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Managing the biodiversity extinction crisis requires wise decision-making processes able to account for the limited resources available. In most decision problems in conservation biology, several conflicting objectives have to be taken into account. Most methods used in conservation either provide suboptimal solutions or use strong assumptions about the decision-maker’s preferences. Our paper reviews some of the existing approaches to solve multi-objective decision problems and presents new multi-objective linear programming formulations of two multi-objective optimization problems in conservation, allowing the use of a reference point approach. Reference point approaches solve multi-objective optimization problems by interactively representing the preferences of the decision-maker with a point in the criteria (objectives) space, called the reference point. We modelled and solved the following two problems in conservation: a dynamic multi-species management problem under uncertainty and a spatial allocation resource management problem. Results show that the reference point method outperforms classic methods while illustrating the use of an interactive methodology for solving combinatorial problems with multiple objectives. The method is general and can be adapted to a wide range of ecological combinatorial problems. [ABSTRACT FROM AUTHOR]

Muirhead mean (MM) is a well-known aggregation operator which can consider interrelationships among any number of arguments assigned by a variable vector. Besides, it is a universal operator since it can contain other general operators by assigning some special parameter values. However, the MM can only process the crisp numbers. Inspired by the MM’ advantages, the aim of this paper is to extend MM to process the intuitionistic fuzzy numbers (IFNs) and then to solve the multi-attribute group decision making (MAGDM) problems. Firstly, we develop some intuitionistic fuzzy Muirhead mean (IFMM) operators by extending MM to intuitionistic fuzzy information. Then, we prove some properties and discuss some special cases with respect to the parameter vector. Moreover, we present two new methods to deal with MAGDM problems with the intuitionistic fuzzy information based on the proposed MM operators. Finally, we verify the validity and reliability of our methods by using an application example, and analyze the advantages of our methods by comparing with other existing methods. [ABSTRACT FROM AUTHOR]