Abstract - In the present paper, a method based on a new concept called power fuzzy soft set is proposed for multi- observer decision making problems under uncertain information. The new method applies a weighted conjunctive operator to aggregate these sets into a reliable resultant power fuzzy soft set from the input data set. To decide among the alternatives, a new ranking algorithm is introduced. The effectiveness and feasibility of this method are demonstrated by comparing it to algorithms based on the maximum score in decision making.
Abstract - In this paper, the approach to estimate a fuzzy weight vector from an interval comparison matrix is proposed. The interval comparison allows a decision maker to state his/her uncertain judgment as a range, instead of a crisp value. By increasing and decreasing its upper and lower bounds of the interval comparison by the inverse rates, the processed comparison matrices are derived from the given matrix. The membership function of the fuzzy weight is based on the certainty degrees of the interval weight vectors obtained from the processed matrices. The interval weight vector is defined as a closure of the normalized crisp weight vectors each of which is included in an interval comparison matrix. Its certainty degree is represented as the sum of the lower bounds of all the corresponding interval weights.
Abstract - This paper introduces a novel extension of the Technique for Ordering of Preference by Similarity to Ideal Solution (TOPSIS) method. The method is based on aggregation of rules with different linguistic of the output of fuzzy networks to solve multi criteria decision-making problems whereby both benefit and cost criteria are presented as subsystems. Thus the decision maker evaluates the performance of each alternative for decision process and further observes the performance for both benefit and cost criteria. The aggregation of rule base in a fuzzy system maps the fuzzy membership functions for all rules to an aggregated fuzzy membership function representing the overall output for the rules. This approach improves significantly the transparency of the TOPSIS methods, while ensuring high effectiveness in comparison to established approaches. To ensure practicality and effectiveness, the proposed method is further tested on equity selection problems. The ranking produced by the method is comparatively validated using Spearman rho rank correlation. The results show that the proposed method outperforms the existing TOPSIS approaches in term of ranking performance.
Abstract - Fuzzy AHP is today one of the most used Multiple Criteria Decision-Making (MCDM) techniques. The main argument to introduce fuzzy set theory within AHP lies in its ability to handle uncertainty and vagueness arising from decision makers (when performing pairwise comparisons between a set of criteria/alternatives). As humans usually reason with granular information rather than precise one, such pairwise comparisons may contain some degree of inconsistency that needs to be properly tackled to guarantee the relevance of the result/ranking. Over the last decades, several consistency indexes designed for fuzzy pairwise comparison matrices (FPCMs) were proposed, as will be discussed in this article. However, for some decision theory specialists, it appears that most of these indexes fail to be properly "axiomatically" founded, thus leading to misleading results. To overcome this, a new index, referred to as KCI (Knowledge-based Consistency Index) is introduced in this paper, and later compared with an existing index that is axiomatically well founded. The comparison results show that (i) both indexes perform similarly from a consistency measurement perspective, but (ii) KCI contributes to significantly reduce the computation time, which can save expert's time in some MCDM problems.
Abstract - In this study, the effect of concentration, intensification and dilation of three common linguistic hedges (LHs), namely, very, indeed, and more or less on the performance of a fuzzy system for evaluating student's academic evaluation is presented. A LH may be viewed as an operator that acts on a fuzzy set representing the meaning of its operand. As an example, the operator very acts on the fuzzy meaning of the term high grade to have a secondary meaning of very high grade. This property changes the shape of the fuzzy sets and hence the amount of overlap between adjacent sets. It, in turn, improves the meaning of the fuzzy rules and hence the accuracy of the proposed fuzzy evaluation systems. The proposed LHs based fuzzy evaluator systems are compared with a standard fuzzy sets based fuzzy evaluator system using an example drawn from literature. Empirical results of the example presented in this paper show that concentration and dilation effect of LHs is not significant compared to standard fuzzy sets.