scholarly journals Ranking Fuzzy Numbers with a Distance Method using Circumcenter of Centroids and an Index of Modality

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
P. Phani Bushan Rao ◽  
N. Ravi Shankar
Keyword(s):  
Decision Making ◽  
Decision Maker ◽  
Satisfactory Result ◽  
Fuzzy Numbers ◽  
New Method ◽  
Triangular Fuzzy Numbers ◽  
Distance Method ◽  
Fuzzy Environment ◽  
Index Of Optimism

Ranking fuzzy numbers are an important aspect of decision making in a fuzzy environment. Since their inception in 1965, many authors have proposed different methods for ranking fuzzy numbers. However, there is no method which gives a satisfactory result to all situations. Most of the methods proposed so far are nondiscriminating and counterintuitive. This paper proposes a new method for ranking fuzzy numbers based on the Circumcenter of Centroids and uses an index of optimism to reflect the decision maker's optimistic attitude and also an index of modality that represents the neutrality of the decision maker. This method ranks various types of fuzzy numbers which include normal, generalized trapezoidal, and triangular fuzzy numbers along with crisp numbers with the particularity that crisp numbers are to be considered particular cases of fuzzy numbers.

scholarly journals Inventory Model with Demand Dependant on Unit Cost- Input Parameters as Triangular Fuzzy Numbers

2021 ◽  
Vol 12 (2) ◽  
Author(s):  
R. Kasthuri, Et. al.
Keyword(s):  
Fuzzy Numbers ◽  
Unit Cost ◽  
Inventory Model ◽  
Average Total Cost ◽  
Triangular Fuzzy Numbers ◽  
Lot Size ◽  
Distance Method ◽  
Total Cost ◽  
Signed Distance ◽  
Fuzzy Environment

This paper considers an inventory model in which the shortages are backlogged and the demand is dependent on unit cost. An optimum value for average total cost is calculated by considering various input costs, lot size and maximum inventory under fuzzy environment. The process of defuzzification is done by using the signed distance method. Numerical example and sensitivity analysis is given for calculating both crisp and fuzzy values of the total cost.

A NEW METHOD FOR RANKING TRIANGULAR FUZZY NUMBERS

2012 ◽  
Vol 20 (05) ◽  
pp. 729-740 ◽  
Author(s):  
EMRAH AKYAR ◽  
HANDAN AKYAR ◽  
SERKAN ALİ DÜZCE
Keyword(s):  
Decision Making ◽  
Risk Analysis ◽  
Fuzzy Numbers ◽  
New Method ◽  
Triangular Fuzzy Numbers ◽  
Application Systems ◽  
Systems Control

The ranking and comparing of fuzzy numbers have important practical uses, such as in risk analysis problems, decision-making, optimization, forecasting, socioeconomic systems, control and certain other fuzzy application systems. Several methods for ranking fuzzy numbers have been widely-discussed though most of them have shortcomings. In this paper, we present a new method for ranking triangular fuzzy numbers based on their incenter and inradius. The proposed method is much simpler and more efficient than other methods in the literature. Some comparative examples are also given to illustrate the advantages of the proposed method.

scholarly journals Multi-Criteria Decision-Making for Airport Operation Performance Using Triangular Fuzzy Numbers

2019 ◽  
Vol 3 (3) ◽  
pp. 01-15
Author(s):  
Adeel Ahmad ◽  
Sana Akram ◽  
Muhammad Farhan Tabassum ◽  
Alia Kausar ◽  
Nousheen Ilyas
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Decision Makers ◽  
Multi Criteria Decision Making ◽  
Triangular Fuzzy Numbers ◽  
Operation Performance ◽  
Linguistic Form ◽  
Fuzzy Environment ◽  
Simple Additive Weighting

This paper advocates Multi-Criteria Decision-Making (MCDM) which evaluates the operation performance of airports using Fuzzy Simple Additive Weighting (FSAW) method. Assigned weights by decision- makers were in a linguistic form. These linguistic forms were converted into triangular fuzzy numbers. We chose three airports designated as A1, A2 and A3 and examined by four decision makers D1, D2, D3 and D4 under a fuzzy environment for performance against the chosen criteria. FSAW method gives similar decision results which shows that this method is effective, relevant and reliable for this kind of MCDM.

scholarly journals Inventory Model with Demand Dependant on Unit Cost- Input Parameters as Triangular Fuzzy Numbers

2021 ◽  
Vol 12 (2) ◽  
Author(s):  
R. Kasthuria
Keyword(s):  
Fuzzy Numbers ◽  
Unit Cost ◽  
Inventory Model ◽  
Average Total Cost ◽  
Triangular Fuzzy Numbers ◽  
Lot Size ◽  
Distance Method ◽  
Total Cost ◽  
Signed Distance ◽  
Fuzzy Environment

This paper considers an inventory model in which the shortages are backlogged and the demand is dependent on unit cost. An optimum value for average total cost is calculated by considering various input costs, lot size and maximum inventory under fuzzy environment. The process of defuzzification is done by using the signed distance method. Numerical example and sensitivity analysis is given for calculating both crisp and fuzzy values of the total cost.

scholarly journals AN EXTENSION OF THE RATIO SYSTEM APPROACH OF MOORA METHOD FOR GROUP DECISION-MAKING BASED ON INTERVAL-VALUED TRIANGULAR FUZZY NUMBERS

2015 ◽  
Vol 22 (1) ◽  
pp. 122-141 ◽  
Author(s):  
Dragisa STANUJKIC
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
System Approach ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Weighted Averaging ◽  
Performance Ratings ◽  
Triangular Fuzzy Numbers ◽  
Moora Method ◽  
Interval Valued

Decision-making in fuzzy environment is often a very complex, especially when related to predictions and assessments. The Ratio system approach of the MOORA method and Intervalvalued fuzzy numbers have already proved themselves as the effective tools for solving complex decision-making problems. Therefore, in this paper an extension of the Ratio system approach of the MOORA method, which allows a group decision-making as well as the use of interval-valued triangular fuzzy numbers, is proposed. Interval-fuzzy numbers are rather complex, and therefore, they are not practical for direct assigning performance ratings. For this reason, in this paper it has also been suggested the approach which allows the expression of individual performance ratings using crisp, interval or fuzzy numbers, and their further transformation into the group performance ratings, expressed in the form of interval-valued triangular fuzzy numbers, which provide greater flexibility and reality compared to the use of linguistic variables. Finally, in this paper the weighted averaging operator was proposed for defuzzification of interval-valued triangular fuzzy numbers.

scholarly journals TODIM Method for Multiple Attribute Group Decision Making under 2-Tuple Linguistic Neutrosophic Environment

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 486 ◽  
Author(s):  
Jie Wang ◽  
Guiwu Wei ◽  
Mao Lu
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
New Method ◽  
Calculating Method ◽  
Fuzzy Environment ◽  
Operational Laws ◽  
Multiple Attribute ◽  
Todim Method ◽  
Magdm Problems

In this article, we extend the original TODIM (Portuguese acronym for Interactive Multi-Criteria Decision Making) method to the 2-tuple linguistic neutrosophic fuzzy environment to propose the 2TLNNs TODIM method. In the extended method, we use 2-tuple linguistic neutrosophic numbers (2TLNNs) to present the criteria values in multiple attribute group decision making (MAGDM) problems. Firstly, we briefly introduce the definition, operational laws, some aggregation operators and the distance calculating method of 2TLNNs. Then, the calculation steps of the original TODIM model are presented in simplified form. Thereafter, we extend the original TODIM model to the 2TLNNs environment to build the 2TLNNs TODIM model, our proposed method, which is more reasonable and scientific in considering the subjectivity of DM’s behaviors and the dominance of each alternative over others. Finally, a numerical example for the safety assessment of a construction project is proposed to illustrate the new method, and some comparisons are also conducted to further illustrate the advantages of the new method.

New Einstein Hybrid Aggregation Operators for Intuitionistic Fuzzy Sets and Applications in Multi-Criteria Decision-Making

2019 ◽  
pp. 252-283
Author(s):  
Bhagawati Prasad Joshi ◽  
Abhay Kumar
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Decision Maker ◽  
Intuitionistic Fuzzy Sets ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
Multi Criteria Decision Making ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Decision Making Processes

The fusion of multidimensional intuitionistic fuzzy information plays an important part in decision making processes under an intuitionistic fuzzy environment. In this chapter, it is observed that existing intuitionistic fuzzy Einstein hybrid aggregation operators do not follow the idempotency and boundedness. This leads to sometimes illogical and even absurd results to the decision maker. Hence, some new intuitionistic fuzzy Einstein hybrid aggregation operators such as the new intuitionistic fuzzy Einstein hybrid weighted averaging (IFEHWA) and the new intuitionistic fuzzy Einstein hybrid weighted geometric (IFEHWG) were developed. The new IFEHWA and IFEHWG operators can weigh the arguments as well as their ordered positions the same as the intuitionistic fuzzy Einstein hybrid aggregation operators do. Further, it is validated that the defined operators are idempotent, bounded, monotonic and commutative. Then, based on the developed approach, a multi-criteria decision-making (MCDM) procedure is given. Finally, a numerical example is conducted to demonstrate the proposed method effectively.

Fuzzification of EOQ Model Under the Condition of Permissible Delay in Payments

2012 ◽  
Vol 3 (2) ◽  
pp. 1-19 ◽  
Author(s):  
Chandra K. Jaggi ◽  
Anuj Sharma ◽  
Reena Jain
Keyword(s):  
Fuzzy Numbers ◽  
Delay Period ◽  
Order Quantity ◽  
Distance Method ◽  
Permissible Delay In Payments ◽  
Signed Distance ◽  
Eoq Model ◽  
Fuzzy Environment ◽  
Delay In Payments ◽  
The Cost

This paper formulates an economic order quantity inventory model under the condition of permissible delay in payments in fuzzy environment. All the parameters of the model, excluding permissible delay period and cycle length, are taken to be trapezoidal Fuzzy numbers. The arithmetic operations are defined under the function principle. The cost function has been defuzzified using signed distance method and thereby solved to obtain the optimal replenishment period. The numerical example is presented to show the validity of the model followed by sensitivity analysis.

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