An Approach to solve Hexagonal Fuzzy Assignment Problem using Modified Best Candidate Method and Comparative Study with Existing Methods

The objective of fuzzy assignment problem is to find the least assignment fuzzy cost (maximum fuzzy profit) of workers with varying degree of skills to job. To attain the objective in this article, an approach involving modified best candidate method has been used to solve Hexagonal fuzzy assignment problem. To order the hexagonal fuzzy numbers Robust’s Ranking technique is applied. We examine a numerical example by using new method and compute by existing two methods. Also we compare the optimal solutions among this new method and two existing method .The proposed method is a systematic procedure, easy to apply for solving fuzzy assignment problem.

Fuzzy-Based EOQ Model With Credit Financing and Backorders Under Human Learning

In this paper, an inventory model has been developed with trade credit financing and back orders under human learning. In this model, it is considered that the seller provides a credit period to his buyer to settle the account and the buyer accepts the credit period policy with certain terms and conditions. The impact of learning and credit financing on the size of the lot and the corresponding cost has been presented. For the development of the model, demand and lead times have been taken as the fuzzy triangular numbers are fuzzified, and then learning has been done in the fuzzy numbers. First of all, the consideration of constant fuzziness is relaxed, and then the concept of learning in fuzzy under credit financing is joined with the representation, assuming that the degree of fuzziness reduces over the planning horizon. Finally, the expected total fuzzy cost function is minimized with respect to order quantity and number of shipments under credit financing and learning effect. Lastly, sensitive analysis has been presented as a consequence of some numerical examples.

Search of the Shortest Path in a Communication Network with Fuzzy Cost Functions

A communication network management system takes the measurements of its state variables at specific instants of time, considering them constant in the interval between two consecutive measurements. Nevertheless, this assumption is not true, since these variables evolve in real time. Therefore, uncertainty is inherent in the processing of the measurements during the intervals so that they cannot be efficiently managed using crisp variables. In this paper, we face this problem by modeling the communications network as a type-V fuzzy graph, where both the nodes and the links are described with precision, but the cost of each link is modeled as a triangular fuzzy number. Different fuzzy cost allocation functions and fuzzy optimization strategies are described and applied to the search for the shortest path between two nodes. An experimental study has been conducted using two representative networks: the backbone network of Nippon Telegraph and Telephone Corporation (NTT) and the National Science Foundation’s Network (NFSNET). In these networks, our fuzzy cost functions and strategies have been compared with the well-known crisp equivalents. The optimal search strategies are based on the proposed Fuzzy Dijkstra Algorithm (FDA), which is described deeply. The simulation results demonstrate that in all cases the fuzzy alternatives surpass or equal the crisp equivalents with statistically significant values. Specifically, the so-called Strategy 8 presents the best throughput, as it significantly exceeds the performance of all those evaluated, achieving a Global Mean Delivery Rate (GMDR) close to 1.

Fuzzy Constrained Shortest Path Problem for Location-Based Online Services

One of the important issues under discussion connected with traffic on the roads is improving transportation. In this regard, spatial information, including the shortest path, is of particular importance due to the reduction of economic and environmental costs. Here, the constrained shortest path (CSP) problem which has an important application in location-based online services is considered. The aim of this problem is to find a path with the lowest cost where the traversal time of the path does not exceed from a predetermined time bound. Since precise prediction of cost and time of the paths is not possible due to traffic and weather conditions, this paper discusses the CSP problems with fuzzy cost and fuzzy time. After formulating the CSP problem an efficient algorithm for finding the constrained optimal path is designed. The application of the proposed model is presented on a location-based online service called Snap.

Comparing different ranking functions for solving fuzzy linear programming problems with fuzzy cost coefficients

In many applications of linear programming, the lack of exact information results in various problems. Nevertheless, these types of problems can be handled using fuzzy linear programming. This study aims to compare different ranking functions for solving fuzzy linear programming problems in which the coefficients of the objective function (the cost vector) are fuzzy numbers. A numerical example is introduced from the field of tourism and then solved using five ranking functions. Computations were carried out using the FuzzyLP package implemented in the statistical software R.

On characterizing solution for multi-objective fractional two-stage solid transportation problem under fuzzy environment

This article attempts to study cost minimizing multi-objective fractional solid transportation problem with fuzzy cost coefficients c ˜ i j k r {\tilde{c}}_{ijk}^{r} , fuzzy supply quantities a ˜ i {\tilde{a}}_{i} , fuzzy demands b ˜ j {\tilde{b}}_{j} , and/or fuzzy conveyances e ˜ k {\tilde{e}}_{k} . The fuzzy efficient concept is introduced in which the crisp efficient solution is extended. A necessary and sufficient condition for the solution is established. Fuzzy geometric programming approach is applied to solve the crisp problem by defining membership function so as to obtain the optimal compromise solution of a multi-objective two-stage problem. A linear membership function for the objective function is defined. The stability set of the first kind is defined and determined. A numerical example is given for illustration and to check the validity of the proposed approach.

Solving the Transshipment Problem with Fuzzy Cost Coefficients

This paper presents an optimization based mathematical modelling approach for a transshipment problem with fuzzy cost coefficients is formulated and solved as a quadratic mixed integer linear programming problem. In this paper, it is illustrated how convert the fuzzy form to crisp form an illustrative numerical example is gives to clarify the formulation and the solution.

Fuzzy Cost Modelling of Diving Chamber Control Measures under Uncertainties

The diving chamber is an important system needed for diving operations in the oil and gas industry. Divers use it for various purposes. Thus, the safety level of the diving chamber needs to be very high at all times and the system needs to be in a good state. To achieve this, various control measures such as control measures 1 and 2 can be adopted in preventing failures/hazards or mitigate their consequences. In this study, fuzzy cost algorithm is used to estimate the cost of using control measures 1 and 2 in ensuring optimal operational level for the diving chamber, while the preference degree approach is adopted in prioritizing the aforementioned cost of control measures 1 and 2. The result of the analysis indicated that control measure 2 is the most cost effective approach.

A generalized fuzzy cost efficiency model

The concept of cost efficiency has become tremendously popular in data envelopment analysis (DEA) as it serves to assess a decision-making unit (DMU) in terms of producing minimum-cost outputs. A large variety of precise and imprecise models have been put forward to measure cost efficiency for the DMUs which have a role in constructing the production possibility set; yet, there’s not an extensive literature on the cost efficiency (CE) measurement for sample DMUs (SDMUs). In an effort to remedy the shortcomings of current models, herein is introduced a generalized cost efficiency model that is capable of operating in a fuzzy environment-involving different types of fuzzy numbers-while preserving the Farrell’s decomposition of cost efficiency. Moreover, to the best of our knowledge, the present paper is the first to measure cost efficiency by using vectors. Ultimately, a useful example is provided to confirm the applicability of the proposed methods.