An Improved Score Function for Ranking Neutrosophic Sets and Its Application to Decision-Making Process

2017

Int. J. Intell. Syst.

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138

146

The objective of this work is to present an improved accuracy function for the ranking order of interval-valued Pythagorean fuzzy sets (IVPFSs). Shortcomings of the existing score and accuracy functions in interval-valued Pythagorean environment have been overcome by the proposed accuracy function. In the proposed function, degree of hesitation between the element of IVPFS has been taken into account during the analysis. Based on it, multicriteria decision-making method has been proposed for finding the desirable alternative(s). Finally, an illustrative example for solving the decision-making problem has been presented to demonstrate application of the proposed approach. C 2017 Wiley Periodicals, Inc. GARG for solving the decision-making problem under the IVIFS environment. Nayagam et al. 6 presented a ranking value method for solving the decision-making problem based on IVIFSs. Garg 7 presented a generalized intuitionistic fuzzy interactive geometric aggregation operator using Einstein t-norm and t-conorm operations. Garg, 8 further, developed a new generalized improved score function for ranking the IVIFSs. Nancy and Garg 9 presented an improved score function for ranking the different neutrosophic sets. Kumar and Garg 10 presented an approach related to the technique for order of preference by similarity to ideal solution (TOPSIS) method for ranking the different IVIFSs using the set pair analysis theory. From these above-described studies, it has been concluded that they are valid under the restrictions that the sum of the grades of memberships is not greater than one. However, in day-to-day life, it is not always possible for the decision makers to give their preferences under this restriction. For instance, a person may express his preference toward any object is 0.8 while dissatisfaction is 0.6 then clearly 0.8 + 0.6 1. Thus, these types of situations are not handled with IFS theory. To overcome it, Yager 11,12 relaxed the IFS condition to its square sum that is not greater than 1 and called their corresponding set to be Pythagorean fuzzy set (PFS). After their pioneering work, Yager and Abbasov 13 studied the relationship between the Pythagorean fuzzy numbers (PFNs) and the complex numbers. Yager 12 presented some aggregator operators under PFS environment, whereas Zhang and Xu 14 extended the TOPSIS approach in terms of Pythagorean fuzzy environment. Later on, Peng and Yang 15 defined some new operations on PFNs and their corresponding properties. Garg, 16,17 presented a generalized averaging aggregation operator under the PFS environment by utilizing the Einstein norm operations. Garg 18 proposed the confidence-level-based Pythagorean fuzzy aggregation operators by incorporating the level of the confidence of the decision maker during the decision-making aggregation process. Furthermore, considering the fact the information provided by the decision makers are always be an imprecise number due to various constraints and hence that it is not possible for the decision maker to give their preference in term...

Section: Introductionmentioning

confidence: 99%

A Novel Improved Accuracy Function for Interval Valued Pythagorean Fuzzy Sets and Its Applications in the Decision-Making Process

2017

Int. J. Intell. Syst.

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138

146

“…A bibliometric analysis of NS is presented by Peng and Dai [26]. However, apart from them, several other approaches had presented by the various researchers under the NS environment to solve the decision-making problems [27][28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Algorithms for possibility linguistic single-valued neutrosophic decision-making based on COPRAS and aggregation operators with new information measures

nancy

2019

Measurement

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The objective of this work is to introduce the concept of the possibility linguistic single-valued neutrosophic set (PLSVNS) for better dealing with the imprecise and uncertain information during the decision-making process. The prominent characteristics of this set are that it considers two distinctive sorts of information such as the membership, indeterminacy, non-membership degrees, and their corresponding possibility degree. In it, first, we stated some operational laws, score and accuracy functions, comparison laws between the pairs of the set. Then, we define weighted averaging and geometric aggregation operators (AOs) to collaborate the PLSVNSs into a single one. Further, we present two algorithms based on a complex proportional assessment (COPRAS) method and AOs based method under PLSVNS information to solve the decision-making problems. In these methods, the information related to weights of decision makers and criteria is determined with the help of a distance and entropy measures. Finally, a practical real-life example is provided to expose the materialness and the viability of our work.

“…Later on, Garg [11,12] extended the theory of the IFS to the Pythagorean fuzzy set in which the condition of sum of their membership function has been relaxed to square sum of its membership functions is less than one, and presented a generalized geometric as well as averaging aggregation operators. Apart from that, various researchers pay more attention on decision-making process for aggregating the different alternatives using different aggregation operators [13][14][15][16][17][18][19][20][21][22][23] and their corresponding references.…”

Section: Introductionmentioning

confidence: 99%

A novel correlation coefficient of intuitionistic fuzzy sets based on the connection number of set pair analysis and its application

Kumar

2017

Scientia Iranica

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Set pair analysis (SPA) is an updated theory for dealing with the uncertainty, which overlaps the other theories of uncertainty such as probability, vague, fuzzy and intuitionistic fuzzy set (IFS). Considering the fact that the correlation coefficient plays an important role during the decision-making process, in this paper, after pointing out the weakness of the existing correlation coefficients between the IFSs, we propose a novel correlation coefficient and weighted correlation coefficients formulation to measure the relative strength of the different IFSs. For it, firstly corresponding to each intuitionistic fuzzy number, the connection number of the SPA theory has been formulated in the form of the degree of identity, discrepancy and contrary and then based on its, a novel correlation coefficient measures have been defined. Pairs of identity, discrepancy and contrary of the connection number have been taken as a vector representation during the formulation. Lastly, a decision-making approach based on the proposed measures has been presented which has been illustrated by two numerical examples in pattern recognition and medical diagnosis.