Narrow Results

The VIKOR-F method has been developed to solve fuzzy multicriteria problem with conflicting and noncommensurable (different units) criteria. It determines the compromise solution that is the "closest" to the ideal. Imprecision in multicriteria decision making can be modelled using fuzzy set theory to define criteria and the importance of criteria. This method solves problem in a fuzzy environment where both criteria and weights could be fuzzy sets. The triangular fuzzy numbers are used to handle imprecise numerical quantities. It is based on the aggregating fuzzy merit that represents distance of an alternative to the ideal solution. The fuzzy operations and procedures for ranking fuzzy numbers are used in developing the VIKOR-F algorithm. A numerical example illustrates an application of the VIKOR-F method.

This work considers providing a common base for measuring the relative efficiency of a group of homogeneous decision making units in a fuzzy environment. The principle of compromise of the technique for order preference by similarity ideal solution is employed for solving the data envelopment analysis model with fuzzy objectives and constraints. An algorithm with the entropic regularization implementation for finding the compromise solution of the fuzzy data envelopment analysis model is developed. An illustrative example verifying the idea of this paper is provided. The contribution of this work is represented by the improvement of the discriminatory power of the fuzzy DEA, gained through the common weight evaluation.

This paper describes a study on bi-level multi-objective transportation problem in fuzzy environment. To alleviate a difficulty of transporting goods within nodes for long distances, we venture to formulate a transportation problem using bi-level criteria. Again, in this paper, we incorporate the real-life uncertain situation in bi-level transportation system through fuzziness. It produces a new class of transportation problem, namely fuzzy bi-level multi-objective transportation problem (FBMOTP). We solve FBMOTP with and without priority of the 1st level of transportation problem (TP) using the Vogal Approximation Method (VAM) which are called respectively Approach 1 and Approach 2. A special emphasis of this paper is to introduce a new approach namely Approach 3 for solving the FBMOTP in addition to the considered two approaches. In this regard, we incorporate an algorithm for Approach 3 to find compromise solution of the FBMOTP using VAM. Thereafter, the proposed algorithm is illustrated to show the usefulness by taking a numerical example. A comparative analysis with the existing studies is provided to understand the effectiveness of the proposed methodology. At last, conclusions are described with the lines of future study of the paper.

Most multicriteria methods focus on ranking and selecting from a set of alternatives. These methods are usually used to compare all alternatives based on the synthesized scorings within a normalized scale with respect to the same criteria in multicriteria problems. However, the decision makers often simultaneously manage one or several alternatives/projects with conflicting and noncommensurable criteria to reduce the gaps to achieve the aspired grade in practice. They then need to rank the gaps that have not been reduced or improved (the unimproved gaps) for the alternatives/projects or aspects of a project to get the most benefit. Because these compared alternatives/projects do not usually have the same criteria/aspects, traditional methods are unsuitable to deal with them. Thus, this research proposes a new VIKOR method to solve this problem; this new method allows the decision maker to understand these gaps of the projects/aspects and rank them to improve these large gaps in control items to achieve the aspired level. Its concept originates in compromise solutions, in particular the VIKOR method. In addition, this research also provides an example of improving information security risk to demonstrate the suitability of this new method. The results show the effectiveness of the new method.

The multiple attribute decision making (MADM) is an important research field in decision science and operations research. Recently, several commonly used methods such as the TOPSIS and the VIKOR were proposed to solve the MADM problems. The TOPSIS and VIKOR are based on aggregating functions representing closeness to the ideal, which originated in the compromise programming method. The aim of this paper is to develop a new methodology called the relative ratio (RR) for the MADM problems. In this RR method, a compromise solution/alternative is determined based on the concept that the chosen alternative should be as close to the ideal solution as possible and as far away from the negative-ideal solution as possible simultaneously. The computation principle and procedure of the RR method are described in detail in this paper. Moreover comparisons of the RR method with the TOPSIS as well as the VIKOR are made theoretically and illustrated with a numerical example.