scholarly journals Some Novel Geometric Aggregation Operators of Spherical Cubic Fuzzy Information with Application

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Zafar Ullah ◽  
Huma Bashir ◽  
Rukhshanda Anjum ◽  
Mabrook Al-Rakhami ◽  
Suheer Al-Hadhrami ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Score Function ◽  
Membership Degree ◽  
Fuzzy Information ◽  
Numerical Illustration ◽  
Decision Making Processes ◽  
Risks Factors ◽  
Excellent Tool ◽  
Interval Valued

Technology is quickly evolving and becoming part of our lives. Life has become better and easier due to the technologies. Although it has lots of benefits, it also brings serious risks and threats, known as cyberattacks, which are neutralized by cybersecurities. Since spherical fuzzy sets (SFSs) and interval-valued SFS (IVSFS) are an excellent tool in coping with uncertainty and fuzziness, the current study discusses the idea of spherical cubic FSs (SCFSs). These sets are characterized by three mappings known as membership degree, neutral degree, and nonmembership degree. Each of these degrees is spherical cubic fuzzy numbers (SCFNs) such that the summation of their squares does not exceed one. The score function and accuracy function are presented for the comparison of SCFNs. Moreover, the spherical cubic fuzzy weighted geometric (SCFWG) operators and SCF ordered weighted geometric (SCFOWG) operators are established for determining the distance between two SCFNs. Furthermore, some operational rules of the proposed operators are analyzed and multiattribute decision-making (MADM) approach based on these operators is presented. These methods are applied to make the best decision on the basis of risks factors as a numerical illustration. Additionally, the comparison of the proposed method with the existing methods is carried out; since the proposed methods and operators are the generalizations of existing methods, they provide more general, exact, and accurate results. Finally, for the legitimacy, practicality, and usefulness of the decision-making processes, a detailed illustration is given.

Linguistic interval-valued intuitionistic fuzzy copula power aggregation operators for multiattribute group decision making

2021 ◽  
Vol 40 (1) ◽  
pp. 605-624 ◽  
Author(s):  
Lei Xu ◽  
Yi Liu ◽  
Haobin Liu
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Uncertain Information ◽  
Fuzzy Information ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

For the sake of better handle the imprecise and uncertain information in decision making problems(DMPs), linguistic interval-valued intuitionistic fuzzy numbers(LIVIFNs) based aggregation operators (AOS) are proposed by combining extended Copulas (ECs), extended Co-copulas (ECCs), power average operator and linguistic interval-valued intuitionistic fuzzy information (LIVIFI). First of all, ECs and ECCs, some specifics of ECs and ECCs, score and accuracy functions of LIVIFNs are gained. Then, based on ECs and ECCs, several aggregation operators are proposed to aggregate LIVIFI, which can offer decision makers (DMs) desirable generality and flexibility. In addition, the desired properties of proposed AOS are discussed. Last but not least, a MAGDM approach is constructed based on proposed AOs; Consequently, the effectiveness of the proposed approach is verified by a numerical example, and then the advantages are showed by comparing with other approaches.

scholarly journals Interval-Valued Pythagorean Hesitant Fuzzy Set and Its Application to Multiattribute Group Decision-Making

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-26
Author(s):  
Maoyin Zhang ◽  
Tingting Zheng ◽  
Wanrong Zheng ◽  
Ligang Zhou
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Set ◽  
Group Decision ◽  
Score Function ◽  
Hesitant Fuzzy Set ◽  
Fuzzy Information ◽  
Interval Numbers ◽  
Operational Laws ◽  
Interval Valued

Pythagorean hesitant fuzzy sets are widely watched because of their excellent ability to deal with uncertainty, imprecise and vague information. This paper extends Pythagorean hesitant fuzzy environments to interval-valued Pythagorean hesitant fuzzy environments and proposes the concept of interval-valued Pythagorean hesitant fuzzy set (IVPHFS), which allows the membership of each object to be a set of several pairs of possible interval-valued Pythagorean fuzzy elements. Furthermore, we develop a series of aggregation operators for interval-valued Pythagorean hesitant fuzzy information and apply them to multiattribute group decision-making (MAGDM) problems. Then, some desired operational laws and properties of IVPHFSs are studied. Especially, considering an interval-valued Pythagorean fuzzy element (IVPHFE) is formed by several pairs of interval values, this paper proposes the concepts of score function and accuracy function in the form of two interval numbers which can retain interval-valued Pythagorean fuzzy information as much as possible. Then, the relationship among these operators is discussed by comparing the interval numbers. Eventually, an illustrative example fully shows the feasibility, practicality, and effectiveness of the proposed approach.

A Linear Programming Method Based on an Improved Score Function for Interval-Valued Pythagorean Fuzzy Numbers and Its Application to Decision-Making

2018 ◽  
Vol 26 (01) ◽  
pp. 67-80 ◽  
Author(s):  
Harish Garg
Keyword(s):  
Decision Making ◽  
Linear Programming ◽  
Fuzzy Numbers ◽  
Score Function ◽  
Decision Making Process ◽  
Linear Programming Method ◽  
Attribute Weights ◽  
Pythagorean Fuzzy Numbers ◽  
Interval Valued ◽  
Score Matrix

The present paper proposes an improved score function for solving multi-criteria decision-making (MCDM) problem with partially known weight information, In it, the preferences related to criteria are taken in the form of interval-valued Pythagorean fuzzy sets. Based on these preferences and an improved score function, a score matrix has been formulated and then a linear programming based method has been proposed to solve MCDM problems with unknown attribute weights. Some generalized properties have also been proven for justification. Illustrative examples have been given for showing the superiority of the approach with the other existing functions in the decision-making process.

SOME CONTINUOUS AGGREGATION OPERATORS WITH INTERVAL-VALUED INTUITIONISTIC FUZZY INFORMATION AND THEIR APPLICATION TO DECISION MAKING

2012 ◽  
Vol 20 (02) ◽  
pp. 185-209 ◽  
Author(s):  
JIAN LIN ◽  
QIANG ZHANG
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Multiple Attribute Decision Making ◽  
Aggregation Operators ◽  
Fuzzy Information ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Interval Valued

In this paper, some new operators for aggregating interval-valued intuitionistic fuzzy information are proposed to deal with multiple attribute decision making problems. Firstly, the C-IFOWA operator and C-IFOWG operator are developed to aggregate all the values in the interval-valued intuitionistic fuzzy numbers. Some of their desirable properties are also studied. Secondly, in order to aggregate a set of interval-valued intuitionistic fuzzy numbers, some new aggregation operators are proposed based on the C-IFOWA operator and C-IFOWG operator. Thirdly, two methods for multiple attribute decision making, in which the attribute values are given in the forms of interval-valued intuitionistic fuzzy numbers are presented. Finally, two numerical examples are provided to illustrate the practicality and validity of the proposed methods.

scholarly journals On Interval-Valued Fuzzy Soft Preordered Sets and Associated Applications in Decision-Making

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3142
Author(s):  
Mabruka Ali ◽  
Adem Kılıçman
Keyword(s):  
Decision Making ◽  
Score Function ◽  
Research Area ◽  
Soft Sets ◽  
Decision Making Processes ◽  
Important Research Area ◽  
Fuzzy Soft Sets ◽  
Relationship Of ◽  
Preordered Sets ◽  
Interval Valued

Recently, using interval-valued fuzzy soft sets to rank alternatives has become an important research area in decision-making because it provides decision-makers with the best option in a vague and uncertain environment. The present study aims to give an extensive insight into decision-making processes relying on a preference relationship of interval-valued fuzzy soft sets. Firstly, interval-valued fuzzy soft preorderings and an interval-valued fuzzy soft equivalence are established based on the interval-valued fuzzy soft topology. Then, two crisp preordering sets, namely lower crisp and upper crisp preordering sets, are proposed. Next, a score function depending on comparison matrices is expressed in solving multi-group decision-making problems. Finally, a numerical example is given to illustrate the validity and efficacy of the proposed method.

scholarly journals Methods for Multiple Attribute Decision Making with Interval-Valued Pythagorean Fuzzy Information

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 228 ◽  
Author(s):  
Zengxian Li ◽  
Guiwu Wei ◽  
Hui Gao
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Multiple Attribute Decision Making ◽  
Fuzzy Information ◽  
Good Tool ◽  
New Methods ◽  
Multiple Attribute ◽  
Pythagorean Fuzzy Numbers ◽  
Interval Valued

Interval-valued Pythagorean fuzzy numbers (IVPFNs) can easily describe the incomplete and indeterminate information by degrees of membership and non-membership, and the Hamy mean (HM) operator and dual HM (DHM) operators are a good tool for dealing with multiple attribute decision making (MADM) problems because it can capture the interrelationship among the multi-input arguments. Motivated by the studies regarding the HM operator and dual HM operator, we expand the HM operator and dual HM (DMM) operator to process the interval-valued Pythagorean fuzzy numbers (IVPFNs) and then to solve the MADM problems. Firstly, we propose some HM and DHM operators with IVPFNs. Moreover, we present some new methods to solve MADM problems with the IVPFNs. Finally, an applicable example is given.

scholarly journals Novel Dombi Aggregation Operators in Spherical Cubic Fuzzy Information with Applications in Multiple Attribute Decision-Making

2021 ◽  
Vol 2021 ◽  
pp. 1-25
Author(s):  
Tehreem ◽  
Amjad Hussain ◽  
Ahmed Alsanad
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Score Function ◽  
Multiple Attribute Decision Making ◽  
Weighted Averaging ◽  
Fuzzy Information ◽  
Existing Structures ◽  
Multiple Attribute ◽  
Decision Making Processes

The notion of spherical fuzzy sets (SFSs) is one of the most effective ways to model the fuzzy information in decision-making processes. The sum of squares of membership, neutral, and nonmembership degrees in SFSs lies in the interval [0, 1] and accommodates more uncertainties. Henceforth, in this article, the idea of spherical cubic fuzzy sets (SCFSs) is introduced, which is the generalization of SFSs. Spherical cubic fuzzy set is the combination of spherical fuzzy sets and interval-valued spherical fuzzy sets. The membership, neutral, and nonmembership degrees in an SCFS are cubic fuzzy numbers (CFNs). Consequently, this set outperforms the pre-existing structures of fuzzy set theory. Moreover, some fundamental operations for the comparison of two spherical CFNs are defined such as score function and accuracy function. Further, several new operations through Dombi t-norm and Dombi t-conorms are characterized to get the best results during the decision criteria. Furthermore, spherical cubic fuzzy Dombi weighted averaging (SCFDWA), SCFD ordered weighted averaging (SCFDOWA), SCFD hybrid weighted averaging (SCFDHWA), SCFD weighted geometric (SCFDWG), SCFD ordered weighted geometric (SCFDOWG), and the SCFD hybrid weighted geometric (SCFDHWG) aggregated operators are discussed, and their characteristics are examined. In addition, some of the operational laws of these operators are defined. Also, a decision-making approach based on these operators is proposed. Since the proposed methods and operators are the generalizations of the existing methods and operators, therefore, these techniques produce more general, accurate, and precise results as compared with existing ones. Finally, a descriptive example is given in order to describe the validity, practicality, and effectiveness of the proposed methods.

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

Axioms ◽  
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 ◽  
Multi Attribute Decision Making ◽  
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.

Multi-criteria decision-making algorithm based on aggregation operators under the complex interval-valued q-rung orthopair uncertain linguistic information

2021 ◽  
pp. 1-30
Author(s):  
Harish Garg ◽  
Zeeshan Ali ◽  
Zaoli Yang ◽  
Tahir Mahmood ◽  
Sultan Aljahdali
Keyword(s):  
Decision Making ◽  
Brain Tumors ◽  
Score Function ◽  
Aggregation Operators ◽  
Multi Criteria Decision Making ◽  
Linguistic Features ◽  
Interval Numbers ◽  
Fundamental Properties ◽  
Interval Valued

The paper aims to present a concept of a Complex interval-valued q-rung orthopair uncertain linguistic set (CIVQROULS) and investigated their properties. In the presented set, the membership grades are considered in terms of the interval numbers under the complex domain while the linguistic features are added to address the uncertainties in the data. To further discuss more, we have presented the operation laws and score function for CIVQROULS. In addition to them, we present some averaging and geometric operators to aggregate the different pairs of the CIVQROULS. Some fundamental properties of the proposed operators are stated. Afterward, an algorithm for solving the decision-making problems is addressed based on the proposed operator using the CIVQROULS features. The applicability of the algorithm is demonstrated through a case study related to brain tumors and their effectiveness is compared with the existing studies.

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