Credibility Measure for Intuitionistic Fuzzy Variables

Comparison of fuzzy variables is considered one of the most important topics in fuzzy theory. A new approach for ranking fuzzy variable via credibility measure — fuzzy dominance is presented in this paper. Some basic properties of fuzzy dominance are investigated. As an illustration, the cases of fuzzy dominance rule for triangular fuzzy variables are examined.

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Handling Optimization Under Uncertainty Using Intuitionistic Fuzzy-Logic-Based Expected Value Model

Handbook of Research on Emergent Applications of Optimization Algorithms - Advances in Business Information Systems and Analytics ◽

10.4018/978-1-5225-2990-3.ch032 ◽

2018 ◽

pp. 750-776 ◽

Cited By ~ 1

Author(s):

Nagajyothi Virivinti ◽

Kishalay Mitra

Keyword(s):

Real Life ◽

Expected Value ◽

Optimization Under Uncertainty ◽

Uncertain Parameters ◽

Fuel Price ◽

Deterministic Optimization ◽

Fuzzy Variables ◽

Intuitionistic Fuzzy ◽

Expected Value Model ◽

Value Model

Uncertainty in parameters during deterministic optimization studies can have large impact on the outcome of the optimization result. It is pragmatic that these parameters are uncertain as they have direct link with real life scenarios, e.g. fuel price appearing as a parameter in objective function or constraints. However, their variability is ignored while solving the problem in a deterministic optimization framework. While mitigating the above mentioned scenario, it is, therefore, necessary to investigate the development of uncertainty handling techniques for a realistic optimization problem. In this work, we propose intuitionistic fuzzy expected value model (IFEVM), which assumes uncertain parameters as intuitionistic fuzzy variables and derives the solution out of an equivalent transformed deterministic formulation while defining the expected values of the objective functions and constraints. Intuitionistic fuzzy parameters can be regarded as a superset of the conventional fuzzy set where the aspect of non-determinacy of a fuzzy member to a set is additionally taken into account. The proposed IFEVM technique has been applied on two examples: first, with the Binh-korn's multi-objective test function where uncertain parameters are linearly related and next with a real life case study of industrial grinding operation having multiple numbers of non-linearly related uncertain parameters. The technique has been further applied to these case studies considering three different levels of risk scenarios e.g. optimistic, pessimistic and intermediate approaches. The IFEVM technique is fairly generic and advantageous, can be applied to any kind of system for handling uncertainty in parameters.

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Fixed Charged Solid Transportation Problem With Budget Constraints in Type-2 Fuzzy Variables

Soft Computing Techniques and Applications in Mechanical Engineering - Advances in Mechatronics and Mechanical Engineering ◽

10.4018/978-1-5225-3035-0.ch002 ◽

2018 ◽

pp. 35-71 ◽

Cited By ~ 1

Author(s):

Dhiman Dutta ◽

Mausumi Sen

Keyword(s):

Programming Model ◽

Credibility Measure ◽

Chance Constrained Programming ◽

Budget Constraints ◽

Fuzzy Variables ◽

Gradient Technique ◽

Objective Function Values ◽

Generalized Reduced Gradient ◽

Constrained Programming

A multi-objective fixed charged solid transportation model with criterion e.g. transportation penalty, amounts, demands, carriages and budget constraints as type-2 triangular fuzzy variables with condition on few components and carriages is proposed here. With the critical value based reductions of corresponding type-2 fuzzy variables, a nearest interval approximation model and a chance constrained programming model applying generalized credibility measure for the constraints is proposed for this particular problem. The credibility measure is also applied to the objective functions of the chance constrained programming model. The model is then transformed into the corresponding crisp deterministic form by these two methods. A numerical example is provided to explain the model with hypothetical data and is then worked out by applying a gradient based optimization - Generalized Reduced Gradient technique (applying LINGO 16). The corresponding objective function values are compared numerically by two approaches after transforming it to crisp form by these two methods.

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