Certain investigations on intuitionistic fuzzy and neutrosophic optimization problems

Abstract

Optimization stands as a potent tool for attaining desired design newlineparameters, encompassing a variety of mathematical models that articulate newlineand forecast process behavior. In reality, intricate problems manifest in newlinediverse structures, including multi-objective linear programming, fractional newlinelinear programming, multi-objective fractional linear programming, mixed newlinefractional linear programming, production planning, transportation problems, newlineand more. Thus, linear programming (LP) emerges as the most adept newlineinstrument for aiding workers in real-time decision-making quandaries. In newlineclassical optimization quandaries, parameters are regarded as real or precise newlinenumbers. Yet, numerous situations involve different forms of uncertainty that newlinedefy resolution through conventional mathematical theory. Zadeh introduced newlinefuzzy set theory, characterized by membership grades, to grapple with scenarios newlineentailing imprecise or ambiguous information. Nonetheless, in many instances, newlinedecisions or outputs predicated on available data fall short of satisfactory newlineprecision. The concept of an Intuitionistic Fuzzy Set (IFS) confronts the newlinechallenges tied to imprecise data due to its incorporation of membership and newlinenon-membership values. Consequently, IFS theory has found application newlinein resolving a wide array of real-world decision-making dilemmas. While newlineIFS theory adeptly handles insufficient data, it falters when confronted with newlineindeterminate or inconsistent data. newlineTo address this shortcoming, the Neutrosophic Set (NS) emerges newlineas a generalization of classical sets, fuzzy sets (FS), and IFS. It surmounts newlinethe challenge of dealing with indeterminate and inconsistent data by newlineincorporating components such as the Truth-Membership (TM) degree, newlineIndeterminacy-Membership (IM) degree, and Falsity-Membership (FM) degree. newline newline