Triangular interval type-2 fuzzy soft set and its application
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ORIGINAL ARTICLE
Triangular interval type-2 fuzzy soft set and its application M. Lathamaheswari1 · D. Nagarajan1 · J. Kavikumar2 · Said Broumi3 Received: 19 January 2020 / Accepted: 28 April 2020 © The Author(s) 2020
Abstract Decision-making is an essential task in Science and Engineering. Since most of the real-world problems have uncertainty in nature, making the decision is challengeable one for the decision makers. Soft set has the advantage of free from the deficiency of the parameterization tools of existing theories, namely probability, fuzzy theory and the theory of rough sets. Linguistic terms mean different things to different people, so variability in expert’s acceptance degree is possible. Here usage of type-1 fuzzy leads to noisy and uncertain, and the parameters also may be noisy and hence type-2 fuzzy sets may be used to address the mentioned issues. Therefore, a triangular interval type-2 fuzzy soft set has been considered in the present work by combining triangular interval type-2 fuzzy set and soft set. In this paper, a triangular interval type-2 fuzzy soft weighted arithmetic operator (TIT2FSWA) has been proposed with its desired mathematical properties; also applied the proposed methodology in a decision-making problem for profit analysis. Further comparative analysis has been made with the existing methods to show the effectiveness of the proposed method. Keywords Triangular interval type-2 fuzzy soft set · Aggregation operators · Properties · Decision-making problem
Introduction Decision-making is a very important process for leadership and management. There are processes and techniques available for decision-making and improve the quality of the decision as well. This process involves numerous information, and the collected information need to be aggregated to find the desired result. Hence, aggregation operators are playing a vital role especially in the decision-making process. Triangular inequalities were protracted by the theoretical
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D. Nagarajan [email protected] M. Lathamaheswari [email protected] J. Kavikumar [email protected] Said Broumi [email protected]
1
Department of Mathematics, Hindustan Institute of Technology and Science, Chennai, India
2
Department of Mathematics and Statistics, Faculty of Applied Science and Technology, Universiti Tun Hussein Onn, Batu Pahat, Malaysia
3
Laboratory of Information Processing, Faculty of Science Ben M’Sik, University Hassan II, Casablanca, Morocco
concept of triangular norms which are introduced from the scope of prospect metric [1]. To date, different operators have been used under different set environments. As the real-world problems contain uncertainty we need to use the concept of fuzzy and its extensions. Soft set theory is a general mathematical tool to handle with uncertainty of the real-world problems. Some of the operations on soft sets have been introduced and applied in various fields. The application of fuzzy soft set in decision-making problem has received more attention among the researchers. It has been ap
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