aggregation operators

Linguistic variables (LVs) provide a reliable expression of cognitive information. By inheriting the advantages of LVs, we can express uncertain and incomplete cognitive information in multiple attribute decision-making (MADM), and they do so better than existing methods.  In the decision-making process, we can consider decision experts’ (DEs’) bounded rationality, such as cognition toward loss caused by the DEs’ cognitive limitations during the decision process. Therefore, it is necessary to propose a novel cognitive decision approach to handle MADM problems in which the cognitive information is expressed by LVs. In this paper, we employ LVs to represent uncertain and hesitant cognitive information. Then, we propose a mathematical programming approach to solve the MADM problems where attributes or cognitive preferences are not independent.  Moreover, the validity and superiority of the presented approach are verified by dealing with a practical problem.

Multi-attribute decision making (MADM) is a hot research area in fuzzy mathematics and to deal with that, the averaging and geometric aggregation operators (AOs) are the widely used tools. The aim of this manuscript is to propose the notion of averaging and geometric AOs in the environment of T-spherical fuzzy sets (TSFSs). TSFS enables the selection of grades of memberships from considerably a larger domain and hence overcome the drawbacks of the existing fuzzy frameworks. In this paper, we develop some novel operations for TSFSs including algebraic sum, product etc. Based on new operations some averaging AOs including T-spherical fuzzy weighted averaging (TSFWA) and T-spherical fuzzy weighted geometric (TSFWG) operators are developed. The monotonicity, idempotency and boundedness of the defined operators are investigated, and their fitness is validated using induction method. With the help of an illustrative example, the problem of policy decision making using a MADM algorithm is solved. The new proposed work and the existing literature is compared numerically and the advantages of the TSFWA and TSFWG operators are investigated over existing work.

In most of the multi–criteria decision–analysis (MCDA) problems in which the Choquet integral is used as aggregation function, the coefficients of Choquet integral (capacity) are not known in advance. Actually, they could be calculated by capacity definition methods. In these methods, the preference information of decision maker (DM) is used to constitute a possible solution space. The methods which are based on optimizing an objective function most often suffer from three drawbacks. Firstly, the selection of the ultimate solution from solution set is arbitrarily done. Secondly, the solution may provide more information than whatever proposed by DM. Thirdly, DM may not fully interpret the results. Robust capacity definition methods are proposed to overcome these kinds of drawbacks, on the other hand these methods do not consider evenness (uniformity) which is a major property of capacity. Since in capacity definition methods, the preference information on only a subset of alternatives called reference alternatives, is used, defining the capacity as uniform as possible could improve its capability in evaluating non–reference alternatives. This paper proposes an algorithm to define a capacity that is based only on the preference information of DM and consequently is representative. Furthermore, it improves evenness of capacity and consequently its reliability in evaluating non–reference alternatives. The algorithm is used to evaluate power plant projects. Power plant projects are of the most important national projects in Iran and a major portion of national capital is invested on them, so these projects should be scientifically evaluated in order to figure out their performance. Case–specific criteria are considered in addition to general criteria used in project performance evaluation. The evaluation results obtained from proposed algorithm are compared with those of the most representative utility function method.