Fuzzy sets and their variants
Kamala Rafig Aliyeva
Abstract
Group decision making in capital investment involves a collaborative process where multiple stakeholders contribute their perspectives, insights, and expertise to evaluate investment opportunities and make informed decisions. The practical and methodological aims of this process can vary depending on ...
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Group decision making in capital investment involves a collaborative process where multiple stakeholders contribute their perspectives, insights, and expertise to evaluate investment opportunities and make informed decisions. The practical and methodological aims of this process can vary depending on the organization's goals, industry, and market conditions. Conducting research on capital investment group decision making is motivated by several factors such as optimizing investment decisions, enhancing performance, managing risk, adapting to changing conditions, building knowledge and expertise. The investment decision relates to the distribution of financial resources. Investors select the most appropriate investment opportunities based on risk profiles, investment aims and expected returns. Fuzzy multicriteria group decision making in capital investment extends the traditional decision-making process to accommodate multiple criteria that are often uncertain, vague, or subjective in nature. The goal of this paper is to suggest a technique known as the Fuzzy Technique for Order Preference by Similarity to Ideal Solution (fuzzy TOPSIS) for group decision making about investment in the respective vehicle. Fuzzy TOPSIS technique represents a decision for experts, which is multi-criteria and includes an aggregated decision-making process. This paper shows the application of this method when choosing the best alternative, considering the choice of vehicle.
Fuzzy sets and their variants
Gia Sirbiladze
Abstract
The Ordered Weighted Averaging (OWA) operator was introduced by Yager [34] to provide a method for aggregating inputs that lie between the max and min operators. In this article we continue to present some extensions of OWA-type aggregation operators. Several variants of the generalizations of the ...
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The Ordered Weighted Averaging (OWA) operator was introduced by Yager [34] to provide a method for aggregating inputs that lie between the max and min operators. In this article we continue to present some extensions of OWA-type aggregation operators. Several variants of the generalizations of the fuzzy-probabilistic OWA operator-FPOWA (introduced by Merigo [13], [14]) are presented in the environment of fuzzy uncertainty, where different monotone measures (fuzzy measure) are used as uncertainty measures. The considered monotone measures are: possibility measure, Sugeno additive measure, monotone measure associated with Belief Structure and Choquet capacity of order two. New aggregation operators are introduced: AsFPOWA and SA-AsFPOWA. Some properties of new aggregation operators and their information measures are proved. Concrete faces of new operators are presented with respect to different monotone measures and mean operators. Concrete operators are induced by the Monotone Expectation (Choquet integral) or Fuzzy Expected Value (Sugeno Integral) and the Associated Probability Class (APC) of a monotone measure. New aggregation operators belong to the Information Structure I6 (see Part I, Section 3). For the illustration of new constructions of AsFPOWA and SA-AsFPOWA operators an example of a fuzzy decision-making problem regarding the political management with possibility uncertainty is considered. Several aggregation operators (“classic” and new operators) are used for the comparing of the results of decision making.
Fuzzy sets and their variants
Gia Sirbiladze
Abstract
The Ordered Weighted Averaging (OWA) operator was introduced by Yager [57] to provide a method for aggregating inputs that lie between the max and min operators. In this article two variants of probabilistic extensions the OWA operator-POWA and FPOWA (introduced by Merigo [26] and [27]) are considered ...
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The Ordered Weighted Averaging (OWA) operator was introduced by Yager [57] to provide a method for aggregating inputs that lie between the max and min operators. In this article two variants of probabilistic extensions the OWA operator-POWA and FPOWA (introduced by Merigo [26] and [27]) are considered as a basis of our generalizations in the environment of fuzzy uncertainty (parts II and III of this work), where different monotone measures (fuzzy measure) are used as uncertainty measures instead of the probability measure. For the identification of “classic” OWA and new operators (presented in parts II and III) of aggregations, the Information Structure is introduced where the incomplete available information in the general decision-making system is presented as a condensation of uncertainty measure, imprecision variable and objective function of weights.
Intuitionistic fuzzy sets and their variants
Suresh Mohan; Arun Prakash Kannusamy; Vengataasalam Samiappan
Abstract
The concept of an intuitionistic fuzzy number (IFN) is of importance for representing an ill-known quantity. Ranking fuzzy numbers plays a very important role in the decision process, data analysis and applications. The concept of an IFN is of importance for quantifying an ill-known quantity. Ranking ...
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The concept of an intuitionistic fuzzy number (IFN) is of importance for representing an ill-known quantity. Ranking fuzzy numbers plays a very important role in the decision process, data analysis and applications. The concept of an IFN is of importance for quantifying an ill-known quantity. Ranking of intuitionistic fuzzy numbers plays a vital role in decision making and linear programming problems. Also, ranking of intuitionistic fuzzy numbers is a very difficult problem. In this paper, a new method for ranking intuitionistic fuzzy number is developed by means of magnitude for different forms of intuitionistic fuzzy numbers. In Particular ranking is done for trapezoidal intuitionistic fuzzy numbers, triangular intuitionistic fuzzy numbers, symmetric trapezoidal intuitionistic fuzzy numbers, and symmetric triangular intuitionistic fuzzy numbers. Numerical examples are illustrated for all the defined different forms of intuitionistic fuzzy numbers. Finally some comparative numerical examples are illustrated to express the advantage of the proposed method.
