Group Decision-Making Based on Set Theory and Weighted Geometric Operator with Interval Rough Multiplicative Reciprocal
- PDF / 521,633 Bytes
- 17 Pages / 595.276 x 790.866 pts Page_size
- 75 Downloads / 230 Views
Group Decision-Making Based on Set Theory and Weighted Geometric Operator with Interval Rough Multiplicative Reciprocal Matrix Rui-lu Huang1 • Hong-yu Zhang1 • Juan-juan Peng2 • Jian-qiang Wang1
•
Yue-jin Lv3
Received: 3 November 2019 / Revised: 17 May 2020 / Accepted: 26 May 2020 ˘ Taiwan Fuzzy Systems Association 2020
Abstract Interval rough numbers play an important role in dealing with complex fuzzy relationships. In this paper, a group decision-making (GDM) model based on interval rough multiplicative reciprocal (IRMR) matrix is proposed. Firstly, the inconsistency, satisfactory consistency and complete consistency of the IRMR matrix are defined from the perspective of set theory. Secondly, an improved method for the inconsistent IRMR matrix is introduced to address the inconsistent preference matrix in GDM. We define the uniform approximation matrix of the IRMR matrix, prove its existence, and provide a new calculation method for the sorting vector of IRMR matrix. Finally, the multiplicative reciprocal matrix obtained with a weighted geometric operator assembly is still the IRMR matrix. A GDM algorithm of the IRMR matrix is presented. The proposed algorithm is demonstrated using an illustrative example, and its feasibility and effectiveness are verified through comparison with other existing methods. Keywords Interval rough multiplicative reciprocal matrix Consistency Uniform approximation matrix Group decision-making
& Jian-qiang Wang [email protected] 1
School of Business, Central South University, Changsha 410083, People’s Republic of China
2
School of Information, Zhejiang University of Finance & Economics, Hangzhou 310018, People’s Republic of China
3
College of Mathematics and Information Science, Guangxi University, Nanning 530004, People’s Republic of China
1 Introduction In practice, people frequently encounter various decisionmaking (DM) problems. As the socioeconomic environment becomes increasingly complex, experts cannot consider all the relevant aspects of DM problems [1]. Therefore, several or more decision-makers (DMs) frequently make decisions, that is, group DM (GDM). For several complex multi-objective DM problems, directly providing the target value of an alternative is occasionally difficult, but the use of analytic hierarchy process (AHP) can better solve the problem. AHP establishes preference matrices by comparing the importance of elements between pairs and obtains the order of alternatives on the basis of preference matrices [2]. The preference matrix is the core of the AHP, and is the major research object in this paper. At present, the common preference matrix is divided into real preference [3], interval preference [4], fuzzy preference [5], intuitionistic fuzzy preference [6] and linguistic preference matrices [7–9] in accordance with the preference representation formats. The multiplicative reciprocal (MR) and additive complementary matrices [10] are included under the characteristics of the preference matrix. GDM methods based on these preference matrices could
Data Loading...
