A novel method to rank fuzzy numbers using the developed golden rule representative value

Considering the characteristics such as fuzziness and greyness in real decision-making, the interval grey triangular fuzzy number is easy to express fuzzy and grey information simultaneously. And the partition Bonferroni mean (PBM) operator has the ability to calculate the interrelationship among the attributes. In this study, we combine the PBM operator into the interval grey triangular fuzzy numbers to increase the applicable scope of PBM operators. First of all, we introduced the definition, properties, expectation, and distance of the interval grey triangular fuzzy numbers, and then we proposed the interval grey triangular fuzzy numbers partitioned Bonferroni mean (IGTFPBM) and the interval grey triangular fuzzy numbers weighted partitioned Bonferroni mean (IGTFWPBM), the adjusting of parameters in the operator can bring symmetry effect to the evaluation results. After that, a novel method based on IGTFWPBM is developed for solving the grey fuzzy multiple attribute group decision-making (GFMAGDM) problems. Finally, we give an example to expound the practicability and superiority of this method.

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A novel method for ranking fuzzy numbers based on the different areas fuzzy number

International Journal of Mathematics in Operational Research ◽

10.1504/ijmor.2017.087745 ◽

2017 ◽

Vol 11 (4) ◽

pp. 544 ◽

Cited By ~ 1

Author(s):

Nasser Shahsavari pour ◽

Azim Heydari ◽

Mojtaba Kazemi ◽

Mehdi Karami

Keyword(s):

Fuzzy Number ◽

Fuzzy Numbers ◽

Novel Method

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A New Method for Defuzzification and Ranking of Fuzzy Numbers Based on the Statistical Beta Distribution

Advances in Fuzzy Systems ◽

10.1155/2016/6945184 ◽

2016 ◽

Vol 2016 ◽

pp. 1-8 ◽

Cited By ~ 8

Author(s):

A. Rahmani ◽

F. Hosseinzadeh Lotfi ◽

M. Rostamy-Malkhalifeh ◽

T. Allahviranloo

Keyword(s):

Beta Distribution ◽

Granular Computing ◽

Fuzzy Numbers ◽

Mean Value ◽

Human Reasoning ◽

Fuzzy Information ◽

Numerical Examples ◽

Novel Method ◽

The Mean ◽

Ranking Of Fuzzy Numbers

Granular computing is an emerging computing theory and paradigm that deals with the processing of information granules, which are defined as a number of information entities grouped together due to their similarity, physical adjacency, or indistinguishability. In most aspects of human reasoning, these granules have an uncertain formation, so the concept of granularity of fuzzy information could be of special interest for the applications where fuzzy sets must be converted to crisp sets to avoid uncertainty. This paper proposes a novel method of defuzzification based on the mean value of statistical Beta distribution and an algorithm for ranking fuzzy numbers based on the crisp number ranking system on R. The proposed method is quite easy to use, but the main reason for following this approach is the equality of left spread, right spread, and mode of Beta distribution with their corresponding values in fuzzy numbers within(0,1)interval, in addition to the fact that the resulting method can satisfy all reasonable properties of fuzzy quantity ordering defined by Wang et al. The algorithm is illustrated through several numerical examples and it is then compared with some of the other methods provided by literature.

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A novel method of ranking intuitionistic fuzzy numbers using value and $$\theta $$ multiple of ambiguity at flexibility parameters

Soft Computing ◽

10.1007/s00500-021-06102-8 ◽

2021 ◽

Author(s):

Rituparna Chutia

Keyword(s):

Fuzzy Numbers ◽

Intuitionistic Fuzzy Numbers ◽

Intuitionistic Fuzzy ◽

Novel Method ◽

Flexibility Parameters

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A new multi-criteria decision-making method utilizing power heronian operators with picture hesitant fuzzy information

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-211569 ◽

2021 ◽

pp. 1-22

Author(s):

Baolin Li ◽

Lihua Yang ◽

Jie Qian

Keyword(s):

Decision Making ◽

Fuzzy Sets ◽

Fuzzy Numbers ◽

Distance Measure ◽

Multi Criteria Decision Making ◽

Comparison Analysis ◽

Fuzzy Information ◽

Hesitant Fuzzy Sets ◽

Novel Method ◽

Picture Fuzzy Sets

In practice, picture hesitant fuzzy sets (PHFSs) combining the picture fuzzy sets (PFSs) and hesitant fuzzy sets (HFSs) are suitable to represent more complex multi-criteria decision-making (MCDM) information. The power heronian (PH) operators, which have the merits of power average (PA) and heronian mean (HM) operators, are extended to the environment of PHFSs in this article. First, some algebraic operations of picture hesitant fuzzy numbers (PHFNs), comparative functions and distance measure are introduced. Second, two novel operators, called as picture hesitant fuzzy weighted power heronian (PHFWPH) operator and picture hesitant fuzzy weighted geometric power heronian (PHFWGPH) operator, are defined. Meanwhile, some desirable characteristics and special instances of two operators are investigated as well. Third, a novel MCDM approach applying the proposed PH operators to handle PHFNs is explored. Lastly, to indicate the effectiveness of this novel method, an example regarding MCDM problem is conducted, as well as sensitivity and comparison analysis.

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An Advanced Arithmetic Approach to GTIFNs and Its Application in Medical Analysis

New Mathematics and Natural Computation ◽

10.1142/s179300572150006x ◽

2020 ◽

pp. 1-39

Author(s):

Palash Dutta

Keyword(s):

Fuzzy Set ◽

Fuzzy Numbers ◽

Arithmetic Operation ◽

Intuitionistic Fuzzy Set ◽

Intuitionistic Fuzzy Numbers ◽

Intuitionistic Fuzzy ◽

Novel Method ◽

Set Up ◽

Decomposition Theorems ◽

Medical Analysis

Intuitionistic fuzzy set (IFS) is the straight simplification of fuzzy set theory (FST). Nevertheless, estimation of the arithmetic operation on generalized intuitionistic fuzzy number (GIFNs) is a critical apprehension. This paper presents an attempt to set up a novel method for effectively resolving the drawbacks of conform arithmetic operations on generalized triangular intuitionistic fuzzy numbers (GTIFNs). For this purpose, decomposition theorems for generalized trapezoidal intuitionistic fuzzy numbers (GTrFNs) are studied. Numerical examples are illustrated herewith. Finally, to validate the requirement of a novel elucidation, an application in medical analysis has been carried out under this setting.

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