A unified method of defuzzification for type-2 fuzzy numbers with its application to multiobjective decision making

Biswas, Animesh; De, Arnab Kumar

doi:10.1007/s41066-017-0068-z

Cited by 21 publications

(11 citation statements)

References 59 publications

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“…The T2TpFN is defuzzified using the technique discussed by Biswas and De (2018). In their proposed work, the T2TpFN is presented in four T1TpFNs, i.e., the four membership function of a T2TpFN are T1TpFNs that constitutes the FOU of the corresponding T2TpFN.…”

Section: Transportation Problem Under T2tpfnmentioning

confidence: 99%

“…In the Phase 1, the defuzzification technique converts T2TpFN to T1TpFN, and further again (Phase 2) applied to T1TpFNs to obtain the defuzzified value of the T2TpFN. The defuzzification procedure is depicted in Figure 1 Biswas (2018).…”

Section: Transportation Problem Under T2tpfnmentioning

confidence: 99%

“…Definition 1: T1FS (Biswas (2018)) A T1FS λ  has defined on the set of real numbers Y than its membership function ( )…”

Section: Transportation Problem Under T2tpfnmentioning

confidence: 99%

“…Li and Lai (2000) presented a FCP approach to MOTPs at which the synthetic membership degree of the global evaluation for all objectives at maximum. Biswas and De (2018) introduce a process of defuzzification for ranking of T2TpFN in which a two-phase defuzzification method has developed for using PDF of the random variables associates with the fuzzy numbers. FGP technique is used for achieving the highest degree of each of the defined membership goals to the extent possible in the decision-making.…”

Section: Introductionmentioning

confidence: 99%

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Multi-Objective Transportation Problem Under Type-2 Trapezoidal Fuzzy Numbers With Parameters Estimation and Goodness of Fit

et al. 2021

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The problem of transportation in real-life is an uncertain multi-objective decision-making problem. In particular, by taking into account the conflicting objectives, Decision-Makers (DMs) are looking for the best transport set up to determine the optimum shipping quantity subject to certain capacity constraints on each route. This paper presented a Multi-Objective Transportation Problem (MOTP) where the objective functions are considered as Type-2 trapezoidal fuzzy numbers (T2TpFN), respectively. Demand and supply in constraints are in multi-choice and probabilistic random variables, respectively. Also considered the “rate of increment in Transportation Cost (TC) and rate of decrement in profit on transporting the products from ith sources to jth destinations due to” (or additional cost) of each product due to the damage, late deliveries, weather conditions, and any other issues. Due to the presence of all these uncertainties, it is not possible to obtain the optimum solution directly, so first, we need to convert all these uncertainties from the model into a crisp equivalent form. The two-phase defuzzification technique is used to transform T2TpFN into a crisp equivalent form. Multi-choice and probabilistic random variables are transformed into an equivalent value using Stochastic Programming (SP) approach and the binary variable, respectively. It is assumed that the supply and demand parameter follows various types of probabilistic distributions like Weibull, Extreme value, Cauchy and Pareto, Normal distribution, respectively. The unknown parameters of probabilistic distributions estimated using the maximum likelihood estimation method at the defined probability level. The best fit of the probability distributions is determined using the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), respectively. Using the Fuzzy Goal Programming (FGP) method, the final problem is solved for the optimal decision. A case study is intended to provide the effectiveness of the proposed work.

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Section: Transportation Problem Under T2tpfnmentioning

confidence: 99%

Section: Transportation Problem Under T2tpfnmentioning

confidence: 99%

“…Definition 1: T1FS (Biswas (2018)) A T1FS λ  has defined on the set of real numbers Y than its membership function ( )…”

Section: Transportation Problem Under T2tpfnmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multi-Objective Transportation Problem Under Type-2 Trapezoidal Fuzzy Numbers With Parameters Estimation and Goodness of Fit

et al. 2021

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“…[2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] However, some parts of hesitance phenomena deserve further study because hesitance is a very significant human behavior but is subtle, complex, abstruse, and paradoxical. Actually, hesitance can also be regarded as a type of uncertainty phenomenon, [21][22][23][24] and one may recall from Atanassov's intuitionistic fuzzy set theory [25][26][27] that the uncertainty, from a special aspect, is embodied by a closed interval [a, b] of [0, 1] with b a π − = representing the uncertainty or hesitance degree.…”

Section: Introductionmentioning

confidence: 99%

Eliciting and measuring hesitance in decision‐making

Jin

2019

Int J Intell Syst

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Hesitance is an innate human psychological phenomenon pervasive in our daily life. Although it is very complex and still not fully understood, there have been many studies related to this interesting topic. In this study, we proposed two fundamental problems about hesitance: the first is the generating problem, which is related to how to elicit hesitance information from human thinking; the second is the measuring problem, which is related to how to devise effective and reasonable methods to measure hesitance degrees from given hesitance information. With these two fundamental questions, we first discussed and analyzed several examples in real life involving hesitance, showing that it can indeed be recorded and represented. Then we roughly classified the hesitance information into two major classes: static hesitance and dynamic hesitance. Some simple and interesting methods were proposed to elicit hesitance, and more reasonable methods were proposed to measure the hesitance degree from the two classes of hesitance information. All methods that have been discussed in this study try to avoid complexity in every aspect while reserving strictness and reasonability; therefore, the present study provides suitable information for practitioners with different backgrounds.

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Intuitionistic Type-II Fuzzy Logic-Based Inference System and Its Realistic Applications to the Medical Field

Sharma

Dhiman²

2023

Studies in Fuzziness and Soft Computing

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A unified method of defuzzification for type-2 fuzzy numbers with its application to multiobjective decision making

Cited by 21 publications

References 59 publications

Multi-Objective Transportation Problem Under Type-2 Trapezoidal Fuzzy Numbers With Parameters Estimation and Goodness of Fit

Multi-Objective Transportation Problem Under Type-2 Trapezoidal Fuzzy Numbers With Parameters Estimation and Goodness of Fit

Eliciting and measuring hesitance in decision‐making

Intuitionistic Type-II Fuzzy Logic-Based Inference System and Its Realistic Applications to the Medical Field

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