Possibilistic Framework Research Articles

Possibilistic Framework for MFM Modelling and Verification

A framework for implementing Means-end Flow modelling (MFM) using a possibilistic reasoning paradigm is introduced. The possibilistic context means that the degree of reliability associated with the system state is quantified, and support for tracking temporal evaluation of fault conditions is implicitly available. Specifically two central contributions are made. Firstly, we demonstrate how the MFM methodology in conjunction with a Focusing Expert system framework provides the basis for an intuitive FDI architecture. Secondly, a formal basis is provided for deriving the sub-graphs representing deviation from the normative state such that robust sensor validation is possible.

A FORMAL APPROACH TO THE ANALYSIS OF PRIORITIES OF IMPRECISE CONFLICTING REQUIREMENTS

Priority analysis is one of the most important issues in the trade-off analysis of imprecise conflicting requirements whose elasticity is captured using fuzzy logic. Requirement analysts need to know not only the relative ordering of requirements based on their importance but also how much a requirement is more important than another requirement in order to achieve an effective trade-off. This paper presents a formal approach for reasoning about the relative priority by analyzing the customer’s trade-off preference among imprecise conflicting requirements. A possibilistic reasoning framework for inferring the lower bound of relative priority from case analysis under uncertainty is also developed. Consistency and nonredundancy criteria are established to facilitate the conversion of a possibilistic statement on a lower bound of relative priority into a relative priority. Finally, relative priorities are transformed into weights of importance so that they can be used in the aggregation of conflicting requirements to resolve conflicts.

Possibility measures of transmission capacity assessment using a fuzzy approach

A possibilistic framework is proposed to assess the risk possibility of transmission capacity in long-term planning studies. Because the detailed forecasting data always include massive uncertainties relating to environment, the uncertainties in load variations can be dealt with using fuzzy set theory. A promising algorithm is developed to incorporate these uncertainties into the possibility distribution of nodal load power. To explore the impacts of uncertainties in load variations on transfer capacity assessment, nine cases with various future states are compared and classified by different linguistic aspects in terms of load growth rates and forecasting errors. The results of the possibility model are compared with the results of the probability analysis. Results show that the proposed possibility model can consider the exposure to risk of some possible states, and a confident result is attained. Furthermore, some useful rules for assessing transmission capacity are summarized to help planners in the process of decision making. The proposed technique is implemented on the IEEE 25-bus system to demonstrate its feasibility.

APPROXIMATE REASONING ABOUT PRIORITIES OF IMPRECISE CONFLICTING REQUIREMENTS

Elasticity in an imprecise requirement needs to be captured to enable the trade-off analysis of conflicting requirements. One of the most important issues in the trade-off analysis of conflicting requirements is to understand their priorities. Requirement analysts need to know not only the relative ordering of requirements based on their importance but also how much a requirement is more important than another requirement in order to achieve an effective trade-off between conflicting requirements. Existing formal methods for requirement engineering are limited in addressing these issues. This paper presents a formal methodology for reasoning about their priority by analyzing the customer’s trade-off preference among imprecise conflicting requirements. The elasticity in imprecise requirements is captured using fuzzy logic. Conflicting and cooperative relationships are classified to detect the conflicts between requirements. Multiple requirements are combined based fuzzy multi-criteria decision making techniques. We have also developed a possibilistic reasoning framework for inferring the lower bound of relative priority from case analysis. Consistency and nonredundancy criteria are established to facilitate the aggregation of possibilistic statement on the lower bounds of relative priority. Finally, we describe a process for transforming the lower bounds of relative priority into weights of importance so that they can be used in the aggregation of conflicting requirements to resolve conflicts.

Investigation of fuzzy real power flow modeling with probabilistic—heuristic based information

A conceptual possibilistic framework is proposed to manage the input uncertainties encountered in steady-state real power flow analysis. This study is devoted to building the robust input framework of the possibilistic load flow (POLF) algorithm under an uncertain environment. Three probability density functions are transformed consistently into the corresponding possibilistic representations. Under the possibilistic framework, a compromise between transformation consistency and human updating experience can be satisfied. The possibility distribution function (podf) derived yields both a mean interval and a reasonable spread interval. Compared with the results of probabilistic load flow (PLF) analysis, the spread interval of the compromise line flow podf can be derived to cover only the reasonable output region and its mean interval contains most of the significant probability information. Numerical simulations for three extreme line flows in the IEEE 25-bus system indicate the feasibility of the proposed approach.

A survey of belief revision and updating rules in various uncertainty models

The paper proposes a parallel survey of revision and updating operations available in the probability theory and in the possibility theory frameworks. In these two formalisms the current state of knowledge is generally represented by a [0,1]-valued function whose domain is an exhaustive set of mutually exclusive possible states of the world. However, in possibility theory, the unit-interval can be viewed as a purely ordinal scale. Two general kinds of operations can be defined on this assignment function: conditioning, and imaging (or “projection”). the difference between these two operations is analogous to the one made between belief revision à la Gärdenfors and updating à la Katsuno and Mendelzon in the logical framework. In the probabilistic framework these two operations are respectively Bayesian conditioning and Lewis' imaging. Counterparts to these operations are presented for the possibilistic framework including the case of conditioning upon uncertain observations, and justifications are given which parallel the ones existing for the probabilistic operations. More particularly, it is recalled that possibilistic conditioning satisfies all the postulates proposed by Alchourrón, Gärdenfors and Makinson for belief revision (stated in possibilistic terms), and it is proved that possibilistic imaging satisfies all the postulates proposed by Katsuno and Mendelzon. the situation where our current knowledge is stated in terms of weighted logical propositions is discussed in connection to possibility theory. Revision in other more complex numerical formalisms, namely belief and plausibility functions, and upper and lower probabilities is also surveyed. Recent results on the revision of conditional knowledge bases are also reviewed. the frameworks of belief functions, upper and lower probabilities and conditional bases are more sophisticated than the previous ones because they enable to distinguish between factual evidence and generic knowledge in a cognitive state. This, framework leads to two forms of belief revision respectively taking care of the revision of evidence and the revision of knowledge. © 1994 John Wiley & Sons, Inc.