Pythagorean linguistic preference relations and their applications to group decision making using group recommendations based on consistency matrices and feedback mechanism

Abstract

In this paper, we introduce a new type of fuzzy set, called Pythagorean linguistic sets (PLSs), to address the preferred and nonpreferred degrees of linguistic variables. Moreover, it allows decision makers to offer effectively handle uncertain information more flexible than intuitionistic linguistic sets (ILSs) when one compares two alternatives in the process of decision making. Some of the fundamental operational laws, score, accuracy, and aggregation operators are defined, and their properties are investigated. Preference relation (PR) is a useful and efficient tool for decision making that only requires the decision makers to compare two alternatives at one time. Taking the advantages of PLSs and PRs, this paper also introduces Pythagorean linguistic preference relations (PLPRs) and studies their application. We propose an approach for group decision making using group recommendations based on consistency matrices and feedback mechanism. First, the proposed method constructs the collective consistency matrix, the weight collective PRs, and the group collective PRs. Then, it constructs a consensus relation for each expert and determines the group consensus degree (GCD) for all experts. If the GCD is smaller than a predefined threshold value, then a feedback mechanism is activated to update the PLPRs. Finally, after the GCD is greater than or equal to the predefined threshold value, we calculate the arithmetic mathematical average values of the updated group collective PR to select the most appropriate alternative.

Large-scale group decision-making based on Pythagorean linguistic preference relations using experts clustering and consensus measure with non-cooperative behavior analysis of clusters

“…Therefore, no comparison is made here for GDM technique with numerical example. We only provide the characteristics comparison with intuitionistic linguistic sets (ILSs) [44], intuitionistic linguistic preference relations (ILPRs) [39], PLS [35,38], and PLPR [38], which is shown in Table 8.…”

“…Definition 2 [38] The expected value of any PLN p = s θ( p) , (μ(p), ν( p)) is denoted by E( p) and represented as follows:…”

“…Definition 4 [38] For comparing any two PLNs p = s θ( p) , (μ(p), ν( p)) and q = s θ(q) , (μ(q), ν(q)) , then we have the following: Theorem 1 [38] Let p i = s θ( p i ) , (μ(p i ), ν( p i )) (i = 1, 2, . .…”

“…Definition 5 [38] A PLPR P on the set X for the set S is defined as P = ( p i j ) n×n , where p i j = s θ i j , (μ i j , ν i j ) for all i, j ∈ {1, 2, . .…”

“…Maybe, he/she has 75% certain degree and 8% degree of confusion. In this situation, Mandal et al [38] proposed the new type of preference relation called Pythagorean linguistic preference relation (PLPR), which is addressed the preferred degree and non-preferred degree of LVs according to Yagers Pythagorean fuzzy sets (PFSs) [53]. We suggest for interested researchers to see the attractive studies in [4,5,9,34,37].…”