The most widely used technique for solving and optimizing a real-life problem is linear programming (LP), due to its simplicity and efficiency. However, in order to handle the impreciseness in the data, the neutrosophic set theory plays a vital role which makes a simulation of the decision-making process of humans by considering all aspects of decision (i.e., agree, not sure and disagree). By keeping the advantages of it, in the present work, we have introduced the neutrosophic LP models where their parameters are represented with a trapezoidal neutrosophic numbers and presented a technique for solving them. The presented approach has been illustrated with some numerical examples and shows their superiority with the state of the art by comparison. Finally, we conclude that proposed approach is simpler, efficient and capable of solving the LP models as compared to other methods.

A novel method for solving the fully neutrosophic linear programming problems

In this paper, we first define the concept of bipolar single neutrosophic graphs as the generalization of bipolar fuzzy graphs, N-graphs, intuitionistic fuzzy graph, single valued neutrosophic graphs and bipolar intuitionistic fuzzy graphs.

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An Introduction to Bipolar Single Valued Neutrosophic Graph Theory An Introduction to Bipolar Single Valued Neutrosophic Graph Theory

Aggregation operators on intuitionistic trapezoidal fuzzy number and its application to multi-criteria decision making problems

Ranking of intuitionistic fuzzy numbers is a difficult task. Many methods have been proposed for ranking of intuitionistic fuzzy numbers. In this paper we have ranked both trapezoidal intuitionistic fuzzy numbers and triangular intuitionistic fuzzy numbers using the centroid concept. Some of the properties of the ranking function have been studied. Also, comparative examples are given to show the effectiveness of the proposed method.

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A new approach for ranking of intuitionistic fuzzy numbers using a centroid concept

In this paper, we extend the VIKOR VIsekriterijumska optimizacija i KOmpromisno Resenje) strategy to multiple attribute group decision-making (MAGDM) with bipolar neutrosophic set environment. In this paper, we first define VIKOR strategy in bipolar neutrosophic set environment to handle MAGDM problems, which means we combine the VIKOR with bipolar neutrosophic number to deal with MAGDM.

Vikor Based Magdm Strategy Under Bipolar Neutrosophic Set Environment

Ranking fuzzy numbers plays a very important role in the decision process, data analysis and applications. The concept of an intuitionistic fuzzy number (IFN) is of importance for quantifying an ill-known quantity, and the ranking of IFNs is a very difficult problem. In this paper ranking of triangular intuitionistic fuzzy numbers (TIFNs) is made by means of magnitude and applied to solve intuitionistic fuzzy linear programming problem. Numerical examples are examined to demonstrate the implementation of ranking method.

Solving intuitionistic fuzzy linear programming problems by ranking function

In this ebb and flow time, the neutrosophic set is a significant theme to exhibit the uncertain data, as it shows up the presence of three disjunctive segments, and it gives a wide scope of utilization in particular fields for the analysts. Neutrosophic sets are the extension of intuitionistic fuzzy sets to concentrate on the dubious, reluctant, and equivocal figures of genuine scientific problems. Ranking of neutrosophic fuzzy numbers is a challenging task. Only a very few models have been proposed in the literature for the ranking of neutrosophic fuzzy numbers. In this paper, we have first ranked the neutrosophic trapezoidal fuzzy numbers using the Euclidean measure to frame the centroid concept. We have studied a few properties of the ranking function. The effectiveness of the proposed ranking method is shown by comparative examples. Finally, the created positioning system is utilized to make a decision in the purchase problem.

Multi-criteria decision making based on ranking of neutrosophic trapezoidal fuzzy numbers

In this paper, we discuss the solution of transportation problem in intuitionistic fuzzy nature. Optimal solution for the intuitionistic fuzzy transportation problem without converting the intuitionistic fuzzy number into crisp number is obtained. The procedure is illustrated by numerical example.

S. Vengataasalam

Papers

A new approach for ranking of intuitionistic fuzzy numbers using a centroid concept

Solving intuitionistic fuzzy linear programming problems by ranking function

Multi-criteria decision making based on ranking of neutrosophic trapezoidal fuzzy numbers

An Solution of Intuitionistic Fuzzy Transportation Problem