Partitioned Bonferroni mean based on linguistic 2-tuple for dealing with multi-attribute group decision making

In this study, a multi-attribute group decision making (MAGDM) problem is investigated, in which decision makers provide their preferences over alternatives by using linguistic 2-tuple. In the process of decision making, we introduce the idea of a specific structure in the attribute set. We assume that attributes are partitioned into several classes and members of intra-partition are interrelated while no interrelationship exists among inter partition. We emphasize the importance of having an aggregation operator, to capture the expressed inter-relationship structure among the attributes, which we will refer to as partition Bonferroni mean (PBM). We also investigate the behavior of the proposed PBM operator. Further to aggregate the given linguistic information to get overall performance value of each alternative in MAGDM, we analyze PBM operator in linguistic 2-tuple environment and develop three new linguistic aggregation operators: 2-tuple linguistic PBM (2TLPBM), weighted 2-tuple linguistic PBM (W2TLPBM) ulti-attribute group decision making and linguistic weighted 2-tuple linguistic PBM (LW-2TLPBM). Based on the idea that total linguistic deviation between individual decision maker’s opinions and group opinion should be minimized, we develop an approach to determine weight of the decision makers. Finally, a practical example is presented to illustrate the proposed method and comparison analysis demonstrates applicability of the proposed method. © 2015 Published by Elsevier B.V. 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 . Introduction Multi-attribute group decision making (MAGDM) is the process f selecting the best alternative from a set of predefined alternatives hich are assessed by a group of decision makers based on multiple ttributes. In day-to-day life, there are many practical instances, uch as, selecting applicants for different kinds of scholarships, electing projects for different kinds of funding policies, admitting tudents in graduate programs [1] and evaluating design, ‘comfort’ r ‘speed’ of various kinds of cars [2], in which decision makers’ references, cannot be expressed precisely in exact quantitative orm, but may be in qualitative one. In such situations, they preer to provide their assessment in linguistic terms. For example, hen evaluating ‘comfort’ or ‘design’, terms like ‘excellent’, ‘good’ r ‘bad’ are used to express experts’ preferences and for evaluating ars’ ‘speed’, terms like ‘very fast’, ‘fast’ or ‘slow’ are generally used. Please cite this article in press as: B. Dutta, D. Guha, Partitioned Bon attribute group decision making, Appl. Soft Comput. J. (2015), http://d o deal with linguistic information in the decision process, sevral linguistic computational models [3–5] have been proposed. mong them, 2-tuple linguistic model, proposed by Heerra and ∗ Corresponding author. Tel.: +91 8987311432. E-mail address: [email protected] (D. Guha). ttp://dx.doi.org/10.1016/j.asoc.2015.08.017 568-4946/© 2015 Published by Elsevier B.V. 55 56 57 Martinez [5,6], has been successfully applied in MAGDM problems [7–10,12–17] due to its capability in linguistic information processing without any loss or distortion of information. Several aggregation operators have been developed to aggregate 2-tuple linguistic information. In Ref. [5], Herrera and Martinez was the first to develop 2-tuple linguistic aggregation operators. They extended classical arithmetic mean, weighted arithmetic mean and OWA operator in 2-tuple linguistic environment, and denoted them as 2-tuple linguistic averaging operator, 2-tuple linguistic weighted averaging operator and 2-tuple linguistic ordered weighted averaging operator, respectively. Jing and Fan [9] introduced 2-tuple linguistic weighted geometric operator and 2-tuple linguistic ordered weighted geometric operator. Wei [11] presented a MAGDM method based on extended 2-tuple linguistic weighted geometric operator and extended 2-tuple linguistic ordered weighted geometric operator, in which weight of input arguments was modeled by 2-tuple linguistic information. In Ref. [12], Wei introduced several new aggregation operators, such as, generalized 2-tuple linguistic ferroni mean based on linguistic 2-tuple for dealing with multix.doi.org/10.1016/j.asoc.2015.08.017 weighted average operator, generalized 2-tuple linguistic ordered weighted average operator and induced generalized ordered weighted average operator. Wei and Zho [13] developed some dependent 2-tuple linguistic aggregation operators in which the 58 59 60 61