scholarly journals An extension of TOPSIS based on linguistic terms in triangular intuitionistic fuzzy structure

2021 ◽  
pp. 409-424
Author(s):  
Muhammad Saeed ◽  
Asad Mehmood ◽  
Amna Anwar
Keyword(s):  
Euclidean Distance ◽  
Ideal Solution ◽  
Intuitionistic Fuzzy Number ◽  
Linguistic Terms ◽  
Modern Approach ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Triangular Intuitionistic Fuzzy Number ◽  
Negative Ideal Solution ◽  
Fuzzy Framework

Chen [24] introduced the extension of TOPSIS in the fuzzy structure, while this article stretches the modern approach of TOPSIS to the intuitionistic fuzzy framework. Linguistic terms are used in this study to evaluate the weight of each criterion and the rating of alternatives in the context of a triangular intuitionistic fuzzy number. A new intuitionistic fuzzy positive ideal solution (IFPIS) and intuitionistic fuzzy negative ideal solution (IFNIS) are proposed in this model of extended TOPSIS. Euclidean distance is introduced between two triangular intuitionistic fuzzy numbers to calculate separation between each alternative to both (IFPIS) and (IFNIS). The proposed model’s mechanism is presented with the help of an algorithm, and then it is applied to the personal selection problem. Finally, a comparative study is given between this model and other TOPSIS techniques.

Intuitionistic Fuzzy Distance-Based Intuitionistic Fuzzy TOPSIS Method and Application to MADM

2017 ◽  
pp. 72-96
Author(s):  
Jiangxia Nan ◽  
Ting Wang ◽  
Jingjing An
Keyword(s):  
Distance Measure ◽  
Fuzzy Topsis ◽  
Distance Measures ◽  
Ideal Solution ◽  
Intuitionistic Fuzzy Numbers ◽  
Metric Properties ◽  
Fuzzy Distance ◽  
Intuitionistic Fuzzy ◽  
Multi Attribute Decision Making ◽  
Negative Ideal Solution

In this paper, an intuitionistic fuzzy (IF) distance measure between two triangular intuitionistic fuzzy numbers (TIFNs) is developed. The metric properties of the proposed IF distance measures are also studied. Then, based on the IF distance, an extended TOPSIS is developed to solve multi-attribute decision making (MADM) problems with the ratings of alternatives on attributes of TIFNs. In this methodology, the IF distances between each alternative and the TIFN positive ideal-solution are calculated as well as the TIFN negative ideal-solution. Then the relative closeness degrees obtained of each alternative to the TIFN positive ideal solution are TIFNs. Based on the ranking methods of TIFNs the alternatives are ranked. A numerical example is examined to the validity and practicability of the method proposed in this paper.

Intuitionistic Fuzzy Distance Based TOPSIS Method and Application to MADM

2016 ◽  
Vol 5 (1) ◽  
pp. 43-56 ◽  
Author(s):  
Jiangxia Nan ◽  
Ting Wang ◽  
Jingjing An
Keyword(s):  
Distance Measure ◽  
Ideal Solution ◽  
Ranking Methods ◽  
Intuitionistic Fuzzy Numbers ◽  
Metric Properties ◽  
Fuzzy Distance ◽  
Intuitionistic Fuzzy ◽  
Relative Closeness ◽  
Multi Attribute Decision Making ◽  
Negative Ideal Solution

In this paper, an intuitionistic fuzzy (IF) distance measure between two triangular intuitionistic fuzzy numbers (TIFNs) is developed. The metric properties of the proposed IF distance measure are also studied. Then, based on this IF distance, an extended TOPSIS is developed to solve multi-attribute decision making (MADM) problems with the ratings of alternatives on attributes of TIFNs. In this methodology, the IF distances between each alternative and the TIFN positive ideal-solution are calculated as well as the TIFN negative ideal-solution. Then the relative closeness degrees obtained of each alternative to the TIFN positive ideal solution are TIFNs. Based on the ranking methods of TIFNs the alternatives are ranked. A numerical example is examined to the validity and practicability of the method proposed in this paper.

scholarly journals Aggregation Operators on Triangular Intuitionistic Fuzzy Numbers and its Application to Multi-Criteria Decision Making Problems

2014 ◽  
Vol 39 (3) ◽  
pp. 189-208 ◽  
Author(s):  
Changyong Liang ◽  
Shuping Zhao ◽  
Junling Zhang
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Score Function ◽  
Aggregation Operators ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy Number ◽  
New Approach ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Triangular Intuitionistic Fuzzy Number

Abstract The aim of this work is to present some aggregation operators with triangular intuitionistic fuzzy numbers and study their desirable properties. Firstly, the score function and the accuracy function of triangular intuitionistic fuzzy number are given, the method for ranking triangular intuitionistic fuzzy numbers are developed. Then, some geometric aggregation operators for aggregating triangular intuitionistic fuzzy numbers are developed, such as triangular intuitionistic fuzzy weighted geometric (TIFWG) operator, the triangular intuitionistic fuzzy ordered weighted geometric (TIFOWG) operator and the triangular intuitionistic fuzzy hybrid geometric (TIFHG) operator. Moreover, an application of the new approach to multi-criteria decision making method was proposed based on the geometric average operator of TIFNs, and the new ranking method for TIFNs is used to rank the alternatives. Finally, an example analysis is given to verify and demonstrate the practicality and effectiveness of the proposed method.

scholarly journals On statistical convergent sequence spaces of intuitionistic Fuzzy numbers

2018 ◽  
Vol 36 (1) ◽  
pp. 235 ◽  
Author(s):  
Shyamal Debnath ◽  
Vishnu Narayan Mishra ◽  
Jayanta Debnath
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Convergent Sequence ◽  
Sequence Spaces ◽  
Topological Properties ◽  
Intuitionistic Fuzzy Number ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Inclusion Relations ◽  
Bounded Sequences

In the present paper we introduce the classes of sequence stcIFN, stc0IFN and st∞IFN of statistically convergent, statistically null and statistically bounded sequences of intuitionistic fuzzy number based on the newly defined metric on the space of all intuitionistic fuzzy numbers (IFNs). We study some algebraic and topological properties of these spaces and prove some inclusion relations too.

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.

Interval Rough Neutrosophic TOPSIS Strategy for Multi-Attribute Decision Making

2020 ◽  
pp. 98-118
Author(s):  
Rumi Roy ◽  
Surapati Pramanik ◽  
Tapan Kumar Roy
Keyword(s):  
Decision Making ◽  
Euclidean Distance ◽  
Hamming Distance ◽  
Ideal Solution ◽  
Numerical Example ◽  
New Strategy ◽  
Order Preference ◽  
Multi Attribute Decision Making ◽  
Ranking Order ◽  
Negative Ideal Solution

In this chapter, the authors present a new strategy for multi-attribute decision making in interval rough neutrosophic environment. They define Hamming distance and Euclidean distance between interval rough neutrosophic numbers. They also define interval rough neutrosophic relative positive ideal solution (IRNRPIS) and interval rough neutrosophic relative negative ideal solution (IRNRNIS). Then the ranking order of the alternatives is obtained by the technique for order preference by similarity to ideal solution (TOPSIS) strategy. Finally, a numerical example is provided to demonstrate the applicability and effectiveness of the proposed interval rough neutrosophic TOPSIS strategy.

An Improved Fuzzy TOPSIS Method with a New Ranking Index

2021 ◽  
pp. 1-27
Author(s):  
S. A. Sadabadi ◽  
A. Hadi-Vencheh ◽  
A. Jamshidi ◽  
M. Jalali
Keyword(s):  
Real Life ◽  
Similarity Index ◽  
Multiple Criteria Decision Making ◽  
Fuzzy Topsis ◽  
Ideal Solution ◽  
Triangular Fuzzy Numbers ◽  
Linguistic Terms ◽  
Cost Criterion ◽  
Negative Ideal Solution ◽  
Ranking Index

Owing to vague concepts frequently represented in decision data, the crisp values are inadequate to model real-life situations. In this paper, the rating of each alternative and the weight of each criterion is described by linguistic terms which can be expressed in triangular fuzzy numbers. Next, we focus on fuzzy TOPSIS (FTOPSIS) method. We show that, however, the conventional FTOPSIS is interesting, but it suffers from some flaws. The shortcomings of classical FTOPSIS are shown and some solutions are given. Further, a new similarity index is proposed and then is illustrated using numerical examples. By treating the separations of an alternative from the fuzzy positive ideal solution (FPIS) and the fuzzy negative ideal solution (FNIS) as “cost” criterion and “benefit” criterion, respectively, we reduce the original fuzzy multiple criteria decision making (FMCDM) problem to a new one with two criteria. Illustrative examples are given to show the advantages of the proposed approach.

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