ARTICLE | doi:10.20944/preprints201804.0012.v1
Subject: Computer Science And Mathematics, Applied Mathematics Keywords: neutrosophic set; interval bipolar neutrosophic set; multi-attribute decision making; distance measures; similarity measures
Online: 2 April 2018 (08:47:02 CEST)
The paper investigates some similarity measures in interval bipolar neutrosophic environment for multi-attribute decision making problems. At first, we define Hamming and Euclidean distances measures between interval bipolar neutrosophic sets and establish their basic properties. We also propose two similarity measures based on the Hamming and Euclidean distance functions. Using maximum and minimum operators, we define new similarity measures and prove their basic properties. Using the proposed similarity measures, we propose a novel multi attribute decision making strategy in interval bipolar neutrosophic set environment. Lastly, we solve an illustrative example of multi attribute decision making and present comparison analysis to show the feasibility, applicability and effectiveness of the proposed strategy.
ARTICLE | doi:10.20944/preprints201801.0065.v1
Subject: Computer Science And Mathematics, Applied Mathematics Keywords: neutrosophic set; bipolar neutrosophic set; interval bipolar neutrosophic set; multi-attribute decision making; cross entropy measure
Online: 8 January 2018 (11:04:02 CET)
Bipolar neutrosophic set is an important extension of bipolar fuzzy set. This set is a hybridization of bipolar fuzzy set and neutrosophic set. Every element of a bipolar neutrosophic set consists of three independent positive membership functions and three independent negative membership functions. In this paper, we develop cross entropy measures of bipolar neutrosophic sets and prove its properties. We also define cross entropy measures of interval bipolar neutrosophic sets and prove its properties. Thereafter, we develop two novel multi-attribute decision making methods based on the proposed cross entropy measures. In the decision making framework, we calculate the weighted cross entropy measures between each alternative and the ideal alternative to rank the alternatives and choose the best one. We solve two illustrative examples of multi-attribute decision making problems and compare the obtained result with the results of other existing methods to show the applicability and effectiveness of the developed method. In the end, the main conclusion and future scope of research are summarized.