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A similarity measure is used as one of the approaches in comparing fuzzy numbers. Various similarity measures with distance functions and set theoretic elements have been introduced in the literature. However, most of the similarity measures are unable to discriminate two fuzzy numbers with respect to their location. A new similarity measure for comparing generalized trapezoidal fuzzy numbers is proposed. Four features are included in the similarity measure, namely the geometric distance, the center of gravity, Hausdorff distance and Dice similarity coefficient. The properties of the similarity measure are studied. A comparative analysis between the new similarity measure and some existing similarity measures are made over 16 sets of pairs of fuzzy numbers. The analysis shows that the proposed similarity measure is comparable to the existing methods. Furthermore, it has an advantage of able to discriminate the similarity of fuzzy numbers with different horizontal position which other similarity measure methods fail to perform. [ABSTRACT FROM AUTHOR]

Multiaspect fuzzy soft sets (MAFSS) is a generalization of fuzzy soft set and multiaspect soft set. It describes objects based on parameters which are associated with different sets of elements characterized by different types of aspect-related universal sets. The parameter-element relationships in a MAFSS are in the form of fuzzy sets. Distance and entropy for fuzzy sets are two important measures that determine the degree of dissimilarity between fuzzy sets and the degree of fuzziness of fuzzy sets, respectively. As MAFSSs are composed of fuzzy sets, the aforementioned measures can be extended to MAFSS environment. In this paper, we present the axiomatic definitions of distance and distancebased entropy for MAFSSs. A general formula for estimating the entropy based on normalized distances is established. Some normalized distance-based entropy measures are derived and their properties are investigated. [ABSTRACT FROM AUTHOR]

This paper introduces a new set theoretic-based similarity measure for fuzzy soft sets. A fuzzy soft set similarity aggregation procedure for aggregating individual fuzzy soft sets into a collective fuzzy soft set is proposed. The new similarity measure is used to determine the collective coefficient of individual fuzzy soft sets. A group decision making model is then presented and illustrated with numerical example. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel similarity measure for soft sets which is based on Jaccard similarity coefficient. The proposed similarity measure takes into consideration two component i.e. similarity due to the compared parameter set, and similarity between approximate value sets of the overlapping parameters. The efficiency of the proposed measure is compared with existing soft set similarity measures through numerical examples. An application of the new similarity measure in solving a financial diagnostic problem is also illustrated in the paper. [ABSTRACT FROM PUBLISHER]

This paper proposed an integrated fuzzy approach based on Consistent Fuzzy Preference Relations (CFPR) and Generalized TOPSIS. The procedure of CFPR are improved by adapting Centroid-Index as defuzzification operator, in order to represent the whole set of fuzzy numbers correctly. The CFPR requires only (n-1) pair-wise comparisons for n given criteria, where this situation prove that the increasing number of criteria will not exponentially increased the number of pair-wise comparisons in criteria weights determination process. The evaluation of alternative towards criteria is carried out and the ranking can be obtained by using Generalized TOPSIS method. This method introduced Up and Lo operators for the purpose of determining ideal and negative ideal solutions, that are adequate under fuzzy environment and satisfied the partial ordering relations. The implementation of this integrated approach is presented in the selection of best notebook for students, which involved two decision makers, four criteria and four alternatives. The proposed method can be used as an alternative procedure in solving multi-criteria decision making (MCDM) problems. [ABSTRACT FROM PUBLISHER]