Interval-Valued Triangular Neutrosophic Linear Programming Problem

Lower Upper ◽

Key Factor ◽

Interval Valued ◽

In this paper, we have proposed an Interval-valued triangular neutrosophic number (IV-TNN) as a key factor to solve the neutrosophic linear programming problem. In the present neutrosophic linear programming problem IV-TNN is expressed in lower, upper truth membership function, indeterminacy membership function, and falsity membership function. Here, we try the compare our proposed method with existing methods.

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

International Journal of Applied Mathematics and Computer Science ◽

10.1515/amcs-2017-0040 ◽

2017 ◽

Vol 27 (3) ◽

pp. 563-573 ◽

Cited By ~ 3

Author(s):

Rajendran Vidhya ◽

Rajkumar Irene Hepzibah

Keyword(s):

Linear Programming ◽

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.

Neutrosophic Sets in Decision Analysis and Operations Research - Advances in Logistics, Operations, and Management Science ◽

Generalised Single-Valued Neutrosophic Number and Its Application to Neutrosophic Linear Programming

10.4018/978-1-7998-2555-5.ch009 ◽

2020 ◽

pp. 180-214

Author(s):

Nirmal Kumar Mahapatra ◽

Tuhin Bera

Keyword(s):

Linear Programming ◽

Objective Function ◽

Programming Problem ◽

Simplex Method ◽

Real Life ◽

Simplex Algorithm ◽

Real Life Problem ◽

Crisp Linear Programming ◽

In this chapter, the concept of single valued neutrosophic number (SVN-Number) is presented in a generalized way. Using this notion, a crisp linear programming problem (LP-problem) is extended to a neutrosophic linear programming problem (NLP-problem). The coefficients of the objective function of a crisp LP-problem are considered as generalized single valued neutrosophic number (GSVN-Number). This modified form of LP-problem is here called an NLP-problem. An algorithm is developed to solve NLP-problem by simplex method. Finally, this simplex algorithm is applied to a real-life problem. The problem is illustrated and solved numerically.

Neutrosophic number goal programming for multi-objective linear programming problem in neutrosophic number environment

MOJ Current Research & Reviews ◽

10.15406/mojcrr.2018.01.00021 ◽

2018 ◽

Vol 1 (3) ◽

pp. 135-141 ◽

Cited By ~ 2

Author(s):

Surapati Pramanik ◽

Durga Banerjee

Keyword(s):

Linear Programming ◽

Programming Problem ◽

Goal Programming ◽

Multi Objective ◽

Interval-Valued Intuitionistic Fuzzy Linear Programming Problem

New Mathematics and Natural Computation ◽

10.1142/s1793005720500040 ◽

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 ◽

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.

An Approach to Solve the Linear Programming Problem Using Single Valued Trapezoidal Neutrosophic Number

10.54216/ijns.030202 ◽

2020 ◽

pp. 54-66

Author(s):

Tuhin Bera ◽

◽

Nirmal Kumar Mahapatra

Keyword(s):

Linear Programming ◽

Programming Problem ◽

Set Theory ◽

Fuzzy Set ◽

Intuitionistic Fuzzy Set ◽

Neutrosophic Set ◽

Real Field ◽

Trapezoidal Neutrosophic Number ◽

While making a decision, the neutrosophic set theory includes the uncertainty part beside certainty part (i.e., Yes or No). In the present uncertain socio-economic fashion, this pattern is highly acceptable and hence, the limitations of fuzzy set and intuitionistic fuzzy set are overcome with neutrosophic set theory. The present study provides a modified structure of linear programming problem (LP-problem) and its solution approach in neutrosophic sense. A special type of neutrosophic set defined over the set of real number, viz., single valued trapezoidal neutrosophic number (SVTN-number) is adopted here as the coefficients of the objective function, right-hand side coefficients and decision variables itself of an LP-problem. In order to solve such problem, a parameter based ranking function of SVTN-number is newly constructed from the geometrical configuration of the trapezium. It plays a key role in the development of the solution algorithm. An LP-problem is normally solved under the asset of some given constraints. Besides that, there may be some hidden parameters (e.g., awareness level of nearer society for the smooth run of a clinical pharmacy, ruined structure of road to be met a profit from a bus, etc) of an LP-problem and these affect the solution badly when experts ignore them. This study makes an attempt to solve an LP-problem by giving importance to all these to attain a fair outcome. The efficiency of the proposed concept is illustrated in a real field. A real example is stated and is solved numerically under the present view.