Nor Hashimah Sulaiman

Ranking fuzzy numbers using similarity measure with centroid

Ranking fuzzy numbers correctly is essential especially in decision making process. Many techniques of ranking fuzzy numbers have been investigated using variety of approaches. However, most of the techniques have weaknesses one way or another. In this paper, we propose a new method of ranking fuzzy numbers using similarity measure approach with centroid. We investigate its ranking consistency compares to other existing methods using a few benchmarking sets of fuzzy numbers. It is found that our proposed method is able to overcome some of the weaknesses of other methods.

A Jaccard-based similarity measure for soft sets

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.

A set theoretic similarity measure for fuzzy soft sets and its application in group decision making

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.

Solving industrial decision making problems using fuzzy numbers

Human-based industrial decision making normally involves both quantitative and qualitative input factors. Subjectiveness in human evaluation is unavoidable in the decision making process. In fuzzy-based industrial decision making environment where fuzzy numbers are used to evaluate subjective factors, ranking of fuzzy numbers become one of the crucial component which need to be performed before the final decision can be reached. In this paper, a similarity-based method of ranking fuzzy numbers is proposed. The applicability of the proposed method in solving selected industrial-related decision making problems namely the risk evaluation and pattern recognition problems are illustrated.

Mappings on multiaspect fuzzy soft classes

In this paper, mappings on multiaspect fuzzy soft classes are introduced and discussed. Several properties related to image and pre-image of multiaspect fuzzy soft sets are studied and illustratedwith numerical examples.

Multiaspect soft sets

We introduce a novel concept of multiaspect soft set which is an extension of the ordinary soft set by Molodtsov. Some basic concepts, operations, and properties of the multiaspect soft sets are studied. We also define a mapping on multiaspect soft classes and investigate several properties related to the images and preimages of multiaspect soft sets.

An integrated fuzzy approach to solving multi-criteria decision making problems

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.

A distance and set theoretic-based similarity measure for generalized trapezoidal fuzzy numbers

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.

Normalized distance–based entropy measures for multiaspect fuzzy soft sets

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 distance-based 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.

Aggregation operations for multiaspect fuzzy soft sets

Multiaspect fuzzy soft set (MAFSS) is one of the generalized forms of fuzzy soft sets. In this paper, we introduce two types of aggregation operations for MAFSSs, namely the weighted arithmetic mean (WAM)-based MAFSS aggregation, and the ordered weighted aggregation (OWA)-based MAFSS aggregation. The applicability of the two MAFSS-aggregation operations is illustrated with numerical examples in group decision making.