Representing complex intuitionistic fuzzy set by quaternion numbers and applications to decision making

Energy user's choice of energy service company affects the smooth implementation of energy performance contracting. Energy performance contracting is a new mechanism for energy saving. In the energy performance contracting, the energy user and energy service company cooperate to save energy and share the benefit. One difficulty in actualizing the energy performance contracting is to select the optimal energy service company. However, there are few literatures to analyze the efficient selection mechanism. A government is used as the energy user and the energy service company selection based on intuitionistic fuzzy entropy and VIKOR framework is studied in this paper. A group decision-making method based on intuitionistic fuzzy entropy and VIKOR framework is proposed to solve the multi-attribute group decisionmaking problem with the unknown decision-makers' weight and attribute weight. First, the attribute synthetic weight is determined by intuitionistic fuzzy entropy weight method and weight coordination coefficient, and expert weight is determined by objective decision information after considering the intuitionistic fuzzy entropy of decision matrix; then, the intuitionistic fuzzy group decision matrix aggregated by experts is obtained through the aggregation of intuitionistic fuzzy weighted average (IFWA) operator, and the improved intuitionistic fuzzy number distance measure is introduced into the solutions of group utility value and individual regret value to make the evaluation results more accurate and reasonable. Finally, the validity and practicability of decision-making method is analyzed and verified with an example, so as to provide a new method and idea for multi-attribute intuitionistic fuzzy group decision-making. INDEX TERMS Intuitionistic fuzzy entropy, energy service company, multi-attribute group decisionmaking, expert weight, intuitionistic fuzzy weighted average (IFWA) operator.

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“…Definition 4 [36]: Let X be a nonempty set, and ) (X  be the set of all IFSs in X . d is a mapping, and…”

Section: B Improved Intuitionistic Fuzzy Number Distance Measurementioning

confidence: 99%

Optimum Selection of Energy Service Company Based on Intuitionistic Fuzzy Entropy and VIKOR Framework

2020

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“…Also, Garg and Rani 46 proposed a correlation coefficient under CIFS theory and gave its applications in the DM field. Ngan et al 47 presented a new CIFS representation using quaternion numbers and developed a distance measure. Dai et al 48 proposed distance measures under intervalvalued CFS environment and gave their application in DM problems.…”

Section: Introductionmentioning

confidence: 99%

Complex intuitionistic fuzzy preference relations and their applications in individual and group decision‐making problems

Rani

Garg

2021

Int J Intell Syst

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This paper aspires to present single and group decisionmaking methods based on complex intuitionistic fuzzy (CIF) preference relations (CIFPRs). The presented work is divided into three folds. The first fold is that the concept of CIFPRs is introduced in this study in which the pairwise comparison values are represented using CIF numbers which have the characteristic of portraying membership and nonmembership degrees over the unit disc of the complex plane. The conditions for additive consistent CIFPR are defined and the related results are explored. In addition, an algorithm for rectifying inconsistent CIFPR is also developed. The second fold is that two goal programming models are established for generating CIF normalized priority weights corresponding to individual and group decision-making problems. The third fold is to develop the algorithms for handling individual and group decision-making problems with CIFPRs. The practicality of the proposed algorithms is shown by applying them to real-life decision-making problems. The results of the presented methods are compared with several existing studies.

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“…e theory of complex interval-valued IFS was developed by Garg and Rani [22] which contains the degree of truth and falsity in the form of a subinterval of the unit interval. e idea of the CIFS has received a great deal of attention from the scholars [23][24][25][26] and has been widely used in the different areas. e CIFS is limited in access due to their restriction on the sum of the degrees to be 1, for instance, if a person gives 0.6e i2π (7) for truth grade and 0.5e i2π (6) for falsity, then clearly 0.6 + 0.5 > 1 and hence does not satisfy the properties of CIFS.…”

Section: Introductionmentioning

confidence: 99%

Some Similarity and Distance Measures between Complex Interval-Valued q-Rung Orthopair Fuzzy Sets Based on Cosine Function and their Applications

Garg

Ali

Mahmood

et al. 2021

Mathematical Problems in Engineering

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The purpose of this paper is to present a new method to solve the decision-making algorithm based on the cosine similarity and distance measures by utilizing the uncertain and vague information. A complex interval-valued q-rung orthopair fuzzy set (CIVQROFS) is a reliable and competent technique for handling the uncertain information with the help of the complex-valued membership grades. To address the degree of discrimination between the pairs of the sets, cosine similarity measures (CSMs) and distance measures (DMs) are an accomplished technique. Driven by these, in this manuscript, we defined some CSMs and DMs for the pairs of CIVQROFSs and investigated their several properties. Choosing that the CSMs do not justify the axiom of the similarity measure (SM), then we investigate a technique to developing other CIVQROFSs-based SMs using the explored CSMs and Euclidean DMs, and it fulfills the axiom of the SMs. In addition, we find the cosine DMs (CDMs) by considering the inter-relationship between the SM and DMs; then, we have modified the procedure for the rank of partiality by similarity to the ideal solution method for the CDMs under investigation, which can deal with the associated decision-making problems not only individually from the argument of the opinion of geometry but also the fact of the opinion of algebra. Finally, we provide a numerical example to demonstrate the practicality and effectiveness of the proposed procedure, which is also in line with existing procedures. Graphical representations of the measures developed are also used in this manuscript.

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Representing complex intuitionistic fuzzy set by quaternion numbers and applications to decision making

Cited by 65 publications

References 34 publications

Optimum Selection of Energy Service Company Based on Intuitionistic Fuzzy Entropy and VIKOR Framework

Optimum Selection of Energy Service Company Based on Intuitionistic Fuzzy Entropy and VIKOR Framework

Complex intuitionistic fuzzy preference relations and their applications in individual and group decision‐making problems

Some Similarity and Distance Measures between Complex Interval-Valued q-Rung Orthopair Fuzzy Sets Based on Cosine Function and their Applications

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