# Decision Making Approach using Weighted Coefficient of Correlation along with Generalized Parametric Fuzzy Entropy Measure

Priti Gupta (Maharshi Dayanand University, Rohtak, India) and Pratiksha Tiwari (Maharshi Dayanand University, Rohtak, India)
DOI: 10.4018/IJFSA.2016070103

## Abstract

Decision making involves various attributes along with several decision takers. Recently it has become more complex. This gives raise to uncertainty and associated with the information provided. So it may be appropriate to suggest that uncertainty demonstrates itself in numerous forms and of different types. Uncertainties may arise due to human behaviour, fluctuations of information, unknown facts. Fuzzy set theory is tool to deal with uncertainty in a better way. Both Fuzzy set theory and information theory are involved in dealing with various real-world problems such as segmentation of images, medical diagnosis, managerial decision making etc. Several methods and concepts dealing with imprecision and uncertainty have been proposed by many researchers. In the present communication, the authors have proposed a parametric generalization of entropy introduced by De Luca and Termini along with its basic properties. Further, a new measure of weighted coefficient of correlation is developed and applied to solve decision making problems involving uncertainty.
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## Introduction

Fuzzy set theory plays an important role in decision making under uncertain conditions because of its proficiency to model non-statistical vagueness. Therefore, categorization and quantification of fuzziness are vital as it affects the management of uncertainty in many decision making situations. Entropy measures are one of the important topics in fuzzy sets theory and it has been investigated widely by many researchers. Montes, Couso, Gil, & Bertoluzza (2002), Chaira & Ray (2003), Prakash, Sharma & Mahajan (2008), Bajaj & Hooda (2010), Prakash & Gandhi (2011) presented several generalized fuzzy entropy measure and/or fuzzy divergence measure corresponding to a fuzzy set A relative to some other fuzzy set B with its validity together with its properties. Application of aforesaid measures can be found in image segmentation, pattern recognition, fuzzy clustering etc. Usage of fuzzy information theory in handling decision problems has been started way back in 1990’s. Till now various authors applied fuzzy information theory to solve multi-attribute decision making environment. Multi-attribute decision making involves analysis of different course of action on the basis of different aspects. It ranks courses of actions in terms of their relevance to the decision maker(s) by considering all attributes simultaneously and/or to find the optimal alternative with relative priorities of each alternative. Fuzzy set theory has provided various multi-attribute decision making methods such as Technique for Order Performance by Similarity to Ideal Solution (TOPSIS), Aggregation Operators, Score Functions and Entropy Methods. Kahraman (2008) dealt with diffusion of fuzzy set theory with crisp multi-attribute and multi-objective decision making, Merigó & Casanovas (2010) presented fuzzy generalized ordered weighted averaging (FGOWA) operator and extended this operator to GOWA operator under uncertain conditions. Lee & Park (2012) devised fuzzy entropy measure and applied it for the selection from multiple facts. Anisseh & Rao (2012) converts the fuzzy decision makers in to aggregated decision matrix and extends TOPSIS method for heterogeneous group decision making under fuzzy environment. Zang & Yue (2013) developed a method for service quality evaluation based on fuzzy information. Zhao, Lin & Wei (2013) and Verma & Sharma (2014) gave fuzzy prioritized operator and weighted fuzzy prioritized operator respectively with applications in multi-attribute group decision making. Yager (2015) formulated multi-criteria decision function where aggregation method involves usage of fuzzy measure and Choquet integral.

Many investigators mostly emphasized on the multi attribute decision making problems with known or incompletely known criterion weight. But it is not possible to provide equal weights to experts and attribute as knowledge of each expert and importance of attribute differs. In this paper we assign weight in accordance to the caliber of expert and importance of attribute to overcome the mentioned problem. This paper also deals with quantified measures of fuzziness that is fuzzy entropy along with decision making involving various attributes under unknown weights.

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