Water distribution system selection with modified fuzzy VIKOR approach based on novel knowledge and accuracy measure

Manish Garg, Satish Kumar

Abstract: Problem of water distribution is increasing day by day in almost every city due to increasing population, industrialization, etc. It is a great task for government, non-government authorities to fulfill the requirement of water. Various alternatives are there depending upon different parameters that can be opted for this purpose. Selection of best alternative according to various parameters like cost, reliability, environmental impact, etc. can be carried out by using various decision making methods. This paper presents a decision making method in fuzzy environment to solve the problem of water distribution system selection. Fuzzy set is an effective tool for managing ambiguity and uncertainty in real life problems. The level of ambiguity, uncertainty, and fuzziness associated with a fuzzy set is its fuzzy information measure (FIM). Moreover, fuzzy knowledge measure (FKM) represents the quantity of knowledge connected to a fuzzy set. FKM is taken as dual of FIM. In view of this, a new FKM has been proposed in this paper by eradicating limitations of existing information measures and knowledge measures. After that, results of proposed knowledge measure are compared with the existing information measures and knowledge measures to check the reliability of introduced fuzzy knowledge measure. Performance of proposed FKM is tested with the help of various numerical examples. Besides this, a new accuracy measure (FAM) is proposed based on the proposed fuzzy knowledge measure. The practical usefulness of the suggested FKM and FAM is given in optimizing the water distribution system of a city. The aim of the present paper is to propose an efficient solution methodology by associating the proposed FAM with the traditional VIKOR (Vlsekriterijumska Optimizacija I Kompromisno Resenje) method so as to improve the stability of the VIKOR approach. A comparative study has been carried out with the several existing approaches to demonstrate the efficiency of proposed method.