Vakkas Uluçay

Similarity measures of bipolar neutrosophic sets and their application to multiple criteria decision making

Abstract In this paper, we introduced some similarity measures for bipolar neutrosophic sets such as; Dice similarity measure, weighted Dice similarity measure, Hybrid vector similarity measure and weighted Hybrid vector similarity measure. Also we examine the propositions of the similarity measures. Furthermore, a multi-criteria decision-making method for bipolar neutrosophic set is developed based on these given similarity measures. Then, a practical example is shown to verify the feasibility of the new method. Finally, we compare the proposed method with the existing methods in order to demonstrate the practicality and effectiveness of the developed method in this paper.

Soft normed rings.

Molodtsov introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainty. In this paper, we initiate the study of soft normed rings by soft set theory. The notions of soft normed rings, soft normed ideals, soft complete normed rings are introduced and also several related properties and examples are given.

Trapezoidal fuzzy multi-number and its application to multi-criteria decision-making problems

In this paper, the concept of trapezoidal fuzzy multi-number (TFM-number) is proposed and some desired operational laws with properties are introduced. In the TFM-number, the occurrences are more than one with the possibility of the same or the different membership functions and the TFM-number is an extension of both fuzzy number set and fuzzy set, allowing the repeated occurrences of any element. Also, aim of this paper is to investigate a multiple criteria decision-making (MCDM) method under TFM-number environment. To construct this method, we first introduce some operational laws on TFM-number based on t-norm and s-norm. Then, TFM-number arithmetic and geometric operators are proposed. Finally, we develop an MCDM method and apply to an MCDM problem to verify the introduced decision-making methods.

Neutrosophic Sets: An Overview

In this study, we give some concepts concerning the neutrosophic sets, single valued neutrosophic sets, interval-valued neutrosophic sets, bipolar neutrosophic sets, neutrosophic hesitant fuzzy sets, inter-valued neutrosophic hesitant fuzzy sets, refined neutrosophic sets, bipolar neutrosophic refined sets, multi-valued neutrosophic sets, simplified neutrosophic linguistic sets, neutrosophic over/off/under sets, rough neutrosophic sets, rough bipolar neutrosophic sets, rough neutrosophic hyper-complex set, and their basic operations. Then we introduce triangular neutrosophic numbers, trapezoidal neutrosophic fuzzy number and their basic operations. Also some comparative studies between the existing neutrosophic sets and neutrosophic number are provided.

Minimum Spanning Tree in Trapezoidal Fuzzy Neutrosophic Environment

In this paper, an algorithm for searching the minimum spanning tree (MST) in a network having trapezoidal fuzzy neutrosophic edge weight is presented. The network is an undirected neutrosophic weighted connected graph (UNWCG). The proposed algorithm is based on matrix approach to design the MST of UNWCG. A numerical example is provided to check the validity of the proposed algorithm. Next, a comparison example is made with Mullai’s algorithm in neutrosophic graphs.