An intuitionistic fuzzy set, characterized by a membership function and a non-membership function, is a generalization of fuzzy set. In this paper, based on score function and accuracy function, we introduce a method for the comparison between two intuitionistic fuzzy values and then develop some aggregation operators, such as the intuitionistic fuzzy weighted averaging operator, intuitionistic fuzzy ordered weighted averaging operator, and intuitionistic fuzzy hybrid aggregation operator, for aggregating intuitionistic fuzzy values and establish various properties of these operators.

Intuitionistic Fuzzy Aggregation Operators

Theory of fuzzy integrals and its applications

The weighted geometric (WG) operator and the ordered weighted geometric (OWG) operator are two common aggregation operators in the field of information fusion. But these two aggregation operators are usually used in situations where the given arguments are expressed as crisp numbers or linguistic values. In this paper, we develop some new geometric aggregation operators, such as the intuitionistic fuzzy weighted geometric (IFWG) operator, the intuitionistic fuzzy ordered weighted geometric (IFOWG) operator, and the intuitionistic fuzzy hybrid geometric (IFHG) operator, which extend the WG and OWG operators to accommodate the environment in which the given arguments are intuitionistic fuzzy sets which are characterized by a membership function and a non-membership function. Some numerical examples are given to illustrate the developed operators. Finally, we give an application of the IFHG operator to multiple attribute decision making based on intuitionistic fuzzy sets.

Some geometric aggregation operators based on intuitionistic fuzzy sets

Probability and Measure

Supplier selection, the process of finding the right suppliers who are able to provide the buyer with the right quality products and/or services at the right price, at the right time and in the right quantities, is one of the most critical activities for establishing an effective supply chain. On the other hand, it is a hard problem since supplier selection is typically a multi criteria group decision-making problem involving several conflicting criteria on which decision maker's knowledge is usually vague and imprecise. In this study, TOPSIS method combined with intuitionistic fuzzy set is proposed to select appropriate supplier in group decision making environment. Intuitionistic fuzzy weighted averaging (IFWA) operator is utilized to aggregate individual opinions of decision makers for rating the importance of criteria and alternatives. Finally, a numerical example for supplier selection is given to illustrate application of intuitionistic fuzzy TOPSIS method.

A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method

Multicriteria fuzzy decision-making problems based on vague set theory

Average load forecasting errors for the holidays are much higher than those for weekdays. So far, many studies on the short-term load forecasting have been made to improve the prediction accuracy using various methods such as deterministic, stochastic, artificial neural net (ANN) and neural network-fuzzy methods. In order to reduce the load forecasting error of the 24 hourly loads for the holidays, the concept of fuzzy regression analysis is employed in the short-term load forecasting problem. According to the historical load data, the same type of holiday showed a similar trend of load profile as in previous years. The fuzzy linear regression model is made from the load data of the previous three years and the coefficients of the model are found by solving the mixed linear programming problem. The proposed algorithm shows good accuracy, and the average maximum percentage error is 3.57% in the load forecasting of the holidays for the years of 1996-1997.

Short-term load forecasting for the holidays using fuzzy linear regression method

A note on similarity measures between vague sets and between elements

Summary form only given. Average load forecasting errors for the holidays are much higher than those for weekdays. So far, many studies on the short-term load forecasting have been made to improve the prediction accuracy using various methods such as deterministic, stochastic, artificial neural net (ANN) and neural network-fuzzy methods. In order to reduce the load forecasting error of the 24 hourly loads for the holidays, the concept of fuzzy regression analysis is employed in the short-term load forecasting problem. According to the historical load data, the same type of holiday showed a similar trend of load profile as in previous years. The fuzzy linear regression model is made from the load data of the previous three years and the coefficients of the model are found by solving the mixed linear programming problem. The proposed algorithm shows good accuracy, and the average maximum percentage error is 3.57% in the load forecasting of the holidays for the years of 1996-1997.

Dug Hun Hong

Papers

Multicriteria fuzzy decision-making problems based on vague set theory

Short-term load forecasting for the holidays using fuzzy linear regression method

A note on similarity measures between vague sets and between elements

Short-term load forecasting for the holidays using fuzzy linear regression method

Correlation of intuitionistic fuzzy sets in probability spaces