International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

The SQLf query language is an extension of SQL to flexible querying of regular relational databases using fuzzy set theory. In this context, atomic predicates (called vague or fuzzy predicates) are expressing preferences and are defined by fuzzy sets. The main purpose of flexible querying is to provide the user with a set of discriminated answers (in the form of a fuzzy set). Until now, the use of aggregates (such as maximum or average) in SQLf queries is limited to the particular case where the aggregate applies to a crisp set. The objective of this paper is to propose an approach to define SQLf queries where the aggregate applies to a fuzzy set of items. The approach proposed here can indeed be seen as a generalization of Sugeno's fuzzy integral.

Quality function deployment (QFD) is a well-known customer driven system and tool for planning and managing new product development. House of quality (HOQ) is used to translate customer requirements (CRs) into each stage of a product development in QFD. In the conventional QFD model, constant coefficients are employed to present the relationships between “What matrix” and “How matrix” and among “How matrixes". In order to break the hindrance of the representation of simple linear function in the structure of HOQ, an integrative approach considering Kano model into QFD planning are employed, and processes are performed in uncertain and vague environments. Therefore, a fuzzy multi-objective model (FMOQFD-Kano) is proposed to reconcile the tradeoff between customer satisfaction and cost. Not only customer satisfaction is taken into account, but also cost is considered in the proposed model. Moreover, a fuzzy solution approach is applied to solve the model for preferred solutions under different alpha-levels, which can give decision-maker more choices to cater for uncertain environment. An example is presented to illustrate the applicability of the proposed model.

We introduce a variation of the Mountain Method called the S-Mountain Method, an algorithm for finding focus points from data points based on the similarity of a focus point with the data points. An important aspect of this algorithm is the association of energy levels with the data points and the reduction of these energy levels as we discover focus points. The rate of reduction of the energy level at a data point is related to its similarity with the recently discovered focus point. We provide a general form for this reduction operation using the t-norm operators. We show how this S-Mountain algorithm can be used to discover focus elements that are granular objects such as fuzzy subsets. Finally we extend the S-Mountain method to environments where our similarities are drawn from an ordinal scale. Here we discuss the interesting question of comparing objects consisting of collections of ordinal values.

Since almost fifty years, Shannon entropy measure has been used as a very powerful tool when quantifying and processing the amount of randomness contained in probability distributions. In this paper we propose a lattice-valued entropy measure H ascribing to each lattice-valued possibilistic distribution π the value H(π) defined as the expected value (in the sense of lattice-valued Sugeno integral with infimum in the role of t-norm) of certain nonincreasing function of the values ascribed to the elements of the basic space by the possibilistic distribution π in question. The main result reads that, for completely distributive complete lattices, the entropy value ascribed to possibilistically independent product of a finite number of lattice-valued possibilistic distributions is defined by the supremum of the entropy values ascribed to particular distributions.

Software size estimation is an important aspect in software development projects because poor estimations can lead to late delivery, cost overruns and possibly project failure. Backfiring is a popular technique for sizing and predicting the volume of source code by converting the function point metric into source lines of code mathematically using conversion ratios. While this technique is popular and useful, there is a high margin of error in backfiring. This research introduces a new method to reduce this margin of error. Neural networks and fuzzy logic in software prediction models have been demonstrated in the past to have improved performance over traditional techniques. For this reason, a neuro-fuzzy approach is introduced to the backfiring technique to calibrate the conversion ratios. This paper presents the neuro-fuzzy calibration solution and compares the calibrated model against the default conversion ratios currently used by software practitioners.

In this paper, the fuzzy analytic network process (FANP) is proposed. For achieving this purpose, two problems are highlighted and overcome in this paper. First, the postulate of the reciprocal matrix should be released, because this property is not satisfied in the fuzzy comparison matrix. Second, the convergent problem for raising the fuzzy supermatrix to limiting power should be appropriately handled. In this paper, we directly fuzzify Cogger and Yu's method for obtaining the fuzzy local vectors, because their method releases the postulate of the reciprocal matrix in the analytic hierarchy process (AHP). Then, we derive the particular matrix problem for obtaining the fuzzy global weight vector so that the convergent problem in a fuzzy limiting supermatrix can be overcome.

The goal of this work is the further development of neoclassical analysis, which extends the scope and results of the classical mathematical analysis by applying fuzzy logic to conventional mathematical objects, such as functions, sequences, and series. This allows us to reflect and model vagueness and uncertainty of our knowledge, which results from imprecision of measurement and inaccuracy of computation. Basing on the theory of fuzzy limits, we develop the structure of statistical fuzzy convergence and study its properties. Relations between statistical fuzzy convergence and fuzzy convergence are considered in the First Subsequence Theorem and the First Reduction Theorem. Algebraic structures of statistical fuzzy limits are described in the Linearity Theorem. Topological structures of statistical fuzzy limits are described in the Limit Set Theorem and Limit Fuzzy Set theorems. Relations between statistical convergence, statistical fuzzy convergence, ergodic systems, fuzzy convergence and convergence of statistical characteristics, such as the mean (average), and standard deviation, are studied in Secs. 2 and 4. Introduced constructions and obtained results open new directions for further research that are considered in the Conclusion.

This section is maintained by Vladik Kreinovich. Please send your abstracts (or copies of papers that you want to see reviewed here) to vladik@utep.edu, or by regular mail to: V. Kreinovich, Department of Computer Science, University of Texas, El Paso, TX 79968, USA.