it is well known fact that binary relations are generalized mathematical functions. contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. some basic operations on functions such as the inverse and composition are applicable to binary relations as well. depending on the domain or range or both are fuzzy value fuzzy set, i...

‎A new method for the defuzzification of fuzzy numbers is developed in this paper. It is well-known, defuzzification methods allow us to find aggregative crisp numbers or crisp set for fuzzy numbers. But different fuzzy numbers are often converted into one crisp number. In this case the loss of essential information is possible. It may result in inadequate final conclusions, for example, expert...

Measurement results contain different kinds of uncertainty. Besides systematic errors andrandom errors individual measurement results are also subject to another type of uncertainty,so-called emph{fuzziness}. It turns out that special fuzzy subsets of the set of real numbers $RR$are useful to model fuzziness of measurement results. These fuzzy subsets $x^*$ are called emph{fuzzy numbers}. The m...

The decision-making process is a key issue for most manufacturing and services organizations, and forms an essential part of the product design process. Indeed, designers are always confronted with the dilemma of choosing between different alternatives with different parameters, often expressed in fairly vague terms. For this reason, many tools have been proposed offering more and better ways t...

triangular intuitionistic fuzzy numbers (tifns) is a special case of intuitionistic fuzzy (if) set and the ranking of tifns is an important problem. the aim of this paper is to develop a new methodology for ranking tifns by using multiattribute decision making methods (madm). in this methodology, the value and ambiguity indices of tifns may be considered as the attributes and the tifns in compa...

Jaccard index similarity measure which applies the extension principle approach to obtain fuzzy maximum and fuzzy minimum has been proposed in ranking fuzzy numbers. However, the extension principle used is only applicable to normal fuzzy numbers and, therefore, fails to rank non-normal ones. Apart from that, the extension principle does not preserve the type of membership function of fuzzy num...

Since much of human reasoning is based on imprecise, vague and subjective values, most of decision-making processing, in reality, requires handling and evaluation of fuzzy numbers. Zadeh’s (Zadeh 1965) fuzzy logic has given analysts a tool to represent the human behaviour more precisely, especially where relatively few data exist, and where the expert knowledge about the system is vague and lin...

increasing global notices in environmental protection, green supply chain management (gscm) has received much attention by researchers and managers more than the past. commonly, firms have considered cost criteria to select their suppliers. despite the fact that there are various papers considering the formal criteria in supplier selection, there is a few limited numbers considering the environ...

the intuitionistic fuzzy set has been applied to game theory very rarely since it was introduced by atanassov in 1983. the aim of this paper is to develop an effective methodology for solving matrix games with payoffs of atanassov’s triangular intuitionistic fuzzy numbers (tifns). in this methodology, the concepts and ranking order relations of atanassov’s tifns are defined. a pair of bi-object...