A Bonferroni mean considering Shapley fuzzy measure under hesitant bipolar-valued neutrosophic set environment for an investment decision

In investment selection problems, the existence of contingency and uncertainty may result in the loss of attribute information. Then, how to make proper investment decision-making will be a tricky proposition. In this work, a multiattribute group decision making (MAGDM) method based on the generalized probabilistic hesitant fuzzy Bonferroni mean (GPHFBM) operator is constructed, which enables decision-makers to select the proper parameters in decision-making process. Firstly, the GPHFBM operator is proposed by combining the Bonferroni mean operator and Archimedean norm. Secondly, five excellent properties of the GPHFBM operator are discussed in detail. In view of applications, we further develop some special aggregation operators for GPHFBM with the various values of parameters b, d and additive operators g(t). Finally, we propose a probabilistic hesitant fuzzy MAGDM method based on the GPHFBM operator to analyze the aggregated information. A case study of the investment of social insurance funds is given to depict the validity and reasonability of the proposed method. Ultimately, the company X4 is selected as the investment company with the best comprehensive indicator.

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Generalized Weighted Exponential Similarity Measures of Single Valued Neutrosophic Sets

10.54216/ijns.000201 ◽

2019 ◽

pp. 57-66

Author(s):

Abhijit .. ◽

◽

Arnab Paul

Keyword(s):

Decision Making ◽

Membership Function ◽

Fuzzy Set ◽

Investment Decision ◽

Uncertain Data ◽

Intuitionistic Fuzzy Set ◽

Similarity Measures ◽

Neutrosophic Set ◽

Pythagorean Fuzzy Set ◽

Neutrosophic Sets

A single valued neutrsophic set is one of the most successful extensions of the classical set, fuzzy set, intuitionistic fuzzy set, Pythagorean fuzzy set and q-rung orthopair fuzzy set due to the fact that it can handle uncertain data in more wider way. In this paper, we introduce some new generalized weighted similarity measures based on the exponential functions defined on truth-membership function, indeterminacy membership function and falsity membership function of a single valued neutrosophic set to study the independent influences of the truth-membership function, indeterminacy membership function and falsity membership function. The salient features of these proposed similarity measures are studied in detail. Based on the proposed similarity measures, we propose a multi attribute decision making method. To show the feasibility and effectiveness of the proposed method, an investment decision making problem is demonstrated.

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Multiple Criteria Decision Making Approach with Multivalued Neutrosophic Linguistic Normalized Weighted Bonferroni Mean Hamacher Operator

Mathematical Problems in Engineering ◽

10.1155/2018/2432167 ◽

2018 ◽

Vol 2018 ◽

pp. 1-23 ◽

Cited By ~ 3

Author(s):

Bao-lin Li ◽

Juan-ru Wang ◽

Li-hua Yang ◽

Xue-tao Li

Keyword(s):

Decision Making ◽

Multiple Criteria Decision Making ◽

Multiple Criteria ◽

Neutrosophic Set ◽

The Novel ◽

Bonferroni Mean ◽

Novel Approach ◽

Special Cases ◽

Comparison Functions ◽

Einstein Operation

The neutrosophic set and linguistic term set are widely applied in recent years. Motivated by the advantages of them, we combine the multivalued neutrosophic set and linguistic set and define the concept of the multivalued neutrosophic linguistic set (MVNLS). Furthermore, Hamacher operation is an extension of the algebraic and Einstein operation. Additionally, the normalized weighted Bonferroni mean (NWBM) operator can consider the weight of each argument and capture the interrelationship of different arguments. Therefore, the combination of NWBM operator and Hamacher operation is more valuable and agile. Firstly, MVNLS and multivalued neutrosophic linguistic number (MVNLN) are defined, then some new operational rules of MVNLNs on account of Hamacher operations are developed, and the comparison functions for MVNLNs are given. Secondly, multivalued neutrosophic linguistic normalized weighted Bonferroni mean Hamacher operator (MVNLNWBMH) is proposed, and a number of expected characteristics of new operator are investigated. Meanwhile, some special cases of different parametersp,q, andεare analyzed. Thirdly, the approach utilizing the MVNLNWBMH operator is introduced to manage multiple criteria decision making (MCDM) issue in multivalued neutrosophic linguistic environment. Ultimately, a practical example is presented and a comparative analysis is carried out, which validate the effectiveness and generalization of the novel approach.

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Composite Fuzzy Measure and its Application to Decision-Making

Journal of Advanced Computational Intelligence and Intelligent Informatics ◽

10.20965/jaciii.2004.p0252 ◽

2004 ◽

Vol 8 (3) ◽

pp. 252-259

Author(s):

Toshihiro Kaino ◽

◽

Kaoru Hirota ◽

Keyword(s):

Decision Making ◽

Capital Investment ◽

Choquet Integral ◽

Investment Decision ◽

Measurable Space ◽

Fuzzy Measure ◽

Fuzzy Measures ◽

Investment Decision Making ◽

Decision Making Problem ◽

Fuzzy Weights

In applications using fuzzy measures (on real numbers), it becomes a problem how to evaluate in-between intervals each characterized by a fuzzy measure, especially when the Choquet integral is differentiated in real world problems. A composite fuzzy measure built from fuzzy measures defined on fuzzy measurable spaces has been proposed by Kaino and Hirota using composite fuzzy weights, where the measurable space of this composite fuzzy measure is the direct sum of measurable spaces. An associative, composite fuzzy measure built from a finite number of fuzzy measures is proposed and, in a constructive application, it is applied to the automobile plant capital investment decision-making problem. It is assumed that an automobile company plans to sell a new car. The current plant line has a capacity of 3,200 new cars in addition to current car lines. Using this composite fuzzy measure, differentiation of the Choquet integral becomes a quantitative index for decision-making, which is confirmed by this decision-making experiment.

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Multi-Valued Neutrosophic Number Bonferroni Mean Operators with their Applications in Multiple Attribute Group Decision Making

International Journal of Information Technology & Decision Making ◽

10.1142/s0219622016500346 ◽

2016 ◽

Vol 15 (05) ◽

pp. 1181-1210 ◽

Cited By ~ 54

Author(s):

Peide Liu ◽

Lili Zhang ◽

Xi Liu ◽

Peng Wang

Keyword(s):

Decision Making ◽

Group Decision ◽

Comparison Method ◽

Aggregation Operator ◽

Neutrosophic Set ◽

Bonferroni Mean ◽

Operational Laws ◽

Multiple Attribute ◽

Geometric Bonferroni Mean ◽

Parameter Values

Bonferroni mean (BM) is a very useful aggregation operator, which can consider the correlations between the aggregated arguments and the multi-valued neutrosophic set can be much more convenient to denote the incomplete, indeterminate and inconsistent information, in this paper, we applied the Bonferroni mean to the multi-valued neutrosophic set, and proposed some Bonferroni mean operators of multi-valued neutrosophic numbers (MVNNs). First, we gave some operational laws and a comparison method of MVNNs, then we presented the weighted Bonferroni mean (WBM) operator and weighted geometric Bonferroni mean (WGBM) operator. Further, we proposed the multi-valued neutrosophic weighted Bonferroni mean (MVNWBM) operator and the multi-valued neutrosophic weighted geometric Bonferroni mean (MVNWGBM) operator and some properties of them are also investigated. Finally, the decision making methods are developed based on MVNWGBM operator and MVNWBM operator, and an example about investment selection is given to illustrate the applications of the developed methods and the influence of different parameter values on the decision-making results.

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