Intuitionistic Fuzzy Weighted Averaging Operator Research Articles

Emergency alternative evaluation under group decision makers: a new method based on entropy weight and DEMATEL

ABSTRACTWith the increasing occurrence frequency of emergency events, how to select the most desirable alternative has emerged as one critical issue in emergency management. In this paper, we propose a new method combining entropy weight and DEMATEL (decision-making trial and evaluation laboratory) to manage emergency alternative selection under group decision makers. Firstly, IFN (intuitionistic fuzzy number) is introduced to represent linguistic assessment of decision makers under different criteria. Secondly, based on belief entropy, the weight of decision makers is determined and then applied in IFWA (intuitionistic fuzzy weighted averaging) operator to fuse group assessment. Thirdly, with the weight of criteria calculated by DEMATEL, TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) is used to rank emergency alternatives. Two case studies are illustrated to demonstrate the efficiency and practicability of the proposed method through the comparison of other existing methods. The proposed method has three advantages: (1) Via IFN and IFWA operator, it is simple and efficient to address the representation and fusion of linguistic assessment under uncertain information. (2) DEMATEL can help decision-makers weight the importance of criteria considering their direct and indirect effects; (3) Belief entropy can well measure the uncertainty of information and is capable of determining the weight of experts objectively.

Belief intervals aggregation

The combination rule is the core of Dempster-Shafer theory (DST), and there is no uniform aggregation rule adapting to all conditions. The construction of such a rule is still an open and hot topic. In this article, we focus on this point. We focus on the belief interval, which is made up of belief function and plausibility function, in the form of [belief function, plausibility function], instead of basic belief assignment, to represent the DST. We aim at exploring a belief interval combination rule as the combination rule of DST. To do this, we contrast the belief interval with the intuitionistic fuzzy sets and construct the belief interval combination rule based on the intuitionistic fuzzy weighted averaging (IFWA) operator, which opens the door for DST combination rules to the aggregation operator perspective. Further, we find that directly using the IFWA operator as the belief interval combination rule poses three problems: the “‘one’ veto problem,” converge easily close to [1, 1] and the belief function from the belief interval combination rule is not normalized. To solve these problems, we add a normalization process in the belief interval combination rule to modify it, which can address all these three problems well. We also set up a series of examples to illustrate the belief interval combination rule, including a multisensor fusion scenario to compare it with some of the existing rules, which shows its superiorities in better stability and lower operational load.

Extended VIKOR Method for Intuitionistic Fuzzy Multiattribute Decision-Making Based on a New Distance Measure

An intuitionistic fuzzy VIKOR (IF-VIKOR) method is proposed based on a new distance measure considering the waver of intuitionistic fuzzy information. The method aggregates all individual decision-makers’ assessment information based on intuitionistic fuzzy weighted averaging operator (IFWA), determines the weights of decision-makers and attributes objectively using intuitionistic fuzzy entropy, calculates the group utility and individual regret by the new distance measure, and then reaches a compromise solution. It can be effectively applied to multiattribute decision-making (MADM) problems where the weights of decision-makers and attributes are completely unknown and the attribute values are intuitionistic fuzzy numbers (IFNs). The validity and stability of this method are verified by example analysis and sensitivity analysis, and its superiority is illustrated by the comparison with the existing method.

Intuitionistic Fuzzy Genetic Weighted Averaging Operator and its Application for Multiple Attribute Decision Making in E-Learning

Background/Objectives: Adaptation and personalization of E-learning systems require efficient learner modeling. Attributes of learner are evaluated to classify their knowledge without considering the weight difference with respect to their similarity level in E-learning environment for intuitionistic fuzzy data. Methods/Statistical analysis: This paper proposes an Intuitionistic Fuzzy Weighted Averaging (IFWA) operator. The IFWA operator is combined with Genetic Algorithm (GA) to tune the weight of the attributes of learners with respect to their similarity level. The proposed model tests and evaluates the IFWA algorithm on user knowledge modeling data set taken from UC irvine machine learning repository. Findings: The algorithm measures the performance in terms of the best weight values corresponding to the classification. Intuitionistic fuzzy data set is compared based on mean error for different run of generations' with best weight values. The mean square error .002349 proves the consistent performance of the algorithm to allocate weight to the attributes in intuitionistic fuzzy domain. Applications/Improvements: The proposed Intuitionistic Fuzzy Genetic Weighted Averaging Algorithm (IFGWA) can play an efficient role in various decision making problems.