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Different decision algorithms make different assumptions about the structure of a decision maker's anticipations about states and outcomes. A proper fit between the algorithm and the actual information available is needed for good decision support.Show More
This paper examines the use of a parameterized family of implication operators based on Schweizer-Sklar T-norms. Removing a restriction imposed by Schweizer and Sklar when the parameter p is negative leads to improper implication operators for which the truth value can take values outside the unit interval, including complex values. Inferences using increasingly positive p produce inferences incre...Show More
This paper presents a method for generating a global quantification and characterization of the uncertainty in the output of a system with both probabilistic and possibilistic inputs. When we have evidence-based probability distributions of some of the inputs to the system but only possibilistic information about the uncertainties of others, neither standard statistics nor purely possibilistic ana...Show More
A key requirement for using a simulation model to assess a highly complex system is the ability to characterize and quantify the uncertainty in the simulation results with respect to a typically immense set of possible combinations of values of the model's input parameters. Some of these inputs may be sampled from a known or assumed probability distribution, but others are known only possibilistic...Show More
A method of fuzzy ordinal decision analysis is presented in which some outcomes are infinitely bad and some nonzero links are infinitesimally small: not well measurably different from zero. The method is illustrated in the context of community acceptance of a high containment biological research laboratory.Show More
The focus of this paper is on four approaches to decision making about man-made systems which have some potential for catastrophic failure despite the fact that these systems are engineered and managed for safety. The four approaches are categorized in terms of the theory of possibility. If an adverse event is only partially possible and not at all necessary (that is, its complement is completely ...Show More
Comparing risks of rare, high consequence events poses serious challenges to social decision making as well as deep methodological and epistemological problems. It is necessary to assess the merits of countermeasures that are only useful in extremely unlikely circumstances. The value of a conventional conditional probability P(A|B)=P(A∩B)/P(B) becomes too uncertain to be useful when P(B) is not we...Show More
Probably the most widespread and significant existing ldquoperformance metric for intelligent systemsrdquo is the dollar premiums that employers are willing to pay to recruit and retain more intelligent human employees compared to less intelligent ones. This paper examines some of the aspects driving this economic metric in the search for analogies that may be useful in establishing performance me...Show More
A substantial weakness of the risk-assessment guidelines adopted by four US Government agencies is their failure to properly reflect the inherent statistical and non-statistical uncertainties involved in risk measurement. This paper critically reviews the four-stage guideline developed by the National Research Council (NRC) in 1983 and adopted, de facto, by EPA, FDA, OSHA, and the Consumer Product...Show More
We develop a possibility based model with the aim of helping firms to deal with difficult-to- predict catastrophic failures. Our study is motivated by the recent economic turmoil and recent large financial firm failures. Our results suggest that specialization is an alternative to portfolio diversification in predicting catastrophic events.Show More
Some events are so rare that it is impossible to construct any evidence-based probability distribution for them. Judgmental assessment of probability is also suspect because extremely small probabilities are not readily distinguished from one another subjectively. We define a class of extremely rare events called "adventitious events" and illustrate the use of possibility theory to analyze risks a...Show More
This paper presents a simplified version of Tora's Weighted Ordered Weighted Average based on restricting the Ordered Weighted Average component to a Soft Hurwicz Rule. It provides an easily understood, easily implemented tool that respects both the relative inherent importance of criteria and the degree to which tradeoffs among them are appropriate.Show More
This paper discusses an approach to modeling rule interaction using a family of improper S-implications derived from an extension of the Schweizer-Sklar family of parameterized improper t-norms defined over -infin < p <+infin. Improper S-implications define a relation whose membership grade can exceed 100%. The advantage of this is that when improper S-implications are used to interpolate between ...Show More
This paper presents a method for estimating a random walk which is observed subject to additive noise. The method is based on an optimal weighted average, conceptualized as defining a fuzzy set of "recent" data. A Monte Carlo experiment compares the method's effectiveness against the naive method, ordinary least squares regression, and regression with fuzzily recent data.Show More
A simulation experiment demonstrates the effectiveness of using a fuzzy set of "recent data" to train a forecasting model when the underlying process is time-varying.Show More
Schweizer and Sklar (1961, 1963) define a family of T-norms from [0,1]X[0,1] to [0,1] using a parameter p as follows: T(a,b)=(/spl alpha//sup p/+ b/sup -p/-1)/sup -1/p/ if (a/sup -p/+b/sup -p/-1)/spl ges/0,0 otherwise. This paper considers the effects of removing the requirement that (a/sup -p/+b/sup -p/-1)/spl ges/0. This produces a family of complex improper T-norms, which can be used to define ...Show More
The paper presents the results of an experiment comparing the degree to which two systems of linguistic labeling correspond to the way that human beings interpret quantitative linguistic terms. Subjects with minimal training in fuzzy mathematics consistently preferred the output of a new system based on piecewise decomposition to an older system based on the convex hull.Show More
The authors' recent work, "Decision risk minimization by computation semiotics" produced nonconvex membership functions describing the risk profiles of alternative strategies. Arguably, linguistic approximation of these fuzzy membership functions facilitates the choice decision by a human agent. As is often the case, membership functions are not convex when they result from aggregated or computed ...Show More
This paper presents a method for supporting the decision making process for multiattribute decisions by applying quadratic programming to screen alternatives when the degree to which various alternatives satisfy, each attribute and/or the relative importance of the attributes are only roughly specified. In particular, we will work with verbal specifications of these quantities, like low, medium, a...Show More
The article examines the joint effects of the strength of a knowledge granule implemented as a fuzzy if-then rule under a parameterized R-implication, and the parameter of the implication. A novel implication operator, the quadratic R-implication, is found to confer some special advantages.Show More
A knowledge granule expressed as a material implication rule is strong to the degree that the fuzzy restriction it imposes is a strict one. When two rules interact strongly, there is no y value that is 100% compatible with both rules for x between the rules' antecedent cores. This paper considers the effects on the behavior of strongly interacting R-implications based on the Schweizer-Sklar parame...Show More
We attempt to demonstrate the nonmonotonicity in material implication fuzzy logics, explain its source, and seek remedies. Alternatives to Mamdani logic systems have not shared the research effort afforded to the very successful Mamdani systems and their extensions for fuzzy controllers. We consider a special member of the family of t-norm logic systems with special emphasis on defuzzification met...Show More
The article focuses on three dimensional representations of crisp and fuzzy interpolation lines and surfaces on a poster. The X and Y dimensions will lie in the plane of the poster, while the membership grade of each (X, Y) pair will be represented by a surface constructed of styrofoam projecting away from the poster in the third dimension. Cubic Spline, Sugeno, and Defuzzified Mamdani interpolati...Show More
A great many logical implication operators have been proposed to represent the fuzzy if-then relation. Within a parameterized family of operators, these operators lead to differently-shaped interpolation functions which vary systematically according to the parameter. This shape can be summarized by a continuum from selection to consensus. The paper explores the use of this variation to build a fuz...Show More