scholarly journals Similarity measures for Fermatean fuzzy sets and its applications in group decision-making

2022 ◽  
Vol 11 (2) ◽  
pp. 167-180
Author(s):  
Laxminarayan Sahoo
Keyword(s):  
Decision Making ◽  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Group Decision Making ◽  
Group Decision ◽  
Similarity Measures ◽  
Cosine Similarity ◽  
Future Research ◽  
Uncertain Information

The intention of this paper is to propose some similarity measures between Fermatean fuzzy sets (FFSs). Firstly, we propose some score based similarity measures for finding similarity measures of FFSs and also propose score based cosine similarity measures between FFSs. Furthermore, we introduce three newly scored functions for effective uses of Fermatean fuzzy sets and discuss some relevant properties of cosine similarity measure. Fermatean fuzzy sets introduced by Senapati and Yager can manipulate uncertain information more easily in the process of multi-criteria decision making (MCDM) and group decision making. Here, we investigate score based similarity measures of Fermatean fuzzy sets and scout the uses of FFSs in pattern recognition. Based on different types of similarity measures a pattern recognition problem viz. personnel appointment is presented to describe the use of FFSs and its similarity measure as well as scores. The counterfeit results show that the proposed method is more malleable than the existing method(s). Finally, concluding remarks and the scope of future research of the proposed approach are given.

A cosine similarity measure for multi-criteria group decision making under neutrosophic soft environment

2020 ◽  
Vol 39 (5) ◽  
pp. 7863-7880
Author(s):  
Yuanxiang Dong ◽  
Xiaoting Cheng ◽  
Weijie Chen ◽  
Hongbo Shi ◽  
Ke Gong
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Group Decision Making ◽  
Group Decision ◽  
Evidence Theory ◽  
Cosine Similarity ◽  
Uncertain Information ◽  
Soft Sets ◽  
Cosine Similarity Measure ◽  
Credibility Degree

In actual life, uncertain and inconsistent information exists widely. How to deal with the information so that it can be better applied is a problem that has to be solved. Neutrosophic soft sets can process uncertain and inconsistent information. Also, Dempster-Shafer evidence theory has the advantage of dealing with uncertain information, and it can synthesize uncertain information and deal with subjective judgments effectively. Therefore, this paper creatively combines the Dempster-Shafer evidence theory with the neutrosophic soft sets, and proposes a cosine similarity measure for multi-criteria group decision making. Different from the previous studies, the proposed similarity measure is utilized to measure the similarity between two objects in the structure of neutrosophic soft set, rather than two neutrosophic soft sets. We also propose the objective degree and credibility degree which reflect the decision makers’ subjective preference based on the similarity measure. Then parameter weights are calculated by the objective degree. Additionally, based on credibility degree and parameter weights, we propose the modified score function, modified accuracy function, and modified certainty function, which can be employed to obtain partial order relation and make decisions. Later, we construct an aggregation algorithm for multi-criteria group decision making based on Dempster’s rule of combination and apply the algorithm to a case of medical diagnosis. Finally, by testing and comparing the algorithm, the results demonstrate that the proposed algorithm can solve the multi-criteria group decision making problems effectively.

scholarly journals Complex q-Rung Orthopair Fuzzy Aggregation Operators and Their Applications in Multi-Attribute Group Decision Making

Information ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 5 ◽  
Author(s):  
Liu ◽  
Mahmood ◽  
Ali
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Imaginary Part ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Uncertain Information ◽  
Membership Degree ◽  
The Real ◽  
Complex Valued

In this manuscript, the notions of q-rung orthopair fuzzy sets (q-ROFSs) and complex fuzzy sets (CFSs) are combined is to propose the complex q-rung orthopair fuzzy sets (Cq-ROFSs) and their fundamental laws. The Cq-ROFSs are an important way to express uncertain information, and they are superior to the complex intuitionistic fuzzy sets and the complex Pythagorean fuzzy sets. Their eminent characteristic is that the sum of the qth power of the real part (similarly for imaginary part) of complex-valued membership degree and the qth power of the real part (similarly for imaginary part) of complex-valued non‐membership degree is equal to or less than 1, so the space of uncertain information they can describe is broader. Under these environments, we develop the score function, accuracy function and comparison method for two Cq-ROFNs. Based on Cq-ROFSs, some new aggregation operators are called complex q-rung orthopair fuzzy weighted averaging (Cq-ROFWA) and complex q-rung orthopair fuzzy weighted geometric (Cq-ROFWG) operators are investigated, and their properties are described. Further, based on proposed operators, we present a new method to deal with the multi‐attribute group decision making (MAGDM) problems under the environment of fuzzy set theory. Finally, we use some practical examples to illustrate the validity and superiority of the proposed method by comparing with other existing methods.

scholarly journals Generalized Ordered Weighted Simplified Neutrosophic Cosine Similarity Measure for Multiple Attribute Group Decision Making

2020 ◽  
Vol 14 (1) ◽  
pp. 51-62 ◽  
Author(s):  
Jun Ye
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Group Decision Making ◽  
Group Decision ◽  
Information Aggregation ◽  
Cosine Similarity ◽  
Weighted Averaging ◽  
Multiple Attribute ◽  
Special Cases ◽  
Cosine Similarity Measure

The paper proposes a generalized ordered weighted simplified neutrosophic cosine similarity (GOWSNCS) measure by combining the cosine similarity measure of simplified neutrosophic sets (SNSs) with the generalized ordered weighted averaging (GOWA) operator and investigates its properties and special cases. Then, the author develops a simplified neutrosophic group decision-making method based on the GOWSNCS measure to handle multiple attribute group decision-making problems with simplified neutrosophic information. The prominent characteristics of the GOWSNCS measure are that it not only is a generalization of the cosine similarity measure but also considers the associated weights for attributes and decision makers in the aggregation of the cosine similarity measures of SNSs to alleviate the influence of unduly large or small similarities in the process of information aggregation. Finally, an illustrative example of investment alternatives is provided to demonstrate the application and effectiveness of the developed approach.

scholarly journals Similarity Measures of Linguistic Cubic Hesitant Variables for Multiple Attribute Group Decision-Making

Information ◽  
2019 ◽  
Vol 10 (5) ◽  
pp. 168 ◽  
Author(s):  
Xueping Lu ◽  
Jun Ye
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Group Decision Making ◽  
Group Decision ◽  
Similarity Measures ◽  
Weight Changes ◽  
Hybrid Form ◽  
Included Angle ◽  
Multiple Attribute ◽  
Language Variables

A linguistic cubic hesitant variable (LCHV) is a hybrid form of linguistic values in group decision-making environments. It is composed of an interval language variable and multiple single-valued language variables given by different decision-makers (DMs). Due to the uncertainty and hesitation of DMs, the numbers of language variables in different LCHVs are unequal. Thus, the least common multiple number (LCMN) extension method was adopted. Based on the included angle and distance of two LCHVs, we presented two cosine similarity measures and developed a multiple attribute group decision-making (MAGDM) approach. An example of engineer selection was used to implement the proposed LCHV MAGDM method and demonstrate the simplicity and feasibility of the proposed method. The sensitivity analysis of weight changes for the two measures showed that the similarity measure based on distance was more stable than the similarity measure based on included angle in this application.

AN INTUITIONISTIC FUZZY GROUP DECISION-MAKING APPROACH BASED ON ENTROPY AND SIMILARITY MEASURES

2011 ◽  
Vol 10 (06) ◽  
pp. 1111-1130 ◽  
Author(s):  
CUIPING WEI ◽  
XIJIN TANG
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Preference Relation ◽  
Similarity Measures ◽  
Uncertain Information ◽  
Preference Relations ◽  
Average Similarity ◽  
The Individual ◽  
Fuzzy Group Decision Making

In this paper, we study group decision-making problems based on intuitionistic preference relations. By measuring the uncertain information of intuitionistic preference relations and the average similarity degree of one individual intuitionistic preference relation to the others, we propose a new approach to assess the relative importance weights of experts. The approach takes both the objective and subjective information of experts into consideration. We then integrate the weights of experts into the individual intuitionistic preference relations and develop a relative similarity method to derive the priorities of alternatives. The comparison analysis with other methods by two numerical examples illustrates the practicality and effectiveness of the proposed methods.

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