DECISION MAKING UNDER LINGUISTIC UNCERTAINTY CONDITIONS ON BASE OF GENERALIZED FUZZY NUMBERS

This article is devoted to the problem of decision making under linguistic uncertainty. The effective method for modelling linguistic uncertainty is the fuzzy set theory. There are several types of fuzzy number types proposed by L. Zadeh: fuzzy type-1, fuzzy type-2, Z-numbers. Chen proposed concept of generalized fuzzy numbers. Generalized trapezoidal fuzzy numbers (GTFN) one of effective approach which can be used for modeling linguistic uncertainty. GFTN very convenient model which allow take in account second order uncertainty. GFTN are formalized and major operations are described as practical problem is considered group decision making for supplier selection. In this case the criteria assessments are expressed by experts in linguistic form. Group decision making model is presented as 2 step aggregation procedure, in first step is aggregated value of alternative by expert, in second step by criteria. Numerical example with four criteria and three alternatives are presented and solved.This article is devoted to the problem of decision making under linguistic uncertainty. The effective method for modelling linguistic uncertainty is the fuzzy set theory. There are several types of fuzzy number types proposed by L. Zadeh: fuzzy type-1, fuzzy type-2, Z-numbers. Chen proposed concept of generalized fuzzy numbers. Generalized trapezoidal fuzzy numbers (GTFN) one of effective approach which can be used for modeling linguistic uncertainty. GFTN very convenient model which allow take in account second order uncertainty. GFTN are formalized and major operations are described as practical problem is considered group decision making for supplier selection. In this case the criteria assessments are expressed by experts in linguistic form. Group decision making model is presented as 2 step aggregation procedure, in first step is aggregated value of alternative by expert, in second step by criteria. Numerical example with four criteria and three alternatives are presented and solved

Interval type–2 fuzzy decision making

This paper concerns itself with decision making under uncertainty and theconsideration of risk. Type-1 fuzzy logic by its (essentially) crisp nature is limited in modelling decision making as there is no uncertainty in the membership function. We are interested in the role that interval type–2 fuzzy sets might play in enhancing decision making. Previous work by Bellman and Zadeh considered decision making to be based on goals and constraint. They deployed type–1 fuzzy sets. This paper extends this notion to interval type–2 fuzzy sets and presents a new approach to using interval type-2 fuzzy sets in a decision making situation taking into account the risk associated with the decision making. The explicit consideration of risk levels increases the solution space of the decision process and thus enables better decisions. We explain the new approach and provide two examples to show how this new approach works

A reliability based consistent fuzzy preference relations for risk assessment in oil and gas industry

In decision making, linguistic variables tend to be complex to handle but they make more sense than classical fuzzy numbers. Fuzziness is not sufficient enough to deal with information and degree of reliability of information is critical. Z-numbers is proposed to model the uncertainty produced by human judgment when eliciting information. Therefore, the implementation of z-numbers is taken into consideration, where it has more authority to describe the knowledge of human being and extensively used in the uncertain information development. This issue has motivated the authors to propose fuzzy multi criteria decision making methodology using z-numbers. The proposed methodology is demonstrated the capability to handle knowledge of human being and uncertain information for risk assessment in oil and gas industry. This assessment is due to periodic basis, which will give insights from the operational until the strategic level of decision making process that is capable of dealing with uncertainty in human judgment. The consistent fuzzy preference relations is developed to calculate the preference-weights of the criteria related based on the derived network structure and to resolve conflicts arising from differences in information and opinions provided by the decision makers. The proposed methodology is constructed without losing the generality of the consistent fuzzy preference relations under fuzzy environment

SERVER SELECTION ON BASE OF Z-NUMBERS

The paper is devoted to the problem of multi criteria decision making under linguistic uncertainty. Information of different approaches for modeling linguistic uncertainty have been analyzed. The concept of z-numbers proposed by L. Zadeh have been presented. Z-number is presented as cortege of two fuzzy number A and B, where A is analyzed factor, B is reliability of A assessment. The method of conversion z-numbers into generalized fuzzy numbers have been applied. As test have been used server selection problem. As decision making model have been used weighted average method. All calculations and results are presented.The paper is devoted to the problem of multi criteria decision making under linguistic uncertainty. Information of different approaches for modeling linguistic uncertainty have been analyzed. The concept of z-numbers proposed by L. Zadeh have been presented. Z-number is presented as cortege of two fuzzy number A and B, where A is analyzed factor, B is reliability of A assessment. The method of conversion z-numbers into generalized fuzzy numbers have been applied. As test have been used server selection problem. As decision making model have been used weighted average method. All calculations and results are presented

Notes on soft sets and aggregation operators

[EN]Under uncertainty, traditional sets may not be sufficient to represent real-world phenomena, and fuzzy sets can provide a more flexible and natural approach. The concept of fuzzy sets has been widely used in various fields, including artificial intelligence, control theory, decision-making, and pattern recognition. Fuzzy sets can also be combined with other mathematical tools, such as probability theory, to provide a more comprehensive approach to uncertainty management. In these notes, we explore the concept of fuzzy sets under uncertainty, and their applications in various fields. We discuss the fundamental concepts of fuzzy sets, including fuzzy membership functions, fuzzy operations, and fuzzy relations. We also examine different types of uncertainty, including epistemic and aleatory uncertainty, and how fuzzy sets can be used to model and manage uncertainty in these cases

Determining rules for closing customer service centers: A public utility company's fuzzy decision

In the present work, we consider the general problem of knowledge acquisition under uncertainty. A commonly used method is to learn by examples. We observe how the expert solves specific cases and from this infer some rules by which the decision was made. Unique to this work is the fuzzy set representation of the conditions or attributes upon which the decision make may base his fuzzy set decision. From our examples, we infer certain and possible rules containing fuzzy terms. It should be stressed that the procedure determines how closely the expert follows the conditions under consideration in making his decision. We offer two examples pertaining to the possible decision to close a customer service center of a public utility company. In the first example, the decision maker does not follow too closely the conditions. In the second example, the conditions are much more relevant to the decision of the expert

Fuzziness in analytic network process under interval numbers for criteria and alternatives

Because of the lack of data or knowledge or limited time, decision makers could not express their experiences exactly, perhaps they prefer interval numbers for such situations. Whenever uncertainty is involved in the decision making process, fuzzy and stochastic models would be arisen. Recently, fuzzy theory for Multiple Attribute Decision Making (MADM) under interval numbers has attracted a lot of researchers. This paper deals with a fuzzy MADM approach under interval numbers. We propose to apply the approach for Analytic Network Process (ANP) as a new class of decision making methods. The interval numbers are formed for criteria weights and values that have effect on alternatives’ values. The process of this method is clarified by an example