present in a given fuzzy set. We represent the fuzziness of a fuzzy set as a gradual number. Through defuzzification of the gradual number of fuzziness, we determine the required threshold (i.e., some α-cut) used in the formation of the shadowed set. We show that the shadowed set obtained in this way comes with a measure of fuzziness that is equal to the one characterizing the original fuzzy set.