Application of Wald Function to OR and AND Fuzzy Operations in No- Data Problems

Subjective qualifiers of Wald's theory of decision functions are the fuzzy events of the subsequent fuzzy set theory. Wald's notion of subjective qualifiers involves applying integral transforms to convert states of nature into fuzzy events. Probabilities of fuzzy events and arithmetic formulas for fuzzy utility function values are readily derived from Wald's integral transforms. We have applied Zadeh's extension principle to Wald's integral transforms and demonstrated that fuzzy mathematics is effective when applied to multiple subjective probability distributions conjoined by OR and AND operations. In this paper, we focus on no-data problems and construct a fuzzy Bayes' theorem for cases in which a membership function and multiple subjective probability distributions conjoined by OR or AND operations are given. In addition, we devise a formulation for the corresponding decision making problem

Information compression in the context model

The Context Model provides a formal framework for the representation, interpretation, and analysis of vague and uncertain data. The clear semantics of the underlying concepts make it feasible to compare well-known approaches to the modeling of imperfect knowledge like that given in Bayes Theory, Shafer's Evidence Theory, the Transferable Belief Model, and Possibility Theory. In this paper we present the basic ideas of the Context Model and show its applicability as an alternative foundation of Possibility Theory and the epistemic view of fuzzy sets

Fuzzy geometry, entropy, and image information

Presented here are various uncertainty measures arising from grayness ambiguity and spatial ambiguity in an image, and their possible applications as image information measures. Definitions are given of an image in the light of fuzzy set theory, and of information measures and tools relevant for processing/analysis e.g., fuzzy geometrical properties, correlation, bound functions and entropy measures. Also given is a formulation of algorithms along with management of uncertainties for segmentation and object extraction, and edge detection. The output obtained here is both fuzzy and nonfuzzy. Ambiguity in evaluation and assessment of membership function are also described

Analysis of fuzzy queues

AbstractA general approach for queuing systems in a fuzzy environment is proposed based on Zadeh's extension principle, the possibility concept and fuzzy Markov chains. To illustrate the approach, analytical results for M/F/1 and FM/FM/1 systems are presented. Fuzzy queues are much more realistic than the commonly used crisp queues in many practical situations. A simple numerical example is also presented