Linguistic Spherical Fuzzy Aggregation Operators and Their Applications in Multi-Attribute Decision Making Problems

Abstract

The key objective of the proposed work in this paper is to introduce a generalized form of linguistic picture fuzzy set, so-called linguistic spherical fuzzy set (LSFS), combining the notion of linguistic fuzzy set and spherical fuzzy set. In LSFS we deal with the vague and defective information in decision making. LSFS is characterized by linguistic positive, linguistic neutral and linguistic negative membership degree which satisfies the conditions that the square sum of its linguistic membership degrees is less than or equal to 1. In this paper, we investigate the basic operations of linguistic spherical fuzzy sets and discuss some related results. We extend operational laws of aggregation operators and propose linguistic spherical fuzzy weighted averaging and geometric operators based on spherical fuzzy numbers. Further, the proposed aggregation operators of linguistic spherical fuzzy number are applied to multi-attribute group decision-making problems. To implement the proposed models, we provide some numerical applications of group decision-making problems. In addition, compared with the previous model, we conclude that the proposed technique is more effective and reliable.

Analysis of Decision Support System Based on 2-Tuple Spherical Fuzzy Linguistic Aggregation Information

“…In Table 4, we derived the ranking order of the alternatives by utilizing the developed method. From Table 6, we observed that the ranking orders of the alternatives using the developed method were totally matched with those derived by the Jin et al [47] method. Therefore, the proposed technique is also validated.…”

“…Therefore, the proposed technique is also validated. Utilizing the proposed technique, the best alternative is Q 1 , which is the same as the best alternative obtained by the Jin et al [47] method. Thus, the proposed technique is really prominent, because it can effectively avoid any loss of information which formerly occurred during linguistic information processing.…”

“…The concept of linguistic spherical fuzzy sets was introduced by Jin et al [47]. First of all, we convert the data of created problem to linguistic spherical fuzzy numbers, which are shown in Table 5.…”

“…First of all, we convert the data of created problem to linguistic spherical fuzzy numbers, which are shown in Table 5. Then, we apply all the steps of Jin et al [47] approach, and using the weighting vector of the attributes are (0.27, 0.24, 0.23, 0.26) T . We obtain the following ranking (Table 6);…”

“…In the SF set, all the membership grades are satisfying the condition 0 ≤ (µ (r)) 2 + (η (r)) 2 + (ν (r)) 2 ≤ 1 instead of 0 ≤ µ (r)+η (r) + ν (r) ≤ 1 as in picture fuzzy set. Huanhuan et al [47] defined linguistic spherical fuzzy set, combining the idea of linguistic fuzzy set and spherical fuzzy set. Shahzaib et al [48] defined some spherical fuzzy aggregation operators, using Dombi operation, discussed their application on decision making, and also discussed the representation of spherical fuzzy t-norm and t-conorm in [49].…”