METHOD FOR AGGREGATING TRIANGULAR FUZZY INTUITIONISTIC FUZZY INFORMATION AND ITS APPLICATION TO DECISION MAKING / NUMANOMŲ NEAPIBRĖŽTŲJŲ AIBIŲ TEORIJA IR JOS TAIKYMAS PRIIMANT SPRENDIMUS

2010 ◽  
Vol 16 (2) ◽  
pp. 280-290 ◽  
Author(s):  
Xin Zhang ◽  
Peide Liu
Keyword(s):  
Decision Making ◽  
Fuzzy Number ◽  
Intuitionistic Fuzzy Set ◽  
Score Function ◽  
Triangular Fuzzy Number ◽  
Membership Degree ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Weighted Arithmetic ◽  
Operation Rules

On the foundation of the theory of the intuitionistic fuzzy set, this paper uses the triangular fuzzy number to denote the membership degree and the non‐membership degree and proposes the triangular intuitionistic fuzzy number. Then the operation rules of triangular intuitionistic fuzzy numbers are defined. The weighted arithmetic averaging operator and the weighted geometric average operator are presented and used to the decision making area after defined the score function and the accuracy function. An effective solution is offered for multi‐attitude decision‐making problem and an active try is made. Santrauka Remiantis numanomų neapibrežtųjų aibių teorija, šiame straipsnyje aprašomas trečiojo laipsnio neapibrežtasis skaičius, apibūdinantis priklausomumo laipsni. Toliau nustatomos operavimo su tokiais skaičiais taisyklės. Pasiūlytas svertinis aritmetinio vidurkio operatorius, naudojamas priimant sprendimus. Siūlomi efektyvūs daugiaaspekčių problemų sprendimo būdai.

Complex intuitionistic fuzzy Maclaurin symmetric mean operators and its application to emergency program selection

2021 ◽  
pp. 1-22
Author(s):  
Riaz Ali ◽  
Saleem Abdullah ◽  
Shakoor Muhammad ◽  
Muhammad Naeem ◽  
Ronnason Chinram
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Score Functions ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Program Selection ◽  
Maclaurin Symmetric Mean ◽  
Complex Intuitionistic Fuzzy Set

Due to the indeterminacy and uncertainty of the decision-makers (DM) in the complex decision making problems of daily life, evaluation and aggregation of the information usually becomes a complicated task. In literature many theories and fuzzy sets (FS) are presented for the evaluation of these decision tasks, but most of these theories and fuzzy sets have failed to explain the uncertainty and vagueness in the decision making issues. Therefore, we use complex intuitionistic fuzzy set (CIFS) instead of fuzzy set and intuitionistic fuzzy set (IFS). A new type of aggregation operation is also developed by the use of complex intuitionistic fuzzy numbers (CIFNs), their accuracy and the score functions are also discussed in detail. Moreover, we utilized the Maclaurin symmetric mean (MSM) operator, which have the ability to capture the relationship among multi-input arguments, as a result, CIF Maclarurin symmetric mean (CIFMSM) operator and CIF dual Maclaurin symmetric mean (CIFDMSM) operator are presented and their characteristics are discussed in detail. On the basis of these operators, a MAGDM method is presented for the solution of group decision making problems. Finally, the validation of the propounded approach is proved by evaluating a numerical example, and by the comparison with the previously researched results.

A Score Function-Based Method of Forecasting Using Intuitionistic Fuzzy Time Series

2018 ◽  
Vol 14 (01) ◽  
pp. 91-111 ◽  
Author(s):  
Abhishekh ◽  
Surendra Singh Gautam ◽  
S. R. Singh
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Stock Exchange ◽  
Market Price ◽  
Intuitionistic Fuzzy Set ◽  
Score Function ◽  
Fuzzy Time Series ◽  
Series Data ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy

Intuitionistic fuzzy set plays a vital role in data analysis and decision-making problems. In this paper, we propose an enhanced and versatile method of forecasting using the concept of intuitionistic fuzzy time series (FTS) based on their score function. The developed method has been presented in the form of simple computational steps of forecasting instead of complicated max–min compositions operator of intuitionistic fuzzy sets to compute the relational matrix [Formula: see text]. Also, the proposed method is based on the maximum score and minimum accuracy function of intuitionistic fuzzy numbers (IFNs) to fuzzify the historical time series data. Further intuitionistic fuzzy logical relationship groups are defined and also provide a forecasted value and lies in an interval and is more appropriate rather than a crisp value. Furthermore, the proposed method has been implemented on the historical student enrollments data of University of Alabama and obtains the forecasted values which have been compared with the existing methods to show its superiority. The suitability of the proposed model has also been examined to forecast the movement of share market price of State Bank of India (SBI) at Bombay Stock Exchange (BSE). The results of the comparison of MSE and MAPE indicate that the proposed method produces more accurate forecasting results.

A New Method for Ranking Intuitionistic Fuzzy Numbers

2011 ◽  
Vol 2 (1) ◽  
pp. 43-49 ◽  
Author(s):  
Cui-Ping Wei ◽  
Xijin Tang
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Score Function ◽  
Ranking Method ◽  
New Method ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy Numbers ◽  
Additional Information ◽  
Intuitionistic Fuzzy ◽  
Possibility Degree

In this paper the ranking method for intuitionistic fuzzy numbers is studied. The authors first define a possibility degree formula to compare two intuitionistic fuzzy numbers. In comparison with Chen and Tan’s score function, the possibility degree formula provides additional information for the comparison of two intuitionistic fuzzy numbers. Based on the possibility degree formula, the authors give a possibility degree method to rank intuitionistic fuzzy numbers, which is used to rank the alternatives in multi-criteria decision making problems.

A New Method for Ranking Intuitionistic Fuzzy Numbers

2013 ◽  
pp. 45-51
Author(s):  
Cui-Ping Wei ◽  
Xijin Tang
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Score Function ◽  
Ranking Method ◽  
New Method ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy Numbers ◽  
Additional Information ◽  
Intuitionistic Fuzzy ◽  
Possibility Degree

In this paper the ranking method for intuitionistic fuzzy numbers is studied. The authors first define a possibility degree formula to compare two intuitionistic fuzzy numbers. In comparison with Chen and Tan’s score function, the possibility degree formula provides additional information for the comparison of two intuitionistic fuzzy numbers. Based on the possibility degree formula, the authors give a possibility degree method to rank intuitionistic fuzzy numbers, which is used to rank the alternatives in multi-criteria decision making problems.

Human Immunodeficiency Virus (HIV) infection model based on triangular neutrosophic cubic hesitant fuzzy number

2019 ◽  
Vol 12 (05) ◽  
pp. 1950055 ◽  
Author(s):  
Fazli Amin ◽  
Aliya Fahmi
Keyword(s):  
Decision Making ◽  
Human Immunodeficiency Virus ◽  
Fuzzy Number ◽  
Score Function ◽  
Multiple Attribute Decision Making ◽  
Infection Model ◽  
Weighted Arithmetic ◽  
Multiple Attribute ◽  
Immunodeficiency Virus ◽  
Hiv Infection Model

In this paper, we define the basic concept of triangular neutrosophic cubic hesitant fuzzy number and their properties. We develop a triangular neutrosophic cubic hesitant fuzzy ordered weighted arithmetic averaging (TNCHFOWAA) operator and a triangular neutrosophic cubic hesitant fuzzy ordered weighted geometric averaging (TNCHFOWGA) operator to aggregate triangular neutrosophic cubic hesitant fuzzy number (TNCHFN) information and investigate their properties. Furthermore, a multiple attribute decision-making method based on the TNCHFOWAA operator and triangular neutrosophic cubic hesitant fuzzy ordered weighted geometric (TNCHFOWG) operator and the score function of TNCHFN is established under a TNCHFN environment. Finally, an illustrative example of investment alternatives is given to demonstrate the application and effectiveness of the developed approach.

ELECTRE Method Based on Interval-Valued Intuitionistic Fuzzy Number

2012 ◽  
Vol 220-223 ◽  
pp. 2308-2312 ◽  
Author(s):  
Jun Li ◽  
Min Lin ◽  
Jian Hua Chen
Keyword(s):  
Decision Making ◽  
Fuzzy Number ◽  
Preference Relation ◽  
Intuitionistic Fuzzy Set ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy Number ◽  
Intuitionistic Fuzzy ◽  
Electre Method ◽  
Deviation Degree ◽  
Interval Valued

A new multi-criteria decision-making method for interval-valued intuitionistic fuzzy number is proposed by the advantage of intuitionistic fuzzy set and ELECTRE method. Firstly, the possibility-degree and deviation-degree of interval number are used to establish the preference relation of interval-valued intuitionistic fuzzy number. Then, we exposit the decision theory and the steps of this method. Finally, a numerical example is given to illustrate the application of the method. The numerical results show that it is feasible and effective.

scholarly journals Some Complex Intuitionistic Uncertain Linguistic Heronian Mean Operators and Their Application in Multiattribute Group Decision Making

2021 ◽  
Vol 2021 ◽  
pp. 1-31
Author(s):  
Harish Garg ◽  
Zeeshan Ali ◽  
Jeonghwan Gwak ◽  
Tahir Mahmood ◽  
Sultan Aljahdali
Keyword(s):  
Decision Making ◽  
Problem Solving ◽  
Group Decision Making ◽  
Fuzzy Set ◽  
Group Decision ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy ◽  
Weighted Arithmetic ◽  
Decision Making Problem ◽  
Heronian Mean

In this paper, a new decision-making algorithm has been presented in the context of a complex intuitionistic uncertain linguistic set (CIULS) environment. CIULS integrates the concept the complex of a intuitionistic fuzzy set (CIFS) and uncertain linguistic set (ULS) to deal with uncertain and imprecise information in a more proactive manner. To investigate the interrelation between the pairs of CIULSs, we combine the concept of the Heronian mean (HM) and the complex intuitionistic uncertain linguistic (CIUL) to describe some new operators, namely, CIUL arithmetic HM (CIULAHM), CIUL weighted arithmetic HM (CIULWAHM), CIUL geometric HM (CIULGHM), and CIUL weighted geometric HM (CIULWGHM). The main advantage of these suggested operators is that they considered the interaction between pairs of objects during the formulation process. Also, a number of distinct brief cases and properties of the operators are analyzed. In addition, based on these operators, we have stated a MAGDM (“multiattribute group decision-making”) problem-solving algorithm. The consistency of the algorithm is illustrated by a computational example that compares the effects of the algorithm with a number of well-known existing methods.

scholarly journals New Ranking Functions for Interval-Valued Intuitionistic Fuzzy Sets and Their Application to Multi-Criteria Decision-Making Problem

2021 ◽  
Vol 21 (1) ◽  
pp. 3-18
Author(s):  
Melda Kokoç ◽  
Süleyman Ersöz
Keyword(s):  
Decision Making ◽  
High Performance ◽  
Intuitionistic Fuzzy Set ◽  
Real Life ◽  
Score Function ◽  
Multi Criteria Decision Making ◽  
Ranking Functions ◽  
Intuitionistic Fuzzy ◽  
Life Problems ◽  
Interval Valued

Abstract Many authors agree that the Interval-Valued Intuitionistic Fuzzy Set (IVIFS) theory generates as realistic as possible evaluation of real-life problems. One of the real-life problems where IVIFSs are often preferred is the Multi-Criteria Decision-Making (MCDM) problem. For this problem, the ranking of values obtained by fuzzing the opinions corresponding to alternatives is an important step, as a failure in ranking may lead to the selection of the wrong alternative. Therefore, the method used for ranking must have high performance. In this article, a new score function SKE and a new accuracy function HKE are developed to overcome the disadvantages of existing ranking functions for IVIFSs. Then, two illustrative examples of MCDM problems are presented to show the application of the proposed functions and to evaluate their effectiveness. Results show that the functions proposed have high performance and they are the eligibility for the MCDM problem.

An improved fuzzy TODIM method based on entropy measure under Intuitionistic Fuzzy Information

2021 ◽  
Vol 23 (05) ◽  
pp. 464-470
Author(s):  
Sunit Kumar ◽  
◽  
Satish Kumar ◽  
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Score Function ◽  
Entropy Measure ◽  
Multi Criteria Decision Making ◽  
Fuzzy Information ◽  
Numerical Example ◽  
Intuitionistic Fuzzy ◽  
Todim Method

Intuitionistic fuzzy set (IFS) is one of the most extensive and important tool to accommodate more uncertainties than existing fuzzy set structures. In the present paper, we describe an improved entropy based on TODIM procedure for handling multi-criteria decision-making (MCDM) under IF setting and also the weight information is partially known. First, we study the basic notions and operating laws of IFSs, also the accuracy and score function of it. The new entropy has been proposed. Secondly, the IF information-based decision-making technique for MCDM is presented. Lastly, a numerical example is given related, to demonstrate that their results are credible and feasible.

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