An integrated approach to truth-gaps and epistemic uncertainty is described, based on probability distributions defined over a set of three-valued truth models. This combines the explicit representation of borderline cases with both semantic and stochastic uncertainty, in order to define measures of subjective belief in vague propositions. Within this framework we investigate bridges between probability theory and fuzziness in a propositional logic setting. In particular, when the underlying truth model is from Kleene's three-valued logic then we provide a complete characterisation of compositional min–max fuzzy truth degrees. For classical and supervaluationist truth models we find partial bridges, with min and max combination rules only recoverable on a fragment of the language. Across all of these different types of truth valuations, min–max operators are resultant in those cases in which there is uncertainty about the relative sharpness or vagueness of the interpretation of the language.
Semi-supervised learning can be described from different perspectives, which plays a crucial role in the study of machine learning. In this study, a new aspect of semi-supervised learning is explored by investigating the divide-and-conquer strategy based on fuzziness to improve the performance of classifiers. In such an approach, adding a category of samples with low fuzziness in the training set can improve the training accuracy, which is experimentally confirmed and explained in the theory of learning from noisy data. The significance of initial accuracy of a base classifier in improving classifier’s performance is further studied. It is observed that the initial accuracy of a base classifier has a significant impact on the improvement of classifier’s performance. Experimental results exhibit that the improvement of accuracy, which is sensitive to the base classifier, attains its maximum when the initial accuracy is between 70% and 80%.
Managers often deal with uncertainty of a different nature in their decision processes. They can encounter uncertainty in terms of randomness or fuzziness (i.e., mist, obscurity, inaccuracy or vagueness). In the first case (randomness), it can be described, for example, by probability distribution, in the second case (fuzziness) it cannot be characterized in such a way. The methodological part of the paper presents basic tools for dealing with the uncertainty of both of these types, which are techniques of probability theory and fuzzy approach technique. The original contribution of the theoretical part is the interpretation of these different techniques based on the existence of fundamental analogies between them. These techniques are then applied to the problem of the project valuation with its “internal” value. In the first case, the solution is the point value of the statistical E[PV], in the second case the triangular fuzzy number of the subjective E[PV]. The comparison of the results of both techniques shows that the fuzzy approach extends the standard outcome of a series useful information. This informative “superstructure” of the fuzzy approach compared to the standard solution is another original benefit of the paper.
The paper reviews the status of fuzziness, vagueness, uncertainty, and probability in natural language with an emphasis on: aspects of natural language that pertain to each of the four phenomena; methods of their modeling and representation; computational treatment of these phenomena in natural language and information processing. The main thrust of the paper is the procedure for calculating the predominant type of uncertainty for a NL sentence.
This paper proposes a parametric programming approach to address the notion of the time value of delays in the presence of mixed (random and fuzzy) uncertainties that result from unreliable systems. To consider different types of delay time values, the system states are appropriately and carefully identified and defined, and a cost-based fuzzy decision model that incorporates several unreliability factors is constructed. Then, the proposed model is transformed into a pair of nonlinear programs parameterized by the possibility level to identify the lower and upper bounds on the minimal total cost per unit time at and thus construct the membership function. To provide analytical expressions, a special case with analytical results is also presented. In contrast to existing studies, the results derived from the proposed solution procedure conserve the fuzziness of the input information, representing a significant difference from the crisp results obtained using approaches based on probability theory. The results indicate that the proposed approach can provide more precise information to managers and improve decision-making in practical system design.
Purpose - The purpose of this paper is to discuss the applicability of investment decision-making techniques under fuzziness.Design methodology approach - The paper explains how fuzzy sets can be used in investment decision making.Findings - It was found that any classical investment analysis technique can be converted easily to a fuzzy case.Originality value - The paper indicates the necessity for usage of the fuzzy set theory in case of incomplete information.
The possibility theory as a mathematical model of randomness and fuzziness phenomena is considered in a variant that enables the modeling of both probabilistic randomness, including that inherent in unpredictably evolving stochastic objects whose probabilistic models cannot be empirically reconstructed and nonprobabilistic randomness (fuzziness) inherent in real physical, technical, and economical objects, human-machine and expert systems, etc. Some principal distinctions between the considered variant and the known possibility theory variants, in particular, in mathematical formalism and its relationship with probability theory, substantive interpretation, and applications exemplified by solving the problems of identification and estimation optimization, empirical reconstruction of a fuzzy model for a studied object, measurement data analysis and interpretation, etc. (in the paper "Mathematical Modeling of Randomness and Fuzziness Phenomena in Scientific Studies. II. Applications") are shown.
This paper considers some elements of the optimal fuzzy decision theory that are similar to the optimal statistical decision theory, in particular, the theory of optimal fuzzy identification and optimal fuzzy hypothesis testing, such as Neyman-Pearson statistical hypothesis testing and optimal fuzzy estimation along with a sequential fuzzy identification algorithm similar to the Wald sequential statistical criterion. Some elements of the fuzzy measuring and computing transducer theory and its applications in the problems of the analysis and interpretation of measurement experiment data are given.