scholarly journals Some Interval-Valued Intuitionistic Fuzzy Dombi Hamy Mean Operators and Their Application for Evaluating the Elderly Tourism Service Quality in Tourism Destination

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 294 ◽  
Author(s):  
Liangping Wu ◽  
Guiwu Wei ◽  
Hui Gao ◽  
Yu Wei
Keyword(s):  
Service Quality ◽  
Fuzzy Numbers ◽  
The Elderly ◽  
Tourism Destination ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Operator Interval ◽  
Tourism Service ◽  
Dombi Operations ◽  
Interval Valued

In this paper, we expand the Hamy mean (HM) operator and Dombi operations with interval-valued intuitionistic fuzzy numbers (IVIFNs) to propose the interval-valued intuitionistic fuzzy Dombi Hamy mean (IVIFDHM) operator, interval-valued intuitionistic fuzzy weighted Dombi Hamy mean (IVIFWDHM) operator, interval-valued intuitionistic fuzzy dual Dombi Hamy mean (IVIFDDHM) operator, and interval-valued intuitionistic fuzzy weighted dual Dombi Hamy mean (IVIFWDDHM) operator. Then the MADM models are designed with IVIFWDHM and IVIFWDDHM operators. Finally, we gave an example for evaluating the elderly tourism service quality in tourism destination to show the proposed models.

Interval-valued intuitionistic fuzzy multiple attribute decision making and their applications

2021 ◽  
Vol 25 (2) ◽  
pp. 251-277
Author(s):  
Hong-Jun Wang
Keyword(s):  
Supplier Selection ◽  
Fuzzy Numbers ◽  
Multiple Attribute Decision Making ◽  
Green Supply Chain Management ◽  
Green Supply Chain ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Operator Interval ◽  
Multiple Attribute ◽  
Interval Valued

In this paper, we expand the Muirhead mean (MM) operator and dual Muirhead mean (DMM) operator with interval-valued intuitionistic fuzzy numbers (IVIFNs) to propose the interval -valued intuitionistic fuzzy Muirhead mean (IVIFMM) operator, interval-valued intuitionistic fuzzy weighted Muirhead mean (IVIFWMM) operator, interval-valued intuitionistic fuzzy dual Muirhead mean (IVIFDMM) operator and interval-valued intuitionistic fuzzy weighted dual Muirhead mean (IVIFWDMM) operator. Then the MADM methods are proposed with these operators. In the end, we utilize an applicable example for green supplier selection in green supply chain management to prove the proposed methods.

scholarly journals A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi–objective linear programming problem

2017 ◽  
Vol 27 (3) ◽  
pp. 563-573 ◽  
Author(s):  
Rajendran Vidhya ◽  
Rajkumar Irene Hepzibah
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimization Method ◽  
Arithmetic Operations ◽  
Intuitionistic Fuzzy Numbers ◽  
Multi Objective ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

AbstractIn a real world situation, whenever ambiguity exists in the modeling of intuitionistic fuzzy numbers (IFNs), interval valued intuitionistic fuzzy numbers (IVIFNs) are often used in order to represent a range of IFNs unstable from the most pessimistic evaluation to the most optimistic one. IVIFNs are a construction which helps us to avoid such a prohibitive complexity. This paper is focused on two types of arithmetic operations on interval valued intuitionistic fuzzy numbers (IVIFNs) to solve the interval valued intuitionistic fuzzy multi-objective linear programming problem with pentagonal intuitionistic fuzzy numbers (PIFNs) by assuming differentαandβcut values in a comparative manner. The objective functions involved in the problem are ranked by the ratio ranking method and the problem is solved by the preemptive optimization method. An illustrative example with MATLAB outputs is presented in order to clarify the potential approach.

scholarly journals A Heterogeneous MCDM Framework for Sustainable Supplier Evaluation and Selection Based on the IVIF-TODIM Method

2019 ◽  
Vol 11 (18) ◽  
pp. 5057 ◽  
Author(s):  
Ren-Jie Mao ◽  
Jian-Xin You ◽  
Chun-Yan Duan ◽  
Lu-Ning Shao
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Third Party ◽  
Multi Criteria Decision Making ◽  
Interval Numbers ◽  
Intuitionistic Fuzzy Numbers ◽  
Sustainability Performance ◽  
Intuitionistic Fuzzy ◽  
Relative Closeness ◽  
Interval Valued

The third-party platform named ECO system is used by many transnational companies to monitor the sustainability performance of their global suppliers because of its easiness and shareability. Nonetheless, methods used in this platform for evaluating and calculating the sustainability performance of the alternative suppliers are criticized for their lack of accuracy. In response to these problems, this paper presents a heterogeneous multi-criteria decision-making (MCDM) method based on interval-valued intuitionistic fuzzy--an acronym in Portuguese for interactive multi-criteria decision making (IVIF--TODIM) to improve the efficiency of the evaluation model. Considering the varying features of evaluation criteria, i.e., either quantitative or qualitative, the evaluation values under different criteria are expressed in their appropriate information types. In this paper, a general method based on the relative closeness to the technique for order preference by similarity to ideal solution (TOPSIS) method is applied for aggregating the heterogeneous assessment information, including crisp numbers, interval numbers, and triangular fuzzy numbers (TFNs), into interval-valued intuitionistic fuzzy numbers (IVIFNs). Then, the TODIM (an acronym in Portuguese for interactive multi-criteria decision making) is extended and employed to prioritize the alternative suppliers. Finally, the applicability and effectiveness of the proposed method is verified by a practical example of polymer manufacturing company and a comparison analysis with existing methods.

PROJECTION MODELS FOR INTUITIONISTIC FUZZY MULTIPLE ATTRIBUTE DECISION MAKING

2010 ◽  
Vol 09 (02) ◽  
pp. 267-280 ◽  
Author(s):  
ZESHUI XU ◽  
HUI HU
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Ideal Point ◽  
Multiple Attribute Decision Making ◽  
Included Angle ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Fuzzy Ideal ◽  
Interval Valued

The aim of this paper is to investigate the intuitionistic fuzzy multiple attribute decision-making problems where the attribute values are expressed in intuitionistic fuzzy numbers or interval-valued intuitionistic fuzzy numbers. We introduce some notions, such as intuitionistic fuzzy ideal point, interval-valued intuitionistic fuzzy ideal point, the modules of intuitionistic fuzzy numbers, and interval-valued intuitionistic fuzzy numbers. We also introduce the cosine of the included angle between the attribute value vectors of each alternative and the intuitionistic fuzzy ideal point, and the cosine of the included angle between the attribute value vectors of each alternative and the interval-valued intuitionistic fuzzy ideal point. Then we establish two projection models to measure the similarity degrees between each alternative and the intuitionistic fuzzy ideal point, and between each alternative and the interval-valued intuitionistic fuzzy ideal point. Based on the projection models, we can rank the given alternatives and then select the most desirable one. Finally, we illustrate the developed projection models with a numerical example.

A New Interval-Valued Intuitionistic Fuzzy Numbers: Ranking Methodology and Application

2018 ◽  
Vol 14 (03) ◽  
pp. 363-381 ◽  
Author(s):  
S. K. Bharati ◽  
S. R. Singh
Keyword(s):  
Fuzzy Numbers ◽  
Optimal Solutions ◽  
Intuitionistic Fuzzy Number ◽  
Ranking Methods ◽  
Intuitionistic Fuzzy Numbers ◽  
Industrial Management ◽  
Intuitionistic Fuzzy ◽  
Interval Valued ◽  
Better Than ◽  
Real World Problems

Ranking of interval-valued intuitionistic fuzzy (IVIF) numbers is a most popular and elegant work in the area of decision-making of several real-world problems. Some limited methods have been presented concerning the ranking of IVIF sets in literature. In the present paper, we generalize the intuitionistic fuzzy (IF) number to interval-valued intuitionistic fuzzy number by defining interval membership and nonmembership functions instead of fixed-valued function and hence it will present uncertain situation better than IF numbers. It may also be applied in data analysis, industrial management, artificial intelligence, forecasting, time series and so on. In this paper, ranking methodology of IVIF numbers is presented, for this first we define the value and ambiguity of IVIF numbers. Proposed ranking method also is compared with existing ranking methods. Further, IVIF numbers are used to capture fuzziness and hesitation in transportation problem (TP), and we propose a new method to find optimal solutions of TP with IVIF number parameters and finally, a numerical example is given to demonstrate the proposed method.

scholarly journals Foundation of Interval-Valued Intuitionistic Fuzzy Limit and Differential Theory and an Application to Continuous Data

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Zhenghai Ai ◽  
Xiaoqin Shu ◽  
Zeshui Xu
Keyword(s):  
Fuzzy Numbers ◽  
Primary Task ◽  
Continuous Data ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Operational Laws ◽  
Fuzzy Calculus ◽  
Interval Valued

The intuitionistic fuzzy calculus (IFC), based on the basic operational laws of intuitionistic fuzzy numbers (IFNs), has been put forward. However, the interval-valued IFC (IVIFC), based on the basic operational laws of interval-valued IFNs (IVIFNs), is only in the original stage. To further develop the theory of the IVIFC and make it be rigorous, the primary task is to systematically investigate the characteristics of the limits and differentials, which is a foundation of the IVIFC. Moreover, there is quite a lot of literature on IVIFNs; however, the scholars did not reveal the relationships between IFNs and the IVIFNs. To do that, we first investigate the limit of interval-valued intuitionistic fuzzy sequences, and then, we focus on investigating the limit, the continuity, and the differential of IVIFFs in detail and reveal their relationships. After that, due to the fact that the IFC and the IVIFC are based on the basic operational laws of IFNs and IVIFNs, respectively, we reveal the relationships between the IFNs and the IVIFNs via some homomorphic mappings. Finally, a case study about continuous data of IVIFNs is provided to illustrate the advantages of continuous data.

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