International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

Abstract: We discuss the MICA operators and show they provide a very general framework for modeling aggregation operators. We present a generic class of MICA operators that can be adapted to various type of situations through the tuning of parameters. These parameters can be set by a human expert or automatically learned from data through a genetic algorithm.

The classical definitions of ‘expected value’ and ‘standard deviation’ may sometimes lead to quantities which fail to represent a ‘typical’ feature of a given data set, whenever this set consists of more than one cluster. The use of the fuzzy expected value (FEV) and the clustering fuzzy expected value (CFEV) also yield central tendency and in general cannot represent a typical value of the given data. In this work a new quantity—a Most Typical Value (MTV) is defined and investigated. A given fuzzy set in Rⁿ is first clustered and replaced by a finite set of clusters. This set is then represented by a single vector—the most typical value of the set.

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.

This article is an extension of the results of two earlier articles. In [J. Schubert, “On nonspecific evidence”, Int. J. Intell. Syst. 8 (1993) 711–725] we established within Dempster-Shafer theory a criterion function called the metaconflict function. With this criterion we can partition into subsets a set of several pieces of evidence with propositions that are weakly specified in the sense that it may be uncertain to which event a proposition is referring. In a second article [J. Schubert, “Specifying nonspecific evidence”, in “Cluster-based specification techniques in Dempster-Shafer theory for an evidential intelligence analysis of multiple target tracks”, Ph.D. Thesis, TRITA-NA-9410, Royal Institute of Technology, Stockholm, 1994, ISBN 91–7170–801–4] we not only found the most plausible subset for each piece of evidence, we also found the plausibility for every subset that this piece of evidence belongs to the subset. In this article we aim to find a posterior probability distribution regarding the number of subsets. We use the idea that each piece of evidence in a subset supports the existence of that subset to the degree that this piece of evidence supports anything at all. From this we can derive a bpa that is concerned with the question of how many subsets we have. That bpa can then be combined with a given prior domain probability distribution in order to obtain the sought-after posterior domain distribution.

This paper extends previous work on propagating qualitative uncertainty in networks in which a general approach to qualitative propagation was discussed. The work presented here includes results that make it possible to perform evidential and intercausal reasoning, in addition to the predictive reasoning already covered, in networks quantified with probability, possibility and Dempster-Shafer belief values. The use of these forms of reasoning, which include the phenomenon of “explaining away”, is illustrated with the use of a medical example.