[Pramaniik et al., 3(7)): July, 2016]]ISSN 2349‐4 4506
Imp pact Factor: 2 2.545
Global JJournal of f EngineeringScience and RessearchManagement a t G PROGRAMMIN NG NEUTROSOPHIC LINEAR GOAL Surapati Pramanik* *Departm ment of Mathematics, Nanndalal Ghoshh B.T. Colleg ge, Panpur, P.O.-Narayanp P pur, District – North 24 Parganas, P Pinn code-743126, West Benggal, India DOI: KEYWOR RDS:Goal prrogramming, fuzzy goal programming, p intuitionisticc fuzzy goall programminng, neutrosophhic goal prograamming, neutroosophic set, sinngle valued neu utrosophic set.
ACT ABSTRA This paperr proposes the framework f of neutrosophic linear l goal prog gramming (NG GP) approach for f solving muulti objective optimization o prroblems involvving uncertaintty and indeterm minacy. In the pproposed apprroach, the degrree of membeership (acceptaance), indeterrminacy and falsity (rejectiion) of the oobjectives are simultaneoussly consideredd. Three neutroosophic linear goal program mming models have been prooposed. The drrawbacks of thhe existing neeutrosophic opptimization models have beenn addressed annd new directioon of research in neutrosophhic optimizatio on problem haas been proposeed. The essencce of the propoosed approach is that it is caapable of dealinng with indeteerminacy and falsity f simultanneously.
INTROD DUCTION Goal progrramming can be b viewed in tw wo ways. In firsst consideration n, it is an extennsion of linear programming to include muulti objectives, expressed by means of attem mpted achievem ment of goal vaalues. In seconnd consideratioon, linear prog gramming is a special case of o goal program mming having single objectiive. These two considerationns reflect thatt goal program mming lies withhin the paradiggm of multi objjective program mming [1]. Gooal programminng may be chharacterized as an analytical approach deviised to address multi objectiive decision making m problem ms having inhherent multiplee conflicting objectives o wheere targets hav ve been assignned to all the attributes in thhe planning horizon h and wh here decision making m unit is m mainly interested in minimiziing the non-ach hievement of thhe goals.The ethos of goall programmingg lies in the Simon’s S conceept [2] of satiisfying of objectives. GP has h a robust tool for multi objeective decisionn analysis. It appears a to be an appropriatee, powerful, annd appeared as flexible tecchnique in operations researcch for decision making probleems with multiiple conflictingg objectives. Thhe literature on o goal program mming has trem mendously grown. multi criteria deecision makingg (MCDM) app proach. The idea Goal progrramming is perrhaps the most widely used m of GP can be visualized from the conccept of efficienncy introduced by Koopmanss [3] in the con ntext of resourrce allocation planning. Thee roots of goal programmingg lie in the stuudy of Charness, Cooper and Ferguson [4] in w they deaal with executiive compensattion methods. In 1961, Charrnes and Coop per [5] offeredd a 1955 in which, more expliicit definition and a coined the term ‘goal proogramming’. Thereafter,, a large number of studies have been madee by pioneer reesearchers and the significantt methodologiccal developmeent of goal pro ogramming haave been achieeved by Ijiri [66], Lee [7], Iggnizio [8], Scchniederjans [99], Romero [110], Schniederj rjans [11] and other researchhes. The vast literature of ggoal programm ming reflects its i theoretical elegance and significance. In 1980, Narasimhan N [12] employedd the concept of fuzzy set theory introdduced by Zadeeh [13] in gooal programmiing by incorpoorating fuzzy goals g and consstraints withinn the traditionaal goal program mming model in order to addd new dimenssion in modeliing flexibility and accuracy to t the goal proorgramming model m for dealinng with uncerrtainty. Thereaafter, fuzzy goaal progammingg has been furtther developedd by Hannan [114], Ignizio [155], Tiwari et al. a [16, 17], Mohamed [18], Pramanik P and Roy [19, 20], Pramanik andd Dey [21,], Praamanik [22] annd other reseaarchers. Atanassov [23, 24] incorrporated the degree d of non-m membership (rrejection) as ann independent component annd defined inttuitionistic fuzzy set to deal uncertainty u in more flexible way. In 1995 Angelov [25] presented a neew
http: // www.gjesrm.com
©G Global Journall of Engineeriing Science aand Research Managementt