A note on “Transportation problem under interval-valued intuitionistic fuzzy environment”

Based on the operational laws on interval-valued intuitionistic fuzzy sets, the generalized Banzhaf interval-valued intuitionistic fuzzy geometric Choquet (GBIVIFGC) operator is proposed, which is also an interval-valued intuitionistic fuzzy value. It is worth pointing out that the GBIVIFGC operator can be seen as an extension of some geometric mean operators. Since the fuzzy measure is defined on the power set, it makes the problem exponentially complex. In order to overall reflect the interaction among elements and reduce the complexity of solving a fuzzy measure, we further introduce the GBIVIFGC operator w.r.t. 2-additive measures. Furthermore, if the information about weights of experts and attributes is incompletely known, the models of obtaining the optimal 2-additive measures on criteria set and expert set are given by using the introduced cross entropy measure and the Banzhaf index. Finally, an approach to pattern recognition and multi-criteria group decision making under interval-valued intuitionistic fuzzy environment is developed, respectively.

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Multi-objective fixed-charge solid transportation problem with product blending under intuitionistic fuzzy environment

Applied Intelligence ◽

10.1007/s10489-019-01466-9 ◽

2019 ◽

Vol 49 (10) ◽

pp. 3524-3538 ◽

Cited By ~ 17

Author(s):

Sankar Kumar Roy ◽

Sudipta Midya

Keyword(s):

Transportation Problem ◽

Fixed Charge ◽

Solid Transportation Problem ◽

Multi Objective ◽

Intuitionistic Fuzzy ◽

Fuzzy Environment ◽

Product Blending

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The Interval-Valued Intuitionistic Fuzzy Optimized Weighted Bonferroni Means and Their Application

Journal of Applied Mathematics ◽

10.1155/2013/981762 ◽

2013 ◽

Vol 2013 ◽

pp. 1-10 ◽

Cited By ~ 4

Author(s):

Ya-ming Shi ◽

Jian-min He

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Group Decision ◽

Practical Case ◽

Basic Properties ◽

Bonferroni Mean ◽

Intuitionistic Fuzzy ◽

Fuzzy Environment ◽

Aggregation Techniques ◽

Interval Valued

We investigate and propose two new Bonferroni means, that is, the optimized weighted BM (OWBM) and the generalized optimized weighted BM (GOWBM), whose characteristics are to reflect the preference and interrelationship of the aggregated arguments and can satisfy the basic properties of the aggregation techniques simultaneously. Further, we propose the interval-valued intuitionistic fuzzy optimized weighted Bonferroni mean (IIFOWBM) and the generalized interval-valued intuitionistic fuzzy optimized weighted Bonferroni mean (GIIFOWBM) and detailed study of their desirable properties such as idempotency, monotonicity, transformation, and boundary. Finally, based on IIFOWBM and GIIFOWBM, we give an approach to group decision making under the interval-valued intuitionistic fuzzy environment and utilize a practical case involving the assessment of a set of agroecological regions in Hubei Province, China, to illustrate the developed methods.

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A Novel Ranking Approach to Solving Fully LR-Intuitionistic Fuzzy Transportation Problems

New Mathematics and Natural Computation ◽

10.1142/s1793005719500066 ◽

2018 ◽

Vol 15 (01) ◽

pp. 95-112 ◽

Cited By ~ 4

Author(s):

Abhishekh ◽

A. K. Nishad

Keyword(s):

Transportation Problem ◽

Fuzzy Numbers ◽

Optimal Solution ◽

Solution Procedure ◽

Ranking Functions ◽

Transportation Problems ◽

Intuitionistic Fuzzy Numbers ◽

Intuitionistic Fuzzy ◽

Fuzzy Environment ◽

Fuzzy Transportation Problem

To the extent of our knowledge, there is no method in fuzzy environment to solving the fully LR-intuitionistic fuzzy transportation problems (LR-IFTPs) in which all the parameters are represented by LR-intuitionistic fuzzy numbers (LR-IFNs). In this paper, a novel ranking function is proposed to finding an optimal solution of fully LR-intuitionistic fuzzy transportation problem by using the distance minimizer of two LR-IFNs. It is shown that the proposed ranking method for LR-intuitionistic fuzzy numbers satisfies the general axioms of ranking functions. Further, we have applied ranking approach to solve an LR-intuitionistic fuzzy transportation problem in which all the parameters (supply, cost and demand) are transformed into LR-intuitionistic fuzzy numbers. The proposed method is illustrated with a numerical example to show the solution procedure and to demonstrate the efficiency of the proposed method by comparison with some existing ranking methods available in the literature.

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