The q-Rung Orthopair Hesitant Fuzzy Uncertain Linguistic Aggregation Operators and Their Application in Multi-Attribute Decision Making

Abstract

This paper combines the q-rung orthopair hesitant fuzzy sets (q-ROHFSs) with the uncertain linguistic variables, and proposes the q-rung orthopair hesitant fuzzy uncertain linguistic sets (q-ROHFULSs). In addition, the Schweizer-Sklar T-norm is introduced, and a multi-attribute decision-making method based on the q-rung orthopair hesitant fuzzy uncertain linguistic Schweizer-Sklar aggregation operators is established. Firstly, based on the Schweizer-Sklar T-norm, the operational properties of q-rung orthopair hesitant fuzzy uncertain linguistic elements are defined, and the score function, accuracy function and ranking method of the q-rung orthopair hesitant fuzzy uncertain linguistic elements are proposed. Secondly, the q-rung orthopair hesitant fuzzy uncertain linguistic Schweizer-Sklar Bonferroni mean (BM) operator and geometric Bonferroni mean (GBM) operator, Maclaurin symmetric mean (MSM) operator and dual Maclaurin symmetric mean (DMSM) operator, Maclaurin mean (MM) operator and dual Maclaurin mean (DMM) operator are defined. The calculation formulas of the operators are given, the related properties are studied, and the special forms of the operators are discussed. Finally, a multi-attribute decision-making model based on the q-rung orthopair hesitant fuzzy uncertain linguistic aggregation operators is established, and the feasibility and effectiveness of the decision-making method are demonstrated through calculation examples and comparative analyses. INDEX TERMS q-Rung orthopair hesitant fuzzy uncertain linguistic sets (q-ROHFULSs); Schweizer-Sklar T-norm; Bonferroni mean (BM) operator; Maclaurin symmetric mean (MSM) operator; Maclaurin mean (MM) operator; multi-attribute decision making (MADM).

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“…Devaraj and Broumi defined several neutrosophic cubic fuzzy GBMs and proposed a method to solve the financial risk decisionmaking problem [10]. Huang et al presented some GBMs to solve a hesitant fuzzy uncertain linguistic MADM problem [11]. Park et al further propose the optimal weighted GBM and generalized optimal weighted GBM [12].…”

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“…Lin et al [35] developed the linguistic q-rung orthopair fuzzy sets (L q -ROFSs) and their interactional partitioned Heronian mean aggregation operators in order to evaluate the credibility of cloud service productions. For the other notation and application, the reader are referred to [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55] e following arguments and evidences condense the motivation and significance of the theory that shall be studied in this work:…”