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Our aim in this paper is to introduce the notion of (ϵ, ϵ Vq)-fuzzy filters in MTL-algebras, which is a generalization of fuzzy filters of MTL-algebras and related properties are investigated. In particular, we extend the concept of a fuzzy subgroup with thresholds to the concept of a fuzzy filter with thresholds in MTL-algebras. [ABSTRACT FROM AUTHOR]

In this paper we present an algorithm, which helps us to define a similarity relation of fuzzy implications. This similarity relation allows us to partition by clustering fuzzy implications in equivalence classes. [ABSTRACT FROM AUTHOR]

The Cai δ-equality of fuzzy sets corresponds to the Lukasiewicz t-norm. In this paper we study the notion of (*, δ)-equality, a concept which generalizes the δ-equality to the case of the fuzzy set theory based on an arbitrary continuous t-norm *. We investigate the robustness of some fuzzy implication operators in terms of (*, δ)-equality. [ABSTRACT FROM AUTHOR]

In this paper, the notion of BCC-implicative ideal, BCC-commutative ideal, BCC-positive implicative ideal. Fuzzy BCC-implicative ideal and fuzzy BCC-positive implicative ideal and the quotient BCC-algebra induced by fuzzy BCC-ideal is introduced. The following results are obtained, for a BCC-algebra X: 1) BCC-commutative (resp. positive implicative) ideal must be a BCC-ideal. 2) fuzzy BCC-commutative (resp. positive implicative)ideal must be fuzzy BCC-ideal. 3) A fuzzy set µ in a BCC-algebra X is a fuzzy BCC-commutative (resp. implicative, positive implicative) ideal of X, if and only if, for each t ∈ [1, 1], t ≤ µ(0), µt = {x ∈ X, µ(x) ≥ t} is a BCC-commutative (resp, positive implicative, implicative) ideal of X, when µt ≠ Φ, 4) Let µ is a fuzzy BCC-ideal Of BCC-algebra X, and is not a constant, define a binary relation ∼µ on X by putting X ∼micro; y if and only if µ(xy) > 0 and µ(xy) > 0, then ∼micro; is a congruence relation on X. 5) In the end of this paper we give the construction of a quotient BCC-algebra X/µ via a fuzzy BCC-ideal µ. [ABSTRACT FROM AUTHOR]

We introduce and study fundamental relation of fuzzy hypersemigroups. Also we introduce the notion of a complete part of a fuzzy hypersemigroup and investigate its basic properties. Finally, we study the relationship between the fundamental relation and complete parts of a given fuzzy hypersemigroup. [ABSTRACT FROM AUTHOR]

In this paper, the concepts of L-fuzzy countable compactness and the L-fuzzy Lindelöf property are introduced in L-fuzzy topological spaces, where L is a completely distributive DeMorgan algebra. An L-fuzzy compact L-fuzzy set is L-fuzzy countably compact and has the L-fuzzy Lindelöf property. An L-fuzzy set having the L-fuzzy Lindelöf property is L-fuzzy countably compact if and only if it is L-fuzzy com- pact. Many characterizations of L-fuzzy countable compactness and the L-fuzzy Lindelöf property are presented. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of degree to which a fuzzy subset is a fuzzy subgroup by means of the implication operator of [0, 1]. A fuzzy subset μ in a group G is a fuzzy subgroup if and only if its subgroup degree mg(μ) = 1. Some properties of subgroup degrees are investigated. [ABSTRACT FROM AUTHOR]

The aim of this paper to give the category of intuitionistic fuzzy metric spaces with the objects are complete intuitionistic fuzzy metric spaces defined in the sense of Alaca et.al. Furthermore, the existence of solution for domain equation in these intutionistic fuzzy settings by defining a categorical contraction mapping in the sense of Alaca et.al. is investigated. [ABSTRACT FROM AUTHOR]

Abstract: Molodtsov [D. Molodtsov, Soft set theory–First results, Comput. Math. Appl. 37 (1999) 19–31] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. Jun [Y. B. Jun, Soft BCK/BCI-algebras, Comput. Math. Appl. 56 (2008) 1408–1413] applied first the notion of soft sets by Molodtsov to the theory of BCK/BCI-algebras. In this paper we introduce the notion of soft -ideals and -idealistic soft BCI-algebras, and then investigate their basic properties. Using soft sets, we give characterizations of (fuzzy) -ideals in BCI-algebras. We provide relations between fuzzy -ideals and -idealistic soft BCI-algebras. [Copyright &y& Elsevier]

Abstract: This paper, introduces the nearest weighted interval and point approximations of a fuzzy number, and then suggests weighted possibilistic moments about these points of fuzzy numbers. The possibilistic moments play an important role in fuzzy sets and systems, specifically in physics, mathematics and statistics. We provide the definition of the moments of fuzzy numbers as well as the definition of moments in probability theory; some of their applications are mentioned. [Copyright &y& Elsevier]

Abstract: This paper develops a single wholesaler and multi retailers mixture inventory distribution model for a single item involving controllable lead-time with backorder and lost sales. The retailers purchase their items from the wholesaler in lots at some intervals throughout the year to meet the customers’ demand. Not to loose the demands, the retailers offer a price discount to the customers on the stock-out items. Here, it is assumed that the lead-time demands of retailers are uncertain in both stochastic and fuzzy sense, i.e., these are simultaneously random and imprecise. To implement this behavior of the lead-time demands, at first, these demands are assumed to be random, say following a normal distribution. With these random demands, the expected total cost for each retailer is obtained. Now, the mean lead-time demands (which are crisp ones) of the retailers are fuzzified. This fuzzy nature of the lead-time demands implies that the annual average demands of the retailers must be fuzzy numbers, suppose these are triangular fuzzy numbers. Using signed distance technique for defuzzification, the estimate of total costs for each retailer is derived. Therefore, the problem is reduced to optimize the crisp annual costs of wholesaler and retailers separately. The multi-objective model is solved using Global Criteria method. Numerical illustrations have been made with the help of an example taking two retailers into consideration. Mathematical analyses have been made for global pareto-optimal solutions of the multi-objective optimization problem. Sensitivity analyses have been made on backorder ratio and pareto-optimal solutions for wholesaler and different retailers are compared graphically. [Copyright &y& Elsevier]

After the introduction of fuzzy sets by Zadeh, there have been a number of generalizations of this fundamental concept. The notion of intuitionistic fuzzy sets introduced by Aranassov is one among them. In this paper, we apply the concept of an intuitionistic fuzzy set to quasi-associative ideals in BCI-algebras. The notion of an intuitionistic fuzzy quasi-associative ideal of a BCI-algebra is introduced, and some related properties are investigated. Characterizations of an intuitionistic fuzzy quasi-associative ideal are given. Conditions for an intuitionistic fuzzy ideal to be an intuitionistic fuzzy quasi-associative ideal are given. Using a collection of quasi-associative ideals, intuitionistic fuzzy quasi-associative ideals are established. [ABSTRACT FROM AUTHOR]

This paper proposes a new class of functions, i.e., fuzzy majority functions, based on the fuzzy logic which takes any value in the interval [0, 1] as the truth value of its proposition. Fuzzy majority functions are characterized by weights and thresholds, and may be represented by a logic formula involving constants. Specifically, the proposed class intersects with the well-known fuzzy logic functions but is not a subset of then. On the other hand, the logic formula of a fuzzy majority function has a close relation with binary threshold functions. From this viewpoint, a theoretical limit in the utility of the fuzzy majority functions is discussed. [ABSTRACT FROM AUTHOR]

Based on the theory of falling shadows and fuzzy sets, the notions of falling fuzzy (implicative) filters of R0-algebras are introduced. The relations between fuzzy (implicative) filters and falling fuzzy (implicative) filters are provided. Finally, we apply the concept of falling fuzzy inference relations to R0-algebras and obtain some related results. [ABSTRACT FROM AUTHOR]

On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K. Atanassov, the notion of interval valued intuitionistic fuzzy H v –submodules of an H v –module with respect to a t–norm T and an s–norm S is given and the characteristic properties are described. The homomorphic image and the inverse image are investigated. In particular, the connections between interval valued intuitionistic ( S, T)–fuzzy H v –submodules and interval valued intuitionistic ( S, T)–fuzzy submodules are discussed. [ABSTRACT FROM AUTHOR]

This article presents a fuzzy multi-objective optimization model (FMOOM) for Volt/Var control within the frame of distribution management system (DMS) functions. Optimal control actions are of centralized character for the whole distribution system, based on historical operation database and available decentralized set of real-time measurements. Within the set of optimization goals/constraints, real power losses, overall voltage quality index and power factor are considered, with the possibility for the inclusion of other factors, without losing features of the FMOOM and calculation speed. To achieve an optimal defuzzified Volt/Var control solution with flexible input data, the robust technique of genetic algorithm (GA), is used. The application possibility of GA for the solution of real-time problems (like Volt/Var control) is explored. The aim is to give clear recommendations to decision-makers in view of setting GA control parameters that should ensure good quality of the near global optimal solution. The effectiveness of the proposed integrated GA–FMOOM for Volt/Var control, applied to various operation conditions, is verified on the example of a real radial distribution system from the Electric Power Industry of Serbia. [ABSTRACT FROM AUTHOR]