Abstract
This paper presents solution technique for travelling salesman problem (TSP) under intuitionistic fuzzy environment. Travelling salesman problem is a non-deterministic polynomial-time (NP) hard problem in combinatorial optimization, studied in graph theory, operations research and theoretical computer science. It must be noted that a traveling sales man even face a situation in which he is not able to achieve his objectives completely. There must be a set of alternatives from which he can select one that best meets his aspiration level. For Multi-Objective Symmetric TSP, in fuzzy environment, it is converted into a Linear Program using Fuzzy Multi-Objective Linear Programming technique. A route cannot be simply chosen just as it will most minimize time or it will cover the least possible distance. Examples with requirements to consider the degree of rejection or hesitation (or both) are overflowing in our materialistic world. Here comes the need to consider TSP under intuitionistic fuzzy environment. The degree of rejection as well as the degree of hesitancy must be studied to find the solution in a truly optimum sense! Proposed technique is an extension as well as collaboration of ideas of fuzzy traveling salesperson problem and intuitionistic fuzzy (IF) optimization technique.
Highlights
AMS Classification: Fuzzy programming 90C70; Operations research and management science 90Bxx; Decision Theory and Fuzziness 62C86; TYPE (METHOD/APPROACH)
The term “travelling salesman problem” (TSP) [9] is a non-deterministic polynomial-time hard problem in combinatorial optimization studied in graph theory, operations research and theoretical computer science
The fuzzy TSP framework works in all cases, if there is some feasible solution, as suggested by Chaudhuri, Arindam et al In their method, these multiple objective functions are represented in vector form comprising multiple objectives with specified goals and tolerances
Summary
AMS Classification: Fuzzy programming 90C70; Operations research and management science 90Bxx; Decision Theory and Fuzziness 62C86; TYPE (METHOD/APPROACH). It is transformed via Zimmerman method and Bellman-Zadeh's approach in decision making under fuzzy environment, hat gives the following optimization problem: to maximize the degree of membership (acceptance) of the objective(s) as well as of the constraints to the respective fuzzy sets: Max i (x), x Rn , i 1 (p q) , subject to the constraints 0 ≤ μi (x) ≤ 1, where μi (x) denotes degree of acceptance of x in Rn [4].
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