Differential equation with interval valued fuzzy number and its applications

Mondal, Sankar Prasad

doi:10.1007/s13198-016-0474-7

Cited by 21 publications

(3 citation statements)

References 35 publications

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“…Interval-valued fuzzy numbers play a major role in various domains. Mondal and his colleagues [28][29][30] discussed the application of differential equations for intervalvalued fuzzy numbers in various topics. Bharati et al [31][32][33] developed a TP in an interval-valued intuitionistic fuzzy environment.…”

Section: Fuzzy Intuitionistic Interval-valued Intuitionistic Fuzzy In...mentioning

confidence: 99%

Transportation Problem for Interval-Valued Trapezoidal Intuitionistic Fuzzy Numbers

Rani¹,

Manivannan²

2022

IJFIS

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The aim of the decision-makers in the transportation industry is to maximize profit by minimizing the transportation cost. The transportation structure is the center of economic activity in the business logistics system. However, transportation costs may vary owing to various unpredictable factors. In this study, cost of the transporting unit is considered as an interval-valued trapezoidal intuitionistic fuzzy number to deal with these uncertainties. The transportation problem with interval-valued trapezoidal intuitionistic fuzzy cost is discussed here, and the costs are ordered by score and score expected functions. As a special case, the interval-valued trapezoidal intuitionistic cost is not converted into crisp numbers to solve the transportation problem and derive the initial basic feasible (IBF) solution through interval-valued intuitionistic costs. Furthermore, the optimality of the derived initial basic feasible solution is checked using the modified distribution (MODI) method. The effectiveness and validation of the developed approach were illustrated using numerical examples.

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Section: Fuzzy Intuitionistic Interval-valued Intuitionistic Fuzzy In...mentioning

confidence: 99%

Transportation Problem for Interval-Valued Trapezoidal Intuitionistic Fuzzy Numbers

Rani¹,

Manivannan²

2022

IJFIS

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“…Recently noticeable work in the field of fuzzy and interval programming has been done by many researchers. Mondal (2016) proposed an adaptation of solution for differential equations of the first order where the initial conditions are considered fuzzy. They consider initial conditions of the differential equations as interval numbers of triangular fuzzy number type.…”

Section: Literature Reviewmentioning

confidence: 99%

Bi-level decision making models for advertising allocation problem under fuzzy environment

Muneeb

Adhami

Asim

et al. 2018

Int J Syst Assur Eng Manag

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This paper presents bi-level decision making models for advertising planning problem. Advertising planning process consists of multiple objectives and is generally decentralised involving various hierarchical levels of decision making. Considering the cost and impact related factors, long and short duration ads for a single product are made for telecasting. The models presented in the paper are designed so as to allocate the number of advertisements of each kind to different channels under different time zones of a day with the objectives of maximization of ads impact and minimization of net cost at two different levels. We present two models based on minimum impact value to be achieved by advertisement as a constraint considering that the budget available for advertising is uncertain. We extend and present a solution approach developed for fuzzy bi-level integer decision making model with fuzzy constraints. Finally, we provide a numerical illustration to discuss the applicability of the proposed models.

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“…Similar to generalized fuzzy numbers, these numbers can find a trapezoidal shape. For the sake of brevity, the readers could refer to Mondal (2016) for the operation laws and representations of interval-valued triangular fuzzy numbers.…”

Section: A Brief Introduction To Fuzzy Inference Systemmentioning

confidence: 99%

Assessing Construction Labours’ Safety Level: A Fuzzy McDm Approach

Mohandes

Sadeghi

Mahdiyar

et al. 2020

Journal of Civil Engineering and Management

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Risk decision matrix has widely been favoured by the researchers in the area of construction safety risk assessment. Although it provides the construction safety professionals with the final illustration of the risks magnitude, it suffers from major shortcomings, including inability to considering the importance of probability and severity, impaired analysis resulting from the use of raw numbers for ratings, and the limited range of classifications for assessing the risks. All these shortages give an impaired insight to the concerned parties, deteriorating the involved workers' safety. As such, this paper aims to develop a novel Risk Assessment Model (RAM) through the integration of the Fuzzy Best Worst Method (FBWM) with the Interval-Valued Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (IVFTOPSIS). Based on the application of RAM to a real-life case study, it was observed that the developed RAM contributes to the body of construction safety risk assessment in five unique ways: (1) computing the importance of the two risk parameters (i.e. probability and severity) using fuzzy-reference-based comparisons, (2) obviating the needs for having statistical data, (3) prioritizing the identified risks using the combination of interval-valued triangular fuzzy numbers with TOPSIS, (4) providing the safety analysts with wider ranges of classifications for conducting risk assessment, and (5) providing the safety professionals with appropriate evaluation strategies for controlling the analysed risks. The developed model in the study can be applied to any projects, giving a conclusive plan to the concerned safety professionals for adopting the further prudent mitigation measurements.

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Differential equation with interval valued fuzzy number and its applications

Cited by 21 publications

References 35 publications

Transportation Problem for Interval-Valued Trapezoidal Intuitionistic Fuzzy Numbers

Transportation Problem for Interval-Valued Trapezoidal Intuitionistic Fuzzy Numbers

Bi-level decision making models for advertising allocation problem under fuzzy environment

Assessing Construction Labours’ Safety Level: A Fuzzy McDm Approach

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