Novel decision-making approach based on hesitant fuzzy sets and graph theory
- PDF / 791,928 Bytes
- 26 Pages / 439.37 x 666.142 pts Page_size
- 112 Downloads / 219 Views
Novel decision-making approach based on hesitant fuzzy sets and graph theory Sumera Naz1 · Muhammad Akram1 Received: 1 August 2018 / Revised: 28 October 2018 / Accepted: 16 November 2018 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019
Abstract Hesitant fuzzy set is a powerful and effective tool to express uncertain information in multiattribute decision-making (MADM) process, as it permits the membership degree of an element to a set represented by several possible values in [0,1]. In this paper, we develop a new decision-making approach based on graph theory to deal with the MADM problems, in which the decision information is expressed by hesitant fuzzy elements. Meanwhile, we generalize this approach to make it suitable for processing interval-valued hesitant fuzzy and hesitant triangular fuzzy information. Moreover, we utilize the numerical examples concerning the energy project selection and software evaluation to show the detailed implementation procedure and reliability of our method in solving MADM problems under hesitant fuzzy, interval-valued hesitant fuzzy and hesitant triangular fuzzy environment. Keywords Hesitant fuzzy set · Interval-valued hesitant fuzzy set · Hesitant triangular fuzzy set · Graph theory · Expected value Mathematics Subject Classification 68R10 · 03E72
1 Introduction Multi-attribute decision-making (MADM) is to choose the optimal alternative(s) from a given finite set of alternatives with respect to a collection of attributes. It has been prosperously applied in various domains of operational research including the development of large projects (Xia and Xu 2011), an air-condition system selection problem (Zhang and Xu 2014), partner selection in supply chain management (Naz et al. 2018b) and satellite communication system designing (Jiang et al. 2017). In uncertain circumstances, decision makers or experts assign
Communicated by Marcos Eduardo Valle.
B
Muhammad Akram [email protected] Sumera Naz [email protected]
1
Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan
123
S. Naz, M. Akram
imprecise values due to some influencing factors, for instance, expert’s limited knowledge, limited budgets, inflexible deadlines (Liang and Liu 2015), etc. Under this environment, the imprecise decisions may be associated with obscurity and uncertainty such as fuzzy sets (Zadeh 1965), intuitionistic fuzzy sets (Atanassov 1986) and type-2 fuzzy sets (Mendel and John 2002). As another generalization of fuzzy set, hesitant fuzzy set (HFS) was originally proposed by Torra and Narukawa (2009) and Torra (2010). Hesitant fuzzy element (HFE) is a core of HFS, which permits the membership to be a set of possible values from [0,1] and is a new tool to deal with uncertainty in practical decision-making processes (Liang and Liu 2015; Zhao et al. 2017; Xu and Zhang 2013). HFS successfully deals extensive group decision-making problems. For instance, a group decision organization, containing many experts, is authorized to evaluate the satisfi
Data Loading...
