In a recent paper, a functional AM (ambiguity measure) is introduced and an attempt is made to show that this functional qualifies as a measure of total aggregated uncertainty in the Dempster-Shafer theory. We show that this attempt fails due to a particular error in the proof of one of the principal theorems in the paper. Some additional remarks are made regarding recent research pertaining to the subject of the discussed paper.

This article deals with the claims that “a standard version of fuzzy logic collapses mathematically to two-valued logic” made by Charles Elkan in two papers [Proc 11th National Conf on AI, Menlo Park, CA: AAAI Press, 1993, pp 698–703; IEEE Expert 1994;9:3–8]. Although Elkan's effort to trivialize fuzzy logic has been questioned by numerous authors, our aim is to examine in detail his formal arguments and make some new observations. We present alternative, considerably simpler proofs of Elkan's theorems and use these proofs to argue that Elkan's claims are unwarranted. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 203–207, 2007.

Various types of integrals with respect to signed fuzzy measures on finite sets with cardinality n can be presented as corresponding rules for partitioning the integrand. The partition can be expressed as an n-dimensional vector, whereas the signed fuzzy measure is also an n-dimensional vector. Thus, the integration value is the inner product of these two vectors. Two pairs of extremes, the Lebesgue-like integral versus the Choquet integral and the upper integral versus the lower integral, are discussed in detail. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 1073–1092, 2006.

Due to some inherent interactions among diverse information sources, the classical weighted average method is not adequate for information fusion in many real problems. To describe the interactions, an intuitive and effective way is to use an appropriate nonadditive set function. Instead of the weighted average method, which is essentially the Lebesgue integral, we should thus use the Choquet integral or some other nonlinear integrals. To apply this alternative, more realistic approach to information fusion, we need to determine the nonadditive set function from given input-output data, viewing the nonlinear integral as a multi-input one-output system. In this paper, we employ an adaptive genetic algorithm to construct an approximate optimal nonnegative monotone set function from given input-output data in an environment with random perturbation. An example for diverse strengths of random perturbation is shown to demonstrate the efficiency of this algorithm. ©1999 John Wiley & Sons, Inc.

A pair of new integrals, a PFB-integral and a PFA-integral, are introduced. Given a measurable space, these integrals are defined for nonnegative functions with respect to monotone set functions, and they are generalizations of both the Lebesgue integral and the fuzzy integral. Some primary properties of the PFB-integral and PFA-integral are discussed and an inequality between them is established in this paper.

This article further develops one branch of research initiated in an article by Resconi, Klir, and St. Clair (G. Resconi, G. J. Klir, and U. St. Clair, Int. J. Gen. Syst., 21(1), 23-50 (1992) and continued in another article by Resconi et al. (Int. J. Uncertainty, Fuzziness and Knowledge-Based Systems, 1(1), 1993). It fully formulates an interpretation of the Dempster-Shafer theory in terms of the standard semantics of modal logic. It is shown how to represent the basic probability assignment function as well as the commonality function of the Dempster-Shafer theory by modal logic and that this representation is complete for rational-valued functions (basic assignment, belief, or plausibility functions). © 1994 John Wiley & Sons, Inc.

This paper is a continuation in a series of papers started by Resconi et. al. [8] in which we try to develop interpretations of various uncertainty theories within the framework of standard modal logic. In this paper, we deal with possibility theory. We suggest an interpretation of possibility measures and necessity measures and show that this interpretation is complete for rational-valued measures.

This paper discusses recent applications of fuzzy sets and the theory of approximate reasoning. The primary focus is on fuzzy logic control (FLC). We begin with a brief history of the key ideas, a survey of recent applications, and a discussion of the genesis of FLC in Japan. We then turn to a study of the general principles of FLC, considering it as a combination of ideas from conventional control theory, artificial intelligence, and fuzzy sets theory. We next provide a detailed analysis of a simple application in consumer electronics, namely, a fuzzy washing machine developed by Hitachi Corporation. In concluding sections we briefly consider other types of applications, including recent work on pilotless helicopters, fuzzy expert systems, and the concept of a fuzzy computer, and we discuss the potential for future developments. It is our opinion that the subject of FLC is still very much in its infancy, and that recent events mark the beginning of an entirely new genre of "intelligent" control.>

The author identifies some points of his agreement or disagreement with the position taken by Laviolette and Seaman (1994) in their debate paper. In particular, the author argues that some statements regarding the superiority of probabilistic representation of uncertainty, which are made by Laviolette and Seaman in their paper, are untenable.>

Investigations pursued in this paper contribute to a research project introduced by Resconi, Klir, and St. Clair [1] whose purpose is to employ syntactic and semantic structures of modal logic as a unifying framework within which various uncertainty theories can be formalized, compared, and organized hierarchically. This paper focuses on the explicit use of modal logic semantics to formalize fuzzy sets, belief measures, plausibility measures, and Sugeno λ-measures.

The identification problem for systems with fuzzy relations is solved by applying a general method of solving finite fuzzy relation equations. It is shown that the identification uncertainty is characterized in terms of the maximum solution and the infimum of all the minimal solutions. The result is independent of the function used to define the uncertainty measure. A method for calculating the infimum of all the minimal solutions without calculating these minimal solutions is also derived and results in an efficient method for calculating the identification uncertainty.

This correspondence deals with collections of n binary relations between Boolean and/or pseudo-Boolean functions which are combined by an n-ary relation. A new algorithm is described for solving these relations.

A universal logic primitive (ULP) is a logic function by which every logic function can be composed. The total number of all ULPs and all nondegenerate ULPs for n logic variables is derived and a procedure for determining all of them is presented.