Evaluation of compressive strength of concrete in bipolar fuzzy environment

. Concrete is the most widely used building material. Numerous varieties of concrete are available. They are resolved by the formation of binders and the types of aggregate used to suit the application of the engineered material. The quality of the concrete is based on the specific proportions of different materials added to it such cement, slag, ash, water, superplasticizer, coarse aggregate and fine aggregate. The compressive strength of concrete hangs on many factors such as water-cement ratio, cement strength, quality of concrete material during making of concrete which is determined using MCDM methods. In this paper COPRAS and WASPAS methods are used to determine the ranking order of various set of concrete mixtures produced in the laboratory.


Introduction
Zadeh [1] introduced fuzzy set and later, it was extended to bipolar fuzzy set by Zhang [2].Literature review of various MCDM methods was performed by Velasquez et al. [3].Daghouri et al. [4] made a comparative analysis of six MCDM methods for the evaluation of information system success.Zavadskas and Kaklauskas introduced COPRAS method.Zavadskas et al. [5] used COPRAS method for assessment of road design alternatives.Pitchipoo et al. [6] used COPRAS technique for reduction of blind spot areas in heavy vehicles.Nourianfar et al. [7] proposed COPRAS method to deal with selection of suppliers.Parezanovic et al. [8] proposed fuzzy COPRAS method for evaluation of substainable mobility measures.Bekar et al. [9] determined the performance measures in TPM by COPRAS-G and fuzzy COPRAS methods.Rudnik et al. [10] propsed OFN-WASPAS method for portfolio analysis of IP.Chakraborty et al. [11] applied WASPAS method for optimization of NTM process.Goswami et al. [12] investigated the ability of ARAS and COPRAS methods for selection of three MHE problems.Arjina et al. [13] compared MOORA and COPRAS methods on GIS for determining the potential zone of Pasir Batu mining.Dusan et al. [14] used WASPAS method for the selection of hard coating material.Yazdani et al. [15] applied SWARA, QFD and WASPAS methods for supplier selection problem.Kmiecik et al. [16] discussed the parameters required to model concrete under compound stress.Larrad et al. [17] designed high performance concrete mixtures.Based on the above concepts COPRAS and WASPAS bipolar fuzzy methods are developed to determine the compressive strength of concrete materials.

COPRAS method for BF set
COPRAS stands for Complex Proportional Assessment.Utility degree of the alternatives under the influence of conflicting criteria is determined.The main advantages of COPRAS method is the use of utility degree to illustrate which one is better and worse.Bipolar COPRAS method begins with the decision matrix (DM): where p denotes number of alternatives, q number of criteria and ) , ( Step 1.All the informations are represented in the form of matrix as DM is constructed.
Step 2. Normalization of DM with respect to beneficial and non-beneficial criteria.
Step 3.For each criteria, the weight value is determined.
Step 4. Determine the weighted normalized DM with positive and negative membership.
Step 5. Aggregate the membership values of weighted normalized DM.
Step 6. Summation over the beneficial criteria using Definition 2.1.
Step 7. Summation over the non-beneficial criteria using Definition 2.2.

Application
Concrete is a suitable material for construction composed of cement and aggregates, mixed with water which hardens with time.So it does not exist as an independent construction material.Because of its strength, durability, reflectivity and versatility it is globally used for the construction of foundations, columns, beams, slabs and other load bearing elements shown in Fig. 2.

Fig. 2. Concrete
It can be produced in various shapes and sizes.These outstanding properties have made concrete a trustworthy and enduring option of construction companies for both commercial and domestic types of constructions.Materials are mixed in specific proportions to obtain the appropriate compressive strength which is the ability of structure to carry the loads on its surface without any crack or deflection.Its SI unit is mega pascals (MPa).The compressive strength of concrete is a measure of the concrete's ability to resist loads which tends to compress it.Design engineers use the specified concrete mixture to design structural elements.Under a given specific age (days), engineers determined the actual concrete compressive strength of different mixtures of concrete from the laboratory which is given in Table 1.which are evaluated based on the parameters such as cement, slag, ash, water, superplasticizer, coarse aggregate, fine aggregate and ages (Fig. 3).

Definition 2 . 1 .Definition 2 . 2 .Definition 2 . 3 . 4 .
th p alternative with respect to th q criterion.Maximizing index is determined for the criteria to be maximized.Minimizing index is determined for the criteria to be minimized.The relative weight for each alternative is determined by.Utility degree assists in responses ranking which is calculated on evaluation of preferences on all responses with most effective response.

Step 8 .
Determine relative weight over each alternative using Definition 2.3.Step 9. Estimate the utility degree which gives ranking of the responses.The flowchart of BF COPRAS and WASPAS is represented in Fig 1.

Table 1 .
The responses determined by Engineers.