Exponential Laws and Aggregation Operators on Neutrosophic Cubic Sets

Interval Value

This paper presents operational laws along with their cosine measure for the numbers whose base is an interval value and study their properties. Consequent upon these definitions and properties neutrosophic cubic weighted exponential averaging and dual neutrosophic cubic weighted exponential averaging aggregation operators are defined. A multi attribute decision making method is then developed for proposed aggregation operators. An example is constructed as an application. The validity of multi attribute decision making method is also tested and comparative analysis is provided to compare these aggregation operators with existing results.

Complex pythagorean fuzzy aggregation operators based on confidence levels and their applications

Mathematical Biosciences and Engineering ◽

10.3934/mbe.2022050 ◽

2021 ◽

Vol 19 (1) ◽

pp. 1078-1107

Author(s):

Tahir Mahmood ◽

◽

Zeeshan Ali ◽

Kifayat Ullah ◽

Qaisar Khan ◽

...

Keyword(s):

Decision Making ◽

Sensitivity Analysis ◽

Comparative Analysis ◽

Aggregation Operators ◽

Weighted Averaging ◽

Confidence Levels ◽

Ordered Weighted Averaging ◽

Operational Laws ◽

Fuzzy Aggregation ◽

<abstract> <p>The most important influence of this assessment is to analyze some new operational laws based on confidential levels (CLs) for complex Pythagorean fuzzy (CPF) settings. Moreover, to demonstrate the closeness between finite numbers of alternatives, the conception of confidence CPF weighted averaging (CCPFWA), confidence CPF ordered weighted averaging (CCPFOWA), confidence CPF weighted geometric (CCPFWG), and confidence CPF ordered weighted geometric (CCPFOWG) operators are invented. Several significant features of the invented works are also diagnosed. Moreover, to investigate the beneficial optimal from a large number of alternatives, a multi-attribute decision-making (MADM) analysis is analyzed based on CPF data. A lot of examples are demonstrated based on invented works to evaluate the supremacy and ability of the initiated works. For massive convenience, the sensitivity analysis and merits of the identified works are also explored with the help of comparative analysis and they're graphical shown.</p> </abstract>

Approach to Multi-Attribute Decision-Making Methods for Performance Evaluation Process Using Interval-Valued T-Spherical Fuzzy Hamacher Aggregation Information

Axioms ◽

10.3390/axioms10030145 ◽

2021 ◽

Vol 10 (3) ◽

pp. 145

Author(s):

Yun Jin ◽

Zareena Kousar ◽

Kifayat Ullah ◽

Tahir Mahmood ◽

Nimet Yapici Pehlivan ◽

...

Keyword(s):

Decision Making ◽

Fuzzy Set ◽

Evaluation Process ◽

Aggregation Operators ◽

Weighted Averaging ◽

Membership Degree ◽

Operational Laws ◽

Interval Valued ◽

Do So

Interval-valued T-spherical fuzzy set (IVTSFS) handles uncertain and vague information by discussing their membership degree (MD), abstinence degree (AD), non-membership degree (NMD), and refusal degree (RD). MD, AD, NMD, and RD are defined in terms of closed subintervals of that reduce information loss compared to the T-spherical fuzzy set (TSFS), which takes crisp values from intervals; hence, some information may be lost. The purpose of this manuscript is to develop some Hamacher aggregation operators (HAOs) in the environment of IVTSFSs. To do so, some Hamacher operational laws based on Hamacher t-norms (HTNs) and Hamacher t-conorms (HTCNs) are introduced. Using Hamacher operational laws, we develop some aggregation operators (AOs), including an interval-valued T-spherical fuzzy Hamacher (IVTSFH) weighted averaging (IVTSFHWA) operator, an IVTSFH-ordered weighted averaging (IVTSFHOWA) operator, an IVTSFH hybrid averaging (IVTSFHHA) operator, an IVTSFH-weighted geometric (IVTSFHWG) operator, an IVTSFH-ordered weighted geometric (IVTSFHOWG) operator, and an IVTSFH hybrid geometric (IVTSFHHG) operator. The validation of the newly developed HAOs is investigated, and their basic properties are examined. In view of some restrictions, the generalization and proposed HAOs are shown, and a multi-attribute decision-making (MADM) procedure is explored based on the HAOs, which are further exemplified. Finally, a comparative analysis of the proposed work is also discussed with previous literature to show the superiority of our work.

A New Multi-Attribute Decision Making Method with Single-Valued Neutrosophic Graphs

10.54216/ijns.0110202 ◽

2020 ◽

pp. 76-86

Author(s):

admin admin ◽

◽

Wenhui Bai ◽

...

Keyword(s):

Decision Making ◽

Graph Theory ◽

Comparative Analysis ◽

Fuzzy Graph ◽

Neutrosophic Sets ◽

Inconsistent Information ◽

Operational Laws ◽

Engineering Economy ◽

In most realistic situations, the theory and method of multi-attribute decision-making have been widely used in different fields, such as engineering, economy, management, military, and others. Although many studies in some extended fuzzy contexts have been explored with multi-attribute decision-making, it is widely recognized that single-valued neutrosophic sets can describe incomplete, indeterminate and inconsistent information more easier. In this paper, aiming at addressing multi-attribute decision-making problems with single-valued neutrosophic information, related models and multi-attribute decision-making approaches based on the fuzzy graph theory are studied. In specific, the notion of single-valued neutrosophic sets and graphs is firstly introduced together with several common operational laws. Then a multi-attribute decision making method based on single-valued neutrosophic graphs is established. Finally, an illustrative example and a comparative analysis are conducted to verify the feasibility and efficiency of the proposed method.

Spherical uncertain linguistic Hamacher aggregation operators and their application on achieving consistent opinion fusion in group decision making

International Journal of Intelligent Computing and Cybernetics ◽

10.1108/ijicc-09-2020-0120 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Muhammad Qiyas ◽

Saleem Abdullah ◽

Muhammad Naeem

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Group Decision ◽

Aggregation Operator ◽

Aggregation Operators ◽

Content Type ◽

Operational Laws ◽

Decision Making Problem ◽

New Type

PurposeThe aim of this research is to establish a new type of aggregation operator based on Hamacher operational law of spherical uncertain linguistic numbers (SULNs).Design/methodology/approachFirst, the authors define spherical uncertain linguistic sets and develop some operational laws of SULNs. Furthermore, the authors extended these operational laws to the aggregation operator and developed spherical uncertain linguistic Hamacher averaging and geometric aggregation operators.FindingsThe authors were limited in achieving a consistent opinion on the fusion in group decision-making problem with the SULN information.Originality/valueIn order to give an application of the introduced operators, the authors first constrict a system of multi-attribute decision-making algorithm.

On Ranking of Intuitionistic Fuzzy Values Based on Dominance Relations

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488514500160 ◽

2014 ◽

Vol 22 (02) ◽

pp. 315-335 ◽

Cited By ~ 10

Author(s):

Xiaohan Yu ◽

Zeshui Xu ◽

Shousheng Liu ◽

Qi Chen

Keyword(s):

Decision Making ◽

Order Relation ◽

Aggregation Operators ◽

Fuzzy Subset ◽

Dominance Relations ◽

Intuitionistic Fuzzy ◽

Operational Laws ◽

Fuzzy Aggregation ◽

Do So

For intuitionistic fuzzy values (IFVs), there are more or less some drawbacks in the existing comparison methods, so it is necessary for us to develop a more proper technique for comparing or ranking IFVs in this paper. To do so, we first formalize an IFV as a fuzzy subset in order to analyze the fuzzy meaning of an IFV, and then according to the basic properties of the fuzzy subset, we determine the dominance relation (order relation) between two IFVs by defining a dominance degree. In order to explain the feasibility of the dominance relations, we validate the monotonicity of intuitionistic fuzzy operational laws, and additionally, we improve and prove the monotonicity of several intuitionistic fuzzy aggregation operators on the basis of the dominance relations. Because it is of importance for some practical problems (e.g., intuitionistic fuzzy multi-attribute decision making) to rank IFVs, we finally develop a method for ranking IFVs by constructing a dominance matrix based on the dominance degrees. A simple example is taken to illustrate the validity of our ranking method.

Some Interval Neutrosophic Dombi Power Bonferroni Mean Operators and Their Application in Multi–Attribute Decision–Making

Symmetry ◽

10.3390/sym10100459 ◽

2018 ◽

Vol 10 (10) ◽

pp. 459 ◽

Cited By ~ 11

Author(s):

Qaisar Khan ◽

Peide Liu ◽

Tahir Mahmood ◽

Florentin Smarandache ◽

Kifayat Ullah

Keyword(s):

Decision Making ◽

Hybrid Structure ◽

Aggregation Operators ◽

Neutrosophic Sets ◽

Bonferroni Mean ◽

Operational Laws ◽

Geometric Bonferroni Mean ◽

Dombi Operations ◽

The Impact

The power Bonferroni mean (PBM) operator is a hybrid structure and can take the advantage of a power average (PA) operator, which can reduce the impact of inappropriate data given by the prejudiced decision makers (DMs) and Bonferroni mean (BM) operator, which can take into account the correlation between two attributes. In recent years, many researchers have extended the PBM operator to handle fuzzy information. The Dombi operations of T-conorm (TCN) and T-norm (TN), proposed by Dombi, have the supremacy of outstanding flexibility with general parameters. However, in the existing literature, PBM and the Dombi operations have not been combined for the above advantages for interval-neutrosophic sets (INSs). In this article, we first define some operational laws for interval neutrosophic numbers (INNs) based on Dombi TN and TCN and discuss several desirable properties of these operational rules. Secondly, we extend the PBM operator based on Dombi operations to develop an interval-neutrosophic Dombi PBM (INDPBM) operator, an interval-neutrosophic weighted Dombi PBM (INWDPBM) operator, an interval-neutrosophic Dombi power geometric Bonferroni mean (INDPGBM) operator and an interval-neutrosophic weighted Dombi power geometric Bonferroni mean (INWDPGBM) operator, and discuss several properties of these aggregation operators. Then we develop a multi-attribute decision-making (MADM) method, based on these proposed aggregation operators, to deal with interval neutrosophic (IN) information. Lastly, an illustrative example is provided to show the usefulness and realism of the proposed MADM method. The developed aggregation operators are very practical for solving MADM problems, as it considers the interaction among two input arguments and removes the influence of awkward data in the decision-making process at the same time. The other advantage of the proposed aggregation operators is that they are flexible due to general parameter.

Linguistic Spherical Fuzzy Aggregation Operators and Their Applications in Multi-Attribute Decision Making Problems

Mathematics ◽

10.3390/math7050413 ◽

2019 ◽

Vol 7 (5) ◽

pp. 413 ◽

Cited By ~ 19

Author(s):

Huanhuan Jin ◽

Shahzaib Ashraf ◽

Saleem Abdullah ◽

Muhammad Qiyas ◽

Mahwish Bano ◽

...

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Fuzzy Set ◽

Group Decision ◽

Aggregation Operators ◽

Weighted Averaging ◽

Operational Laws ◽

Picture Fuzzy Set ◽

Fuzzy Aggregation ◽

The key objective of the proposed work in this paper is to introduce a generalized form of linguistic picture fuzzy set, so-called linguistic spherical fuzzy set (LSFS), combining the notion of linguistic fuzzy set and spherical fuzzy set. In LSFS we deal with the vague and defective information in decision making. LSFS is characterized by linguistic positive, linguistic neutral and linguistic negative membership degree which satisfies the conditions that the square sum of its linguistic membership degrees is less than or equal to 1. In this paper, we investigate the basic operations of linguistic spherical fuzzy sets and discuss some related results. We extend operational laws of aggregation operators and propose linguistic spherical fuzzy weighted averaging and geometric operators based on spherical fuzzy numbers. Further, the proposed aggregation operators of linguistic spherical fuzzy number are applied to multi-attribute group decision-making problems. To implement the proposed models, we provide some numerical applications of group decision-making problems. In addition, compared with the previous model, we conclude that the proposed technique is more effective and reliable.

Complex T-Spherical Fuzzy Aggregation Operators with Application to Multi-Attribute Decision Making

Symmetry ◽

10.3390/sym12081311 ◽

2020 ◽

Vol 12 (8) ◽

pp. 1311 ◽

Cited By ~ 4

Author(s):

Zeeshan Ali ◽

Tahir Mahmood ◽

Miin-Shen Yang

Keyword(s):

Decision Making ◽

Aggregation Operators ◽

Weighted Averaging ◽

The Novel ◽

Fuzzy Environment ◽

Novel Approach ◽

Operational Laws ◽

Comparison Results ◽

Fuzzy Aggregation ◽

In this paper, the novel approach of complex T-spherical fuzzy sets (CTSFSs) and their operational laws are explored and also verified with the help of examples. CTSFS composes the grade of truth, abstinence, and falsity with a condition that the sum of q-power of the real part (also for imaginary part) of the truth, abstinence, and falsity grades cannot be exceeded from a unit interval. Additionally, to examine the interrelationships among the complex T-spherical fuzzy numbers (CTSFNs), we propose two aggregation operators, called complex T-spherical fuzzy weighted averaging (CTSFWA) and complex T-spherical fuzzy weighted geometric (CTSFWG) operators. A multi-attribute decision making (MADM) problem is resolved based on CTSFNs by using the proposed CTSFWA and CTSFWG operators. To examine the proficiency and reliability of the explored works, we use an example to make comparisons between the proposed operators and some existing operators. Based on the comparison results, the proposed CTSFWA and CTSFWG operators are well suited in the fuzzy environment with legitimacy and prevalence by contrasting other existing operators.

Multi-Attribute Multi-Perception Decision-Making Based on Generalized T-Spherical Fuzzy Weighted Aggregation Operators on Neutrosophic Sets

Mathematics ◽

10.3390/math7090780 ◽

2019 ◽

Vol 7 (9) ◽

pp. 780 ◽

Cited By ~ 11

Author(s):

Quek ◽

Selvachandran ◽

Munir ◽

Mahmood ◽

Ullah ◽

...

Keyword(s):

Decision Making ◽

Set Theory ◽

Fuzzy Set ◽

Fuzzy Set Theory ◽

Aggregation Operators ◽

Neutrosophic Sets ◽

Operational Laws ◽

Fuzzy Aggregation ◽

Do So

The framework of the T-spherical fuzzy set is a recent development in fuzzy set theory that can describe imprecise events using four types of membership grades with no restrictions. The purpose of this manuscript is to point out the limitations of the existing intuitionistic fuzzy Einstein averaging and geometric operators and to develop some improved Einstein aggregation operators. To do so, first some new operational laws were developed for T-spherical fuzzy sets and their properties were investigated. Based on these new operations, two types of Einstein aggregation operators are proposed namely the Einstein interactive averaging aggregation operators and the Einstein interactive geometric aggregation operators. The properties of the newly developed aggregation operators were then investigated and verified. The T-spherical fuzzy aggregation operators were then applied to a multi-attribute decision making (MADM) problem related to the degree of pollution of five major cities in China. Actual datasets sourced from the UCI Machine Learning Repository were used for this purpose. A detailed study was done to determine the most and least polluted city for different perceptions for different situations. Several compliance tests were then outlined to test and verify the accuracy of the results obtained via our proposed decision-making algorithm. It was proved that the results obtained via our proposed decision-making algorithm was fully compliant with all the tests that were outlined, thereby confirming the accuracy of the results obtained via our proposed method.

Q-rung Orthopair Normal Fuzzy Aggregation Operators and Their Application in Multi-Attribute Decision-Making

Mathematics ◽

10.3390/math7121142 ◽

2019 ◽

Vol 7 (12) ◽

pp. 1142 ◽

Cited By ~ 6

Author(s):

Zaoli Yang ◽

Xin Li ◽

Zehong Cao ◽

Jinqiu Li

Keyword(s):

Decision Making ◽

Normal Distribution ◽

Score Function ◽

Information Aggregation ◽

Aggregation Operators ◽

Uncertain Information ◽

Numerical Result ◽

Operational Laws ◽

Fuzzy Aggregation ◽

Q-rung orthopair fuzzy set (q-ROFS) is a powerful tool to describe uncertain information in the process of subjective decision-making, but not express vast objective phenomenons that obey normal distribution. For this situation, by combining the q-ROFS with the normal fuzzy number, we proposed a new concept of q-rung orthopair normal fuzzy (q-RONF) set. Firstly, we defined the conception, the operational laws, score function, and accuracy function of q-RONF set. Secondly, we presented some new aggregation operators to aggregate the q-RONF information, including the q-RONF weighted operators, the q-RONF ordered weighted operators, the q-RONF hybrid operator, and the generalized form of these operators. Furthermore, we discussed some desirable properties of the above operators, such as monotonicity, commutativity, and idempotency. Meanwhile, we applied the proposed operators to the multi-attribute decision-making (MADM) problem and established a novel MADM method. Finally, the proposed MADM method was applied in a numerical example on enterprise partner selection, the numerical result showed the proposed method can effectively handle the objective phenomena with obeying normal distribution and complicated fuzzy information, and has high practicality. The results of comparative and sensitive analysis indicated that our proposed method based on q-RONF aggregation operators over existing methods have stronger information aggregation ability, and are more suitable and flexible for MADM problems.