scholarly journals A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi–objective linear programming problem

2017 ◽  
Vol 27 (3) ◽  
pp. 563-573 ◽  
Author(s):  
Rajendran Vidhya ◽  
Rajkumar Irene Hepzibah
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Optimization Method ◽  
Arithmetic Operations ◽  
Intuitionistic Fuzzy Numbers ◽  
Multi Objective ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

AbstractIn a real world situation, whenever ambiguity exists in the modeling of intuitionistic fuzzy numbers (IFNs), interval valued intuitionistic fuzzy numbers (IVIFNs) are often used in order to represent a range of IFNs unstable from the most pessimistic evaluation to the most optimistic one. IVIFNs are a construction which helps us to avoid such a prohibitive complexity. This paper is focused on two types of arithmetic operations on interval valued intuitionistic fuzzy numbers (IVIFNs) to solve the interval valued intuitionistic fuzzy multi-objective linear programming problem with pentagonal intuitionistic fuzzy numbers (PIFNs) by assuming differentαandβcut values in a comparative manner. The objective functions involved in the problem are ranked by the ratio ranking method and the problem is solved by the preemptive optimization method. An illustrative example with MATLAB outputs is presented in order to clarify the potential approach.

A new approach to solve fully intuitionistic fuzzy linear programming problem with unrestricted decision variables

2021 ◽  
pp. 1-14
Author(s):  
Manisha Malik ◽  
S. K. Gupta ◽  
I. Ahmad
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Fuzzy Set ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Fuzzy Linear Programming ◽  
Planning Problem ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Decision Variables

In many real-world problems, one may encounter uncertainty in the input data. The fuzzy set theory fits well to handle such situations. However, it is not always possible to determine with full satisfaction the membership and non-membership degrees associated with an element of the fuzzy set. The intuitionistic fuzzy sets play a key role in dealing with the hesitation factor along-with the uncertainity involved in the problem and hence, provides more flexibility in the decision-making process. In this article, we introduce a new ordering on the set of intuitionistic fuzzy numbers and propose a simple approach for solving the fully intuitionistic fuzzy linear programming problems with mixed constraints and unrestricted variables where the parameters and decision variables of the problem are represented by intuitionistic fuzzy numbers. The proposed method converts the problem into a crisp non-linear programming problem and further finds the intuitionistic fuzzy optimal solution to the problem. Some of the key significance of the proposed study are also pointed out along-with the limitations of the existing studies. The approach is illustrated step-by-step with the help of a numerical example and further, a production planning problem is also demonstrated to show the applicability of the study in practical situations. Finally, the efficiency of the proposed algorithm is analyzed with the existing studies based on various computational parameters.

MULTI-OBJECTIVE FULLY FUZZIFIED LINEAR PROGAMMING

2001 ◽  
Vol 09 (05) ◽  
pp. 605-621 ◽  
Author(s):  
JAMES J. BUCKLEY ◽  
THOMAS FEURING ◽  
YOICHI HAYASHI
Keyword(s):  
Linear Programming ◽  
Evolutionary Algorithm ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Fuzzy Numbers ◽  
Solution Procedure ◽  
Fuzzy Linear Programming ◽  
Multi Objective ◽  
Linear Programming Problems ◽  
Single Objective

In this paper we wish to solve multi-objective fully fuzzified linear programming problems which are multi-objective linear programming problems where all the parameters and variables are fuzzy numbers. We change this problem into a single objective fuzzy linear programming problem and then show that our solution procedure can be used to explore the whole undominated set. An evolutionary algorithm is then designed to generate undominated solutions. An example is presented showing our evolutionary algorithm solution.

Interval-Valued Intuitionistic Fuzzy Linear Programming Problem

2020 ◽  
Vol 16 (01) ◽  
pp. 53-71
Author(s):  
S. K. Bharati ◽  
S. R. Singh
Keyword(s):  
Linear Programming ◽  
Fuzzy Sets ◽  
Programming Problem ◽  
Fuzzy Set ◽  
Linear Programming Problem ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Linear Programming ◽  
Oil Refineries ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

In many existing methods of linear programming problem (LPP), precise values of parameters have been used but parameters of LPP are imprecise and ambiguous due to incomplete information. Several approaches and theories have been developed for dealing LPP based on fuzzy set (FS), intuitionistic fuzzy set (IFS) which are characterized by membership degree, membership and non-membership degrees, respectively. It’s interesting to note that single membership and non-membership degrees do not deal properly the state of uncertainty and hesitation. Further, we face a kind of uncertainty occurs a kind of uncertainty. Interval-valued intuitionistic fuzzy sets (IV-IFS) is a perfect key for handling uncertainty and hesitation than FS and IFS. In this paper, we define an interval-valued intuitionistic fuzzy number (IV-IFN) and its expected interval and expected values. We also introduce the concept of interval-valued intuitionistic fuzzy linear programming problem (IV-IFLPP). Further, we find the solutions of IV-IFLPP and compare the obtained optimal solutions with existing methods [D. Dubey and A. Mehra, Linear programming with Triangular Intuitionistic Fuzzy Numbers, in Proc. of the 7th Conf. and of the European Society for Fuzzy Logic and Technology (EUSFLAT-LFA 2011), R. Parvathi and C. Malathi, Intuitionistic fuzzy linear optimization, Notes on Intuitionistic Fuzzy Sets 18 (2012) 48–56]. Proposed technique may be used successfully in various areas in the formulation of our country’s five year plans, these include transportation, food-grain storage, urban development, national, state and district level plans, etc., The Indian Railways may use IV-IFLPP technique for linking different railway zones in more realistic way. Agricultural research institutes may use proposed technique for crop rotation mix of cash crops, food crops and fertilizer mix. Airlines can apply IV-IFLPP in the selection of routes and allocation of aircrafts to different routes. Private and public sector oil refineries may use IV-IFLPP for blending of oil ingredients to produce finished petroleum products.

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