Abstract
We investigate multiple criteria group decision-making problems in which there are priority relationships between the decision elements (criteria and experts), and decision information provided by decision makers takes the form of multigranular uncertain linguistic information. Firstly, some operational laws and possibility degree of multi-granular uncertain linguistic variables are introduced. Then, some new linguistic aggregation operators based on the prioritized aggregation operator, such as the multigranular uncertain linguistic prioritized weighted average (MULPWA) operator and the multigranular uncertain linguistic prioritized ordered weighted average (MULPOWA) operator, are developed and their desirable properties are studied. The prominent characteristics of these proposed operators are that they can aggregate directly the uncertain linguistic variables whose values form the linguistic term sets with different granularities and convey the prioritization phenomenon among the aggregated arguments. Furthermore, based on the MULPWA and MULPOWA operators, an approach to deal with multiple criteria group decision-making problems under multi-granular uncertain linguistic environments is developed. Finally, a practical example is provided to illustrate the multiple criteria group decision-making process.
Highlights
Xu [13,14,15,16] presented the concept of uncertain linguistic variables, and various uncertain linguistic aggregation operators have been proposed, such as the uncertain linguistic averaging (ULA) operator, uncertain linguistic weighted averaging (ULWA) operator, uncertain linguistic ordered weighted averaging (ULOWA) operator, uncertain linguistic hybrid aggregation (ULHA) operator, uncertain linguistic geometric mean (ULGM) operator, uncertain linguistic weighted geometric mean (ULWGM) operator, uncertain linguistic ordered weighted geometric (ULOWG) operator, uncertain linguistic hybrid geometric mean (ULHG) operator [17], induced uncertain linguistic OWA (IULOWA), induced uncertain Journal of Applied Mathematics linguistic ordered weighted geometric(IULOWG) operator, uncertain linguistic correlated averaging (ULCA) operator, uncertain linguistic correlated geometric (ULCG) operator, and uncertain linguistic harmonic mean (ULHM) operators [18]
If g1 = g2 = ⋅ ⋅ ⋅ = gn, the multigranular uncertain linguistic prioritized ordered weighted average (MULPOWA) operator returns to an uncertain linguistic prioritized ordered weighted average (ULPOWA) operator; if sα(gjj) = sβ(gjj) for all j = 1, 2, . . . , n, the MULPOWA operator returns to a multigranular linguistic prioritized weighted average (MLPWA) operator
We apply the multigranular uncertain linguistic prioritized weighted average (MULPWA) and MULPOWA operators to multiple criteria group decision making based on multigranular uncertain linguistic information
Summary
Due to the fact that experiences and judgments of humans are usually represented by words in their natural language, decision making with linguistic information is becoming a hot research topic and has received many excellent results in recent years [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35]. The main linguistic computational models can be divided into four kinds: the approximate model based on extension principle [1]; the ordered language model [2]; the 2-tuple model [8], and the virtual linguistic variables model [9]. Chen and Lee [20] proposed interval linguistic labels ordered weighted average (ILLOWA) operator for autocratic decision making. Xu (2009) [28] developed some transformation functions to unify the unbalanced linguistic labels with different granularities and utilized the uncertain linguistic weighted averaging (ULWA) operator to aggregate the unified unbalanced linguistic information. Zhang and Guo (2012) [32] proposed a method for multigranular uncertain linguistic group decision making with incomplete weight information.
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