An overview of intuitionistic linguistic fuzzy information aggregations and applications

Peide Liu,Hui Gao

doi:10.1108/maem-06-2018-003

Abstract

Purpose Intuitionistic linguistic fuzzy information (ILFI), characterized by linguistic terms and intuitionistic fuzzy sets (IFSs), can easily express the fuzzy information in the process of muticriteria decision making (MCDM) and muticriteria group decision making (MCGDM) problems. The purpose of this paper is to provide an overview of aggregation operators (AOs) and applications of ILFI. Design/methodology/approach First, some meaningful AOs for ILFI are summarized, and some extended MCDM approaches for intuitionistic uncertain linguistic variables (IULVs), such as extended TOPSIS, extended TODIM, extended VIKOR, are discussed. Then, the authors summarize and analyze the applications about the AOs of IULVs. Findings IULVs, characterized by linguistic terms and IFSs, can more detailed and comprehensively express the criteria values in the process of MCDM and MCGDM. Therefore, lots of researchers pay more and more attention to the MCDM or MCGDM methods with IULVs. Originality/value The authors summarize and analyze the applications about the AOs of IULVs Finally, the authors point out some possible directions for future research.

Highlights

Due to the increasing complexity of decision-making problems, it is generally difficult to express criteria values of alternatives by exact numbers. Zadeh (1965) originally proposed the fuzzy set (FS) theory, which is an effective tool in dealing with fuzzy information
As the generalization of FS, intuitionistic fuzzy set (IFS) introduced by Atanassov (1986, 1989, 1999) has a membership degree (MD), a non-membership degree (NMD) and a hesitancy degree (HD), which can further overcome the drawbacks of FS
Many contributions have concentrated on the decision-making techniques based on IFSs, which are from three domains: the theory of foundations, for instance, operational rules (Chen and Han, 2018; Dymova and Sevastjanov, 2010, 2012, 2015, 2016), comparative approaches (Deepa and Kumar, 2018), distance and similarity measures (Atanassov, 1989), likelihood ( Jiang and Hu, 2018), ranking function (Hao and Chen, 2018), consensus degree (Cheng, 2017), proximity measure (Ngan et al, 2018) and so on; the extended muticriteria decision-making (MCDM) approaches for IFS, such as TOPSIS

Summary

Introduction

Due to the increasing complexity of decision-making problems, it is generally difficult to express criteria values of alternatives by exact numbers. Zadeh (1965) originally proposed the fuzzy set (FS) theory, which is an effective tool in dealing with fuzzy information. The rest of this paper is organized as follows: in Section 2, we review the basic concepts and operational rules of IFS, LTS, intuitionistic linguistic set (ILS), IULS and IVIULS. For the given element ε, 〈sφ(ε), (uR(ε), vR(ε))〉 iscalled intuitionistic linguistic fuzzy number (ILFN), and for convenience, we can utilize e~ 1⁄4 sjðeÞ; ðuðeÞ; vðeÞÞ to denote an ILFN, which meets the conditions, uR(ε), vR(ε)∈[0, 1] and 0⩽ uR(ε)+vR(ε) ⩽ 1. Let e~1 1⁄4 /1⁄2sjðe1Þ; sWðe_1Þ; ðuðe1Þ; vðe1ÞÞ and e~2 1⁄4 /1⁄2sjðe2Þ; sWðe2Þ; ðuðe2Þ; vðe2ÞÞ be two IULVs, sjðe1Þ; sWðe1Þ; sjðe2Þ; sWðe2Þ A S, δ ⩾ 0, the operations of IULV can be defined as follows (Liu and Jin, 2012): e~1 È e~2 1⁄4 sjðe1Þ þ jðe2Þ; sWðe1Þ þ Wðe2Þ ; ð1Àð1Àuðe1ÞÞð1Àuðe2ÞÞ; vðe1Þvðe2ÞÞ ;.

Some basic intuitionistic linguistic fuzzy AOs

Induced IL fuzzy AOs

Further research directions

Conclusions