Interval Consistency Repairing Method for Double Hierarchy Hesitant Fuzzy Linguistic Preference Relation and Application in the Diagnosis of Lung Cancer

Abstract

Natural language is more in line with the real thoughts of people than crisp numbers considering that qualitative language information is more consistent with the expression habits of experts. Double hierarchy hesitant fuzzy linguistic preference relation (DHHFLPR) can be used to express complex linguistic preference information accurately because the pairwise comparison methods are more accurate than non-pairwise methods. Consistency reflects the rationalization of a preference relation and can be used to judge whether a preference relation is self-contradictory or not. In this paper, an interval consistency index of DHHFLPR is developed, which is consisted by the consistency indices of all double hierarchy linguistic preference relations associated with the DHHFLPR. Additionally, an average consistency index of DHHFLPR is given by calculating the average value of the consistency indices of all double hierarchy linguistic preference relations. Moreover, we develop a consistency checking and repairing method for DHHFLPR. Finally, we apply the proposed method into a practical group decision-making problem that is to identify the most critical factors in developing lung cancer, and some comparative analyses involving the connections and differences among the proposed consistency indices are analysed.

The risk assessment of construction project investment based on prospect theory with linguistic preference orderings

“…In recent years, many scholars began to pay attention to the research of double hierarchy linguistic information and developed a lot of research results including preference relations (Gou et al, 2018a(Gou et al, , 2019(Gou et al, , 2020a(Gou et al, , 2020b(Gou et al, , 2020c(Gou et al, , 2020d, measure methodologies (Fu & Liao, 2019;Gou et al, 2018b) and decision methodologies (Fu & Liao, 2019;Gou et al, 2017Gou et al, , 2018aGou et al, , 2018bGou et al, , 2019Gou et al, , 2020aGou et al, , 2020bGou et al, , 2020cKrishankumar et al, 2019;Liu et al, 2019aLiu et al, , 2019bWang et al, 2020), etc.…”

Probabilistic double hierarchy linguistic alternative queuing method for real economy development evaluation under the perspective of economic financialization

“…For instance, in a group decision-making problem, 30% of a group of experts have the same opinion that the speed is 'a little fast', 50% of them think that it is 'just right fast', and 20% of them may access it is 'much fast'. To deal with these kinds of evaluation information, Gou et al (2020b) defined the concept of PDHLTS by combining the DHLTS and the probabilities information, and it can be shown as follows:…”

“…Then, Gou et al (2020b) defined the score function and the variance of a PDHLE, and developed a comparison method between PDHLEs. Definition 3 (Gou et al, 2020b Let z 1 ðpÞ and z 2 ðpÞ be two PDHLEs, Then:…”

“…However, the representation {a little fast, just right fast, much fast} also neglects the importance degrees of these linguistic terms. To overcome these problems, Gou et al (2020b) defined the concept of probabilistic double hierarchy linguistic term set (PDHLTS), and its basic element is called probabilistic double hierarchy linguistic element (PDHLE), which adds probabilities to all DHLTs to represent the importance degrees or belief degrees of the DHLTs for individual assessment, or the probabilistic distribution of collective DHLTs of all experts in group decision-making processes.…”

“…Additionally, for the second issue, the selection of the MCDM method is very important when solving practical MCDM problems under probabilistic double hierarchy linguistic environment. Generally, two kinds of MCDM methods are very common: The traditional MCDM solution methods (Fu & Liao, 2019;Gou et al, 2017a;2020b;Liu et al, 2020;Wei & Gao, 2020;Wnuczak & Osiichuk, 2020) such as the TOPSIS method (Fu & Liao, 2019), the MULTIMOORA method (Gou et al, 2017a), the VIKOR method (Gou et al, 2020b), the TODIM method (Tian et al, 2020), etc. ; and the outranking-based decision-making methods Wang et al, 2020) such as the PROMETHEE (Liu et al, 2019), the DHHFL-LINMAP , the DHHFL-ORESTE (Wang et al, 2020), etc.…”