International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

A complicated decision-making system usually requires both quantitative and qualitative decision-making tools to collaborate for reaping their benefits concurrently. How to integrate quantitative and qualitative decision-making formalisms with a modeling tool is the focus of this study; hence, a high-level fuzzy Petri net model (HLFPN) is proposed as a unified platform to incorporate fuzzy analytic hierarchy process (FAHP) with fuzzy logic for managing semi-structured decision-making. In the HLFPN model, fuzzy places, fuzzy tokens, weighted arcs and several types of transitions are introduced for the purpose of combining both the FAHP and fuzzy logic. Four types of transitions are identified: (1) synthesis transitions to execute the computation of FAHP; (2) inference transitions to perform fuzzy reasoning; (3) aggregation transitions to combine several fuzzy tokens with the same fuzzy variable; and (4) duplication transitions to reproduce a token as several tokens having the same value. To guide the evolution of the HLFPN, an algorithm is also developed. An example of evaluation the environmental sustainability in 146 countries is used to illustrate the use of the HLFPN for coupling the FAHP and fuzzy logic.

The intuitionistic fuzzy set (IFS) characterized by a membership function and a non-membership function, was introduced by Atanassov [K. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems 20 (1986) 87–96] as a generalization of Zadeh' fuzzy set [L. A. Zadeh, "Fuzzy Sets", Information and Control 8 (1965) 338–353] to deal with fuzziness and uncertainty. In this paper, we investigate the multiple attribute decision making (MADM) problems, in which the information about attribute weights is incomplete, and the attribute values are expressed in intuitionistic fuzzy numbers (IFNs). We first define the concept of intuitionistic fuzzy ideal solution (IFIS), and then, based on the IFIS and the distance measure, we establish some optimization models to derive the attribute weights. Furthermore, based on the developed models, we develop some procedures for the rankings of alternatives under different situations, and extend the developed models and procedures to handle the MADM problems with interval-valued intuitionistic fuzzy information. Finally, we give some illustrative examples to verify the effectiveness and practicability of the developed models and procedures.

In the framework of the representability of ordinal qualitative data by means of interval-valued correspondences, we study interval orders defined on a nonempty set X. We analyse the continuous case, that corresponds to a set endowed with a topology that furnishes an idea of continuity, so that it becomes natural to ask for the existence of quantifications based on interval-valued mappings from the set of data into the real numbers under preservation of order and topology. In the present paper we solve a continuous representability problem for interval orders. We furnish a characterization of the representability of an interval order through a pair of continuous real-valued functions so that each element in X has associated in a continuous manner a characteristic interval or equivalently a symmetric triangular fuzzy number.

This paper presents a framework of website quality evaluation for measuring the performance of government websites. Multiple criteria decision-making (MCDM) is a widely used tool for evaluating and ranking problems containing multiple, usually conflicting criteria. In line with the multi-dimensional characteristics of website quality, MCDM provides an effective framework for an inter-websites comparison involving the evaluation of multiple attributes. It thus ranks different websites compared in terms of their overall performance. This paper models the inter-website comparison problem as an MCDM problem, and presents a practical and selective approach to deal with it. In addition, fuzzy logic is applied to the subjectivity and vagueness in the assessment process. The proposed framework is effectively illustrated to rate Turkish government websites.

Interval-valued fuzzy set theory is an increasingly popular extension of fuzzy set theory where traditional [0,1]-valued membership degrees are replaced by intervals in [0,1] that approximate the (unknown) membership degrees. To construct suitable graded logical connectives in this extended setting, it is both natural and appropriate to "reuse" ingredients from classical fuzzy set theory. In this paper, we compare different ways of representing operations on interval-valued fuzzy sets by corresponding operations on fuzzy sets, study their intuitive semantics, and relate them to an existing, purely order-theoretical approach. Our approach reveals, amongst others, that subtle differences in the representation method can have a major impact on the properties satisfied by the generated operations, and that contrary to popular perception, interval-valued fuzzy set theory hardly corresponds to a mere twofold application of fuzzy set theory. In this way, by making the mathematical machinery behind the interval-valued fuzzy set model fully transparent, we aim to foster new avenues for its exploitation by offering application developers a much more powerful and elaborate mathematical toolbox than existed before.

The VIKOR-F method has been developed to solve fuzzy multicriteria problem with conflicting and noncommensurable (different units) criteria. It determines the compromise solution that is the "closest" to the ideal. Imprecision in multicriteria decision making can be modelled using fuzzy set theory to define criteria and the importance of criteria. This method solves problem in a fuzzy environment where both criteria and weights could be fuzzy sets. The triangular fuzzy numbers are used to handle imprecise numerical quantities. It is based on the aggregating fuzzy merit that represents distance of an alternative to the ideal solution. The fuzzy operations and procedures for ranking fuzzy numbers are used in developing the VIKOR-F algorithm. A numerical example illustrates an application of the VIKOR-F method.

The paper evaluates the performance of a neuro-fuzzy pattern classification system based on the weightless neural network architecture. The system utilizes a Single Layer Weightless Neural Network (SLWNN) to extract the features vector that measures the similarity of the input pattern to the different classification groups. In contrast to the traditional crisp Winner-Takes-All (WTA) classification scheme used by SLWNN, our system uses a Fuzzy Inference System (FIS) for classification. The network is trained by a hybrid learning scheme that combines a single pass learning phase for training the SLWNN followed by a supervised learning phase for extracting a set of fuzzy rules suitable to classify the training set. The FIS learns fuzzy rules from the feature vectors generated by the SLWNN for the set of training patterns. The recognition of handwritten numerals is employed as a test-bed to demonstrate the effectiveness of the proposed neuro-fuzzy system. Experimental results show that the performance of the proposed system surpasses the performance of the traditional SLWNN.

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.